Comments on "Control of a Planar Underactuated

Biped on a Complete Walking Cycle"

Bernard Brogliato

The above paper [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] possesses several approximations and flaws, which we try to explain. Roughly, the topic concerns the problem of trajectory tracking for a class of mechanical Lagrangian systems subject to unilateral constraints on the generalized position (q) 0, (q) 2 IR m . Such multibody mechanical systems also involve a com- plementarity relation between the constraint and a Lagrange multiplier 0 (q) ? 0 (1 ), and generalized velocity jumps (impacts). The complementarity relations and the velocity jump law, form a specific contact model. A contact model is necessary for the chosen model to be meaningful from a mechanical point of view. When dealing with systems of rigid bodies, the complementarity conditions are the simplest way to deal with the contact dynamics: they state that adhesion or magnetic forces are excluded from the model. Such nonsmooth mechanical systems form a special class of complementarity systems, but other formalisms exist [START_REF] Brogliato | Some perspectives on the analysis and control of complementarity systems[END_REF]. It is worth noting that the complementarity conditions are not included in the model presented in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF], which is therefore incomplete. Specifically, the authors deal with a particular biped robots model that fits within a class of impulsive ODEs, or measure differential equations. We will come back on this later in this note. The tracking problem is examined when the system undergoes an infinity of cycles, each cycle being composed of three phases of motion: single-support phase, double-support phase, and the impact when the feet hit the ground. Apart from possible underactuation, the problem is quite similar to what is tackled in [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]- [START_REF] Bourgeot | Contribution à la commande de systèmes mécaniques non-réguliers[END_REF], that concerns fully actuated Lagrangian systems undergoing cycles which consist of free motion phases, constrained motion phases, and transition phases with impacts. The effects of the impacts and of the complementarity relations do not change from one problem to the other one. This is why it is worth understanding the simplest case before tackling more sophisticated control problems (underactuated systems, flexible joint manipulators, to cite a few). It is worth noting that the infinity of cycles (and consequently of impacting and detaching events) is the source of difficulty in this problem.

Globally, there are two main problems with [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. i) As pointed out in the introduction, the dynamical model neglects fundamentals aspects of the contact dynamics of multibody mechanical systems made of rigid bodies and subject to unilateral constraints (q) 0, and this has serious consequences on the tracking control problem. ii) The stability properties of the closed-loop system (24a) (24b) (24c) as claimed in [1, Prop. 2], are wrong. The choice of a model is a delicate matter, and we shall come back on point i) later. Let us deal first with item ii). Proposition 2 in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] states that the origin of the closed-loop system. . .is uniformly Lyapunov stable and all the trajectories converge to zero for almost all t 0 and uniformly in the initial conditions. This statement contains three main sub-statements (the third property has to be guessed from the words all the trajectories converge to zero, which I suppose mean for all initial conditions the trajectories converge to zero) a) the origin of the closed-loop system is Lyapunov stable; b) the stability is asymptotic; c) the stability is global. The last sentence of the proof [1, Prop. 2], i.e. Exponential stability for almost all t follows since the origin of (24c) is also exponentially stable, makes the reader think that the closed-loop system (24a)-(24c) is exponentially stable, which is stronger than the mere asymptotic stability. For the sake of briefness we will disregard this claim of [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] in this comment and focus on (a)-(c) only. Let us first assume that the dynamical model presented in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] represents a satisfactory model, and let us show why items (c) and (b) cannot hold. Point (a) will be examined later.

• Point (c): A first flaw in [1, Prop. 2] is that the presented control algorithm in (17), (18), (22a), (22b), and (13) cannot assure the global stability for at least three reasons.

-The reasoning employed in the proof of [1, Prop. 2], supposes that the feedback gains are chosen large enough so that the convergence rate during the "smooth" (impact-free) phases, is fast enough so that the error state goes into some basin of attraction for the next phase. However, this should be related to the initial tracking error. -Also, the uniformity with respect to the cycles of the feedback gains upperbound which assures the stability, should be proved. Indeed the impacts are seen in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] as a disturbance that has to be compensated for with high enough gains 2 . One should at least compute the "disturbance" or an upperbound of it, and show that indeed the same gains are suitable at the next cycle. This also seems to be related to the frequency of the walk, as longer periods of impactless motion, permit to augment the decrease of the tracking error (indeed the controllers imply the asymptotic stability of the error when applied independently in each phase, on a infinite time interval). If the result holds independently of the speed of the walk, this should be proved and stated as it seems to be an important feature of the control scheme. -Third, as explained in [START_REF] Brogliato | On tracking control of a class of complementary-slackness hybrid mechanical systems[END_REF], the controllers and the systems "modes" (free motion, constrained motion, transition phase for [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]- [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF] or single-support phase, double-support phase for [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]) have to be synchronized. This is a basic assumption. It is likely that stability is lost if the biped is initialized in a double-support phase, with the controller designed for the single-support phase. Synchronicity is what allows one to write the closed-loop dynamics as in [1, (24a)-(24c)]. If the stablity result does not depend on such a synchronicity property then this should be stated as this seems to be an important property. • Point (b): A second flaw in [1, Prop. 2] comes from of a fundamental reason which prevents the asymptotic stability to hold. To clarify this point, let us assume that the system is initialized in a single-support phase, with a zero tracking error. Thus until the first impact occurs, the quadratic function V (q; _ q) playing the role of a Lyapunov function (defined in [1, eq. ( 20)]), keeps its value V (q; _ q) = 0.

At an impact and according to the standard model of nonsmooth mechanics, the velocity undergoes a jump while the position remains continuous. If the desired trajectory and its first derivative are continuous [which seems to be the case in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] where the only available information on the desired trajectory design is given in (13)] then a strictly positive jump occurs in the function V (1) at the impact time, and the Lyapunov function becomes positive. This shows that asymptotic stability is impossible to obtain with "asymptotically stable" controllers, except if the jumps in V (1) tend to zero. This is one of the several subtleties of this tracking control problem, solved in [START_REF] Brogliato | On tracking control of a class of complementary-slackness hybrid mechanical systems[END_REF], [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF] by designing the transition-phase desired trajectory in a very specific way. Possibly other ways to deal with this problem can be invented, see for instance, [START_REF] Menini | Asymptotic tracking of periodic trajectories for a simple mechanical subject to nonsmooth impacts[END_REF] in a quite specific setting, however. To be more precise, the jump in the function V (q; _ q) defined in [1, eq. ( 20)] can be calculated as

V (t + )0V (t 0 ) = 1 2 _ q(t + ) T _ q(t + ) 0 _ q(t 0 ) T _ q(t 0 )+q T _ q(t + )0 _ q(t 0 ) = 1 2 _ q(t + )+ _ q(t 0 )0 _ q d (t + )0 _ q d (t 0 ) T 2 _ q(t + )0 _ q(t 0 )0 _ q d (t + )+ _ q d (t 0 ) + q T _ q(t + )0 _ q d (t + )0 _ q(t 0 )+ _ q d (t 0 ) : (1)
In order to continue the calculation one needs to choose an impact model which allows one to express _ q(t + ) from _ q(t 0 ) and some phys- ical parameters (restitution, unilateral constraints). In [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF] Moreau's rule is chosen and the jump V (t + ) 0 V (t 0 ) is calculated in order to care- fully design the desired trajectory during transition phases. Independently of this restitution rule, it however appears from (1) that: 1) the value of V (t + )0V (t 0 ) depends a lot on the desired trajectory velocity at the impact time, 2) even if perfect tracking occurs before the impact, the jump V (t + ) 0 V (t 0 ) is not necessarily small, 3) when a nonzero tracking error is present before the impact (which seems to be the most general case), the impact time is not known and this complicates even more the study of the jump in (1), and 4) the fact that the kinetic energy decreases at the impacts, is absent from (1) because the function V (q; _ q) does not mimic the systems's kinetic energy. These issues are very vaguely (if not at all) examined in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. Point 4) may not be necessary for the design of a stable controller, however one may guess that it should help and that passivity-based controllers certainly are better candidates than feedback linearizing ones in this sort of problems. Clearly some upperbounds of V (t + ) 0 V (t 0 ) can be calculated as long as the desired trajectory and its velocity are bounded, but this does not contradict point 2) and the fact that asymptotic stability cannot be claimed until a detailed analysis of the variation of V (q; _ q) has been done. The claim in the Proof of Proposition 2 in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] that the perturbation due to the impact may be compensated for, only states an obvious fact: If the function V (q; _ q) has undergone a positive jump, then letting the feedback gains being large enough and the impactless motion being long enough after the impacts, one can decrease arbitrarily V (q; _ q). However, once again this is not sufficient to prove the asymptotic stability in such infinitely-many-cycles tasks. One has to take great care of the definition of q d (1) in the neighborhood of the impacts, in order to correctly examine [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. The upperbounds in [1, eq. (25), Rem. 1] do not help a lot for the asymptotic stability. This is true even in the one degree of freedom case as studied in [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]. A suitable notion of stability has been proposed in [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]- [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF] to cope with this issue. It is noteworthy that designing some jump in _ q d (1) to mimic the impact effect, does not straightforwardly solve the problem because the impact times generally are unknown, so that the jump in _ q(t) and _ q d (t) cannot coincide except if perfect tracking occurs.

About the model: The dynamics as it is stated in (24a)-(24c) in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF], can be considered as a measure differential equation (MDE) or as an impulsive ODE of the type studied for instance in [START_REF] Bainov | Systems With Impulse Effects: Stability, Theory and Applications, ser. Ellis Horwood Series in Mathematics and its Applications[END_REF], i.e., dynamical systems of the form

_ x(t) = f (x(t)) if t 6 = t k x t + k 0 x t 0 k = g t k ; x t 0 k if t = t k (2)
where x = (q T ; _ qT ) T in (24a) and (24c). The sequence ft k g k0 may be purely exogenous, or the times t k may be functions of the state x, with some restrictions so that they satisfy t k+1 0t k > 0 for some 2 IR. Such MDEs do not represent a satisfactory model for unilat- erally constrained mechanical systems, which are measure differential inclusions (MDIs, see, e.g., [START_REF] Brogliato | Nonsmooth Mechanics, ser. CCE[END_REF] and [START_REF] Brogliato | Some perspectives on the analysis and control of complementarity systems[END_REF] for details on this fundamental point). This is because MDEs do not contain any complementarity relations 0 (q) ? 0, whereas MDIs do. The complementarity conditions are as important as the state jumps for the analysis, the control, the numerical simulation. They should not be considered as a secondary ingredient of the dynamics.

The times and states of detachment from the constraints (when the feet take off due to the control action) also depend on the tracking error and are not known analytically. They can be approximated calculating the solution of a linear complementarity problem (LCP) [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF], [START_REF] Brogliato | Some perspectives on the analysis and control of complementarity systems[END_REF], which is constructed in a classical way from the complementarity relation 0 (q) ? 0 and the second-order Lagrangian dynamics to get 0 (t) ?

(q(t)) = A(q(t)) + B(q(t); _ q(t); t) 0 for some semi positive definite matrix A(q) and some vector B(q; _ q; t). No mention of this is made in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] which focuses on the contacting times (impacts) only and considers them as exogeneous as stated in the first sentence of the proof of Proposition 2. 3 This is crucial because the controllers have to be switched at the detachment time, and the desired trajectory has to be adapted. If both the controller structure and the desired trajectory do not jump to new values at the accurate detachment time, then the Lyapunov function will undergo some positive jump. At least, one can say that this induces a kind of "disturbance" similar to that produced by the impact. It is by the way a general feature that the complementarity conditions play an as important role as the velocity jumps, though their role is often wrongly neglected. The dynamical coupling between the tangential and normal directions, due to a non block-diagonal inertia matrix, also play a crucial role in the stability analysis (such a coupling clearly appears when a suitable set of generalized coordinates as those in [START_REF] Mcclamroch | Feedback stabilization and tracking of constrained robots[END_REF] is chosen). Now that the discrepancy between complementarity systems and impulsive ODEs has been clarified, let us come back to item a) above, on Lyapunov stability. There exists a well-developped and abundant literature that copes with the Lyapunov stability of impulsive ODEs as in [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]. Claiming Lyapunov stability results for [1, eq. (24a)-(24c)], should refer to the basic definitions and extensions of Lyapunov's second method for impulsive ODEs (see for instance [8, Def. 7.1, Th. 7.1], [START_REF] Bainov | Systems With Impulse Effects: Stability, Theory and Applications, ser. Ellis Horwood Series in Mathematics and its Applications[END_REF], and the further references therein). This is not done properly in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. Even worse, it is ignored. Assuming that the proposed control strategy allows one to write a closed-loop system as (24a)-(24c) and assuming that this closed-loop system fits within impulsive ODEs as in (2), then it is possible that Lyapunov stability holds, using the quadratic function in (20). But this is not proved in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. Here, some of the arguments contradicting the global and the asymptotic stability can be repeated. In particular one cannot avoid a detailed analysis of (1) to prove that item a) is true. The sentence the perturbation due to the impact may be compensated for to ensure that each DS phase starts off with the right initial condition is not clear to me. What is a right initial condition?

We may conclude that the approach chosen in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] lies somewhere in-between the complementarity modelling and the impulsive ODE modelling, and that this may be the source of imprecisions and flaws in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. Finally, I would like to end this paragraph on the modelling with two comments.

• it is not clear that the proposed controller assures that the closedloop system really fits within (2), despite in [1, eq. ( 24a)-(24c)] is written as an impulsive ODE. Indeed it is stated at the beginning of the proof of [1, Prop. 2] that the reference trajectories are designed so that the impacts take place at precise instants. I do not see how this can be guaranteed with the proposed controllers if there are nonzero initial tracking errors, since the controllers during the SS and DS phases guarantee the asymptotic convergence of the tracking errors to zero; see [1, Prop. 1 and eq. ( 23)]. Except if the initial tracking error is zero, there will always be a difference between the planned time of impact, and the real time of impact.

The impact and detachment times may be estimated. Even if they could be analytically calculated, they would depend on the initial errors. • it is a common feature of unilaterally constrained mechanical systems, that they live on subspaces of the configuration space with varying dimensions. Equation (24c) in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] represents the system in a double-support phase, i.e. with at least two degrees of freedom less than in the single-support phase (corresponding to an additional foot stuck on the ground). This is not visible in (24c), where one would expect to see either a reduced-order dynamical system, or a full-order dynamics with an equality constraint of the form i (q) = 0 for some 1 i m, and a Lagrange multiplier. Consider the simplest case of a one degree-of-freedom mass subject to a unilateral constraint: m q(t) = u(t) + (t), 0 (t) ? q(t) 0. Suppose that u(t) = m q d (t) 0 1 _ q(t) 0 2 q(t).

The closed-loop dynamics is m q(t) + 1 _ q(t) + 2 q(t) = (t), 0 (t) ? q(t) 0. Suppose that on some strictly positive time-interval I one has q(t) = 0. The closed-loop dynamics is m q d (t) + 1 _ q d (t) + 2q d (t) = 0(t), q(t) = 0 on I, 0 (t) ? q(t) 0. This is an algebraic equation relating the con- tact force and the external action (the control). The constraint remains active on I if and only if (t) > 0 on I. Detachment occurs at t 2 I if (t) = 0 and q(t) > 0. At all t 2 I, the multiplier (t) is computed as the unique solution of the LCP 0 (t) ? q(t) = (1=m)u(t) + (1=m)(t) 0. There- fore, detachment or sticking depends on q d (1) and its derivatives. Moreover let us choose a simple quadratic function V (q; _ q) that is a Lyapunov function for the unconstrained case, playing a role similar to (20) in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]. How does this function vary in I and along the infinite switches between constrained and free motion phases? One cannot disregard the value of q d (1) on I to lead a stability analysis. To say nothing on the analysis at the impact times. Control strategies and adapted stability notions that cope with such issues are the object of [START_REF] Brogliato | On the control of finite-dimensional mechanical systems with unilateral constraints[END_REF]- [START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF]. Conclusions: To recapitulate on the mistakes and the imprecisions of [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF]:

• given in [1, eq. ( 24a)-(24c)], points b) and c) above are wrong, point a) is perhaps true but is not proved, • the closed-loop system [1, eq. ( 24a)-(24c)] does not result from the proposed controllers, • the model is incomplete as some contact conditions are missing.

It is possible that the control strategy that is proposed in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF], and which is based solely on the rate of decrease of V (q; _ q) during impactless motion, may yield some kind of ultimate boundedness or practical stability of the state on [0; +1) (in fact the strategy of [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] is quite close to what is examined in [2, § V.B], in which it was already pointed out that except in very special cases, feedback linearization may not be the right method to apply due to the difficulty to estimate the jump in the Lyapunov function at impact times). However, this result is not proved in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] which rather tackles global asymptotic uniform stability. Especially, a detailed computation of (1) at impact times, and the presentation of how detachment is managed, are mandatory before any stability result can be claimed. The problem that is tackled in [START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] can therefore be considered as being still open. One problem the authors could start with is: what happens if the control strategy is applied to a one degree of freedom system (a controlled mass with a complementarity condition and a simple Newton's restitution law)? Then, proceed to the fully actuated n-degree-of-freedom case with any inertia matrix (notice that the dynamical coupling between normal and tangential directions also increases the difficulty of the analysis). Then, reconsider the biped control problem and tackle another type of stability.

The symbol ? means that (q) and have to be orthogonal one to each other. Since they are both non-negative, this is equivalent to the componentwise relation 0 (q), 0 , (q) = 0 for all 1 i m.

This is not the case in[START_REF] Brogliato | On tracking control of a class of complementary-slackness hybrid mechanical systems[END_REF],[START_REF] Bourgeot | Tracking control of complementarity Lagrangian systems[END_REF] in which passivity-based controllers are used, in order to take advantage of the kinetic energy loss at each impact for the stabilization process.

Footnote 3 in[START_REF] Chemori | Control of a planar undercatuated biped on a complete walking cycle[END_REF] points out that a better way to handle impact times would be to include their state dependency. This is a good remark, and this precisely implies to include the complementarity relations in the model.


Shubham Khandelwal

Benjamin Lecouteux

Laurent Besacier

COMPARING GRU AND LSTM FOR AUTOMATIC SPEECH RECOGNITION

Keywords: Speech Recognition, Acoustic Models, LSTM, GRU, RNN

This paper proposes to compare Gated Recurrent Unit (GRU) and Long Short Term Memory (LSTM) for speech recognition acoustic models. While these recurrent models were mainly proposed for simple read speech tasks, we experiment on a large vocabulary continuous speech recognition task: transcription of TED talks. In addition to be simpler compared to LSTM, GRU networks outperform LSTM for all network depths experimented.

We also propose a new model termed as DNN-BGRU-DNN. This model uses Deep Neural Network (DNN) followed by a Bidirectional GRU and another DNN. First DNN acts as a feature processor, BGRU is used to store temporal contextual information and final DNN introduces additional non-linearity. Our best model achieved 13.35% WER on TEDLIUM dataset which is a 16.66% & 17.84% relative improvement on baseline HMM-DNN and HMM-SGMM models respectively.

INTRODUCTION

In recent years, artificial neural networks (ANNs) have been deployed rapidly for Automatic Speech Recognition (ASR) systems. Several factors like huge data availability and advancements in computing power (notably GPUs) helped neural networks to become popular (again). To improve ASR performance, many methods have been proposed such as hybrid Deep Neural Network-Hidden Markov Model (DNN-HMM) systems, Recurrent Neural Networks (e.g. Long Short Term Memory (LSTM), Gated Recurrent Units (GRU)), etc. Contributions. This paper proposes to investigate ASR acoustic modeling using several recurrent neural networks (RNNs). More precisely, we systematically compare LSTMs and GRUs in several architectures. Our findings (for an English transcription task) are that GRUs are not only simpler but also more efficient than LSTMs for ASR. Our best architecture, based on a deep GRU, obtains a WER of 13.35% on the first version of TED-LIUM data set [START_REF] Rousseau | Ted-lium: an automatic speech recognition dedicated corpus[END_REF], which is (to our knowledge) the best result reported so far on TED-LIUM v1.

Outline. The rest of this paper is organized as follows: section 2 is dedicated to related works. We present our proposed method in section 3 while section 4 reports experiments. Finally, section 5 concludes this work and gives some perspectives.

RELATED WORK

Feed forward neural networks have been used as feature extractors in HMM-based speech recognition systems [START_REF] Bourlard | Connectionist speech recognition. a hybrid approach[END_REF][START_REF] Hinton | Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups[END_REF][START_REF] Mohamed | Acoustic modeling using deep belief networks[END_REF]. Lately, Recurrent Neural Networks (RNNs) have also been introduced for speech recognition because of their modeling capabilities for sequences. RNNs allow the model to store temporal contextual information directly without explicitly defining the length of temporal contexts. Among several implementations of RNNs, Long Short Term Memory (LSTM) [START_REF] Hochreiter | Long short-term memory[END_REF] networks have the capability to memorize sequences with long range temporal dependencies and they started to be used for end-to-end speech recognition.

Graves et al [START_REF] Graves | Speech recognition with deep recurrent neural networks[END_REF] proposed the first use of deep Long Short Term Memory (LSTM) for speech recognition. They have shown that bidirectional LSTM (BLSTM) has more advantage over unidirectional LSTM and that depth is more important than layer size. Their combination of deep BLSTMs achieved a phoneme error rate of 17.7% on TIMIT benchmark (test set) which was comparable to state-of-the-art results. To overcome the difficulty of integrating deep BLSTM networks with existing large vocabulary speech recognition systems, Graves et al. [START_REF] Graves | Hybrid speech recognition with deep bidirectional lstm[END_REF] proposed an hybrid HMM-BLSTM architecture. The proposed model outperformed both GMM and DNN benchmarks on a subset of the Wall Street Journal (WSJ) corpus.

More recently, it has been shown that recurrent neural networks can outperform feed-forward neural networks on larger scale speech recognition tasks [8][9]. Geiger et al [START_REF] Jürgen | Robust speech recognition using long short-term memory recurrent neural networks for hybrid acoustic modelling[END_REF] trained BLSTM with HMM states as training targets for acoustic modeling. Their experimental results showed that the hybrid system (using state prediction networks) achieves competitive results on a medium-vocabulary ASR task on read speech data. (from the CHiME challenge). Further improvements were obtained by combining different LSTM acoustic models. Graves et al [START_REF] Graves | Towards end-to-end speech recognition with recurrent neural networks[END_REF] proposed a speech recognition system that directly transcribes the audio data into text with minimal preprocessing using spectrograms and no explicit phonetic representation. They described a novel objective function that allows the network to be directly optimized for WER and directly integrated the network outputs with a language model during decoding. Chan et al [START_REF] Chan | Listen, attend and spell[END_REF] presented Listen, Attend and Spell (LAS), an attention based neural network which can directly transcribe acoustic signals into characters. The Listener (first component), is a pyramidal acoustic RNN encoder that transforms the input sequence into a high level feature representation. The Speller (second component) is a RNN decoder that attends to the high level features and spells out the transcript one character at a time. LAS achieved a WER of 14.1% without any dictionary nor language model, and WER of 10.3% with language model rescoring. By comparison, the state-of-the-art CLDNN-HMM model achieved a WER of 8.0% on the same dataset. Miao et. al [START_REF] Miao | Eesen: End-to-end speech recognition using deep rnn models and wfst-based decoding[END_REF] proposed a framework called EESEN: a single RNN is learned to predict context-independent targets (phonemes or characters). Connectionist temporal classification (CTC) [START_REF] Graves | Connectionist temporal classification[END_REF] objective function is used to infer the alignments between speech and label sequences so that they do not need pre-generated frame labels. 7.87% and 7.34% WER were obtained using phoneme based and character based systems respectively on TIMIT corpus using a trigram LM which is a relative improvement of 15% compared with [START_REF] Graves | Towards end-to-end speech recognition with recurrent neural networks[END_REF].

A novel TC-DNN-BLSTM-DNN acoustic model architecture was proposed by Chan et al [START_REF] Chan | Deep recurrent neural networks for acoustic modelling[END_REF]. The model combines a Deep Neural Network (DNN) with Time Convolution (TC), followed by a Bidirectional Long Short Term Memory (BLSTM), and a final DNN. The first DNN acts as a feature processor to their model, the BLSTM then generates a context from the sequence acoustic signal, and the final DNN takes the context and models the posterior probabilities of the acoustic states. This model achieved 3.47% WER on the Wall Street Journal (WSJ) eval92 task (8% relative improvement over the baseline DNN models).

Finally, Gated Recurrent Unit (GRU) was proposed by [START_REF] Cho | Learning phrase representations using rnn encoder-decoder for statistical machine translation[END_REF] for machine translation. Chung et al [START_REF] Chung | Empirical evaluation of gated recurrent neural networks on sequence modeling[END_REF] evaluated the performance of tanh, LSTM and GRU models on several NLP datasets. They demonstrated the superiority of both LSTM and GRU models over tanh unit. However, no concrete conclusion was drawn on which one is better: LSTM or GRU? Amodei et al [START_REF] Amodei | Deep speech 2: End-to-end speech recognition in english and mandarin[END_REF] tried to compare GRU with simple RNN for speech transcription and their experimental results showed that if the model size is scaled up for a fixed computational budget, then simple RNN performs slightly better than GRU.

This paper is one attempt to compare LSTM and GRU architectures on a large vocabulary continuous speech recognition (LVCSR) task which is more complex than read speech transcription on TIMIT or WSJ. For this, we experiment on the transcription of TED Talks using TED-LIUM corpus [START_REF] Rousseau | Ted-lium: an automatic speech recognition dedicated corpus[END_REF].

PROPOSED METHOD

The proposed model is summarized as DNN-BGRU-DNN acoustic model shown in figure 1. This model uses fixed window context of acoustic features (Feature-space maximum likelihood linear regression (fMLLR) transformed features [START_REF] Povey | Feature and model space speaker adaptation with full covariance gaussians[END_REF]) as an input.

To project the original acoustic features into a high dimensional feature space, 2 layers of DNN (2048 ReLU neurons) are used. Then high dimensional features are consumed by a single layered BGRU which models the temporal dependencies of the speech signal. The output of BGRU is then consumed by another DNN (2048 ReLU neurons) to add additional non-linear transformations before softmax layer to classify the context dependent acoustic states.

Our BGRU is implemented similarly to [START_REF] Cho | Learning phrase representations using rnn encoder-decoder for statistical machine translation[END_REF]. GRU is used to make each recurrent unit adaptively capture dependencies of different time scales. Similar to the LSTM, GRU has gating units used to deal with the flow of information inside the unit without having separate memory cells. The architecture is simpler than LSTMs.

The activation h t of GRU at time t is a linear interpolation between the previous activation h t-1 and the candidate activation ht :

h t = (1 -z t )h t-1 + z t ht
where the update gate z t decides the update weight. This update is computed by:

z t = σ(W z x t + U z h t-1 + b z )
The candidate activation ht is computed similar to the standard RNN:

ht = f (W h x t + r t U h h t-1 + b h )
where r t is a set of reset gates and is an element-wise multiplication. The reset gate r t is computed similarly to the update gate:

r t = σ(W r x t + U r h t-1 + b r )
Bidirectional GRU (BGRU) consumes the input acoustic window. BGRU output is a concatenation of two vectors (one for each direction: forward and backward).

c = h f T h b T
Here, c represents the context of the acoustic signal generated by the BGRU. Context c is further consumed and projected by a second DNN. This DNN is further used to add more non linear transformations. The output of the second DNN is fed to the softmax layer to model the context dependent state priors. The proposed model is trained using backpropagation minimizing the cross entropy. Proposed architecture is inspired from [START_REF] Chan | Deep recurrent neural networks for acoustic modelling[END_REF].

EXPERIMENTS

Experimental setup

The proposed approach is evaluated on a lecture transcription task (TED talks in English). TEDLIUM dataset [START_REF] Rousseau | Ted-lium: an automatic speech recognition dedicated corpus[END_REF] was used for the experimentation of all models. It was developed for large vocabulary continuous speech recognition (LVCSR). The train part of the dataset is composed of 774 talks, representing 118 hours of speech. Evaluation is performed on the dev part of the dataset (19 talks, 4h). The speech transcription process is carried out in two passes: an automatic transcript is generated with a GMM-HMM model of 12000 states and 200000 Gaussians. Then word graphs outputs obtained during the first pass are used to compute a fMLLR-SAT transform on each speaker. The second pass is performed using DNN or SGMM acoustic model trained on acoustic features normalized with the fMLLR matrix.

The English language model is trained with MIT language model toolkit 1 using following corpora:

• News commentary 2007-2012 [START_REF] Tiedemann | Parallel data, tools and interfaces in opus[END_REF] • Gigaword version 5 [START_REF] Graff | English gigaword[END_REF] 1 https://github.com/mitlm/mitlm • TDT 2-4 [START_REF] Mark | Tdt2 multilanguage text version 4.0[END_REF] • TED Train (80%) Then, linear interpolation is applied between the LM trained on the above corpora by tuning the perplexity on the remaining 20% data of TED/train. We will use 3 and 5-gram language models for our experiments.

HMM-SGMM and HMM-DNN baselines

We have used two baseline systems based on Kaldi s5 recipe using HMM-SGMM model and HMM-DNN. The performance using 3-gram and 5-gram language models are provided in Table

Preliminary RNN Experiments

Preliminary experiments were done to compare small size LSTM and GRU (similar or smaller number of parameters compared to our DNN-512-3 baseline).

The experimental results using trigram language model are shown in table 3. The results show that the GRU performs better than the LSTM for equivalent number of parameters (BGRU512-1 better than BLSTM128-1 while both models have the same number of parameters). Also, we observe that deeper GRUs perform better. The result obtained with only 1.8M parameters (GRU256-5, WER=21.32%) outperforms the DNN-512-3 baseline (4.8M parameters, WER=22.98%) as well as the LSTM with similar topology (LSTM256-5, 3M parameters, WER=22.98%).

Proposed Architecture

Different combinations of BLSTM and BGRU with DNN were evaluated. We report here the main results obtained with the architecture proposed in previous section.

We compared our proposed DNN-BGRU-DNN architecture with the DNN-BLSTM-DNN architecture proposed in [START_REF] Chan | Deep recurrent neural networks for acoustic modelling[END_REF]. The results are shown in table 4.

The results show that adding DNN before and after BLSTM and BGRU significantly improves the performances reported in Table 3 for BLSTM and BGRU. The DNN-BGRU-DNN model (2 layered DNN + 1 layer BGRU + 2 layer DNN ; dimension of the GRU recurrent and nonrecurrent node: 512 & DNN: 1024 ) achieved 20.13% WER and 16.85% WER using 3-gram and 5-gram language models respectively which is better than the results obtained with the corresponding DNN-LSTM-DNN architecture, while having less parameters. Surprisingly, it seems that DNN-BGRU-DNN benefits more from a 5-gram LM which would mean that the obtained word graph contain better hypotheses. The proposed model is very easy to train and converge and is equivalent in performance to the deeper DNN baselines (5 and 8 layers) mentioned in Table 2 (which use slightly more parameters). The model is trained using stochastic gradient descent method using a minibatch size of 100. The learning rate was started from 0.0006 and it was decayed by an geometrical distribution in every epoch. The learning rate floor was 0.00006 (that mean the learning rate does not decay beyond this value). The proposed model took around 47 hours to train with GeForce Nvidia GTX Titan 970 GPU. The model evaluated in previous subsection had only one layered bidirectional GRU. So, we experimented with increasing number of bidirectional layers in our model. Firstly, BGRU models with deeper and wider networks were trained and it was found that 3 layered BGRU model (dimension of the GRU recurrent and non-recurrent node: 512) achieved 16.37%, and 13.35% WER using 3-gram and 5-gram language models respectively which is the best performance found among all the models tested so far, as shown in table 5. The BGRU with 3 layers significantly outperforms our deep DNN baseline2 with 8 layers, while having less parameters. It is also better than its BLSTM counterpart with 3 layers. Now, to benefit from more BGRU layers, we should experiment this in our DNN-BGRU-DNN architecture (for instance, 2 layered DNN + 3 layer BGRU + 2 layer DNN; dimension of the GRU recurrent and non-recurrent node: 512 & DNN: 1024). However, such a model requires a massive amount of gpu memory. At the time of this submission, we could not get results with this model yet, but we plan to include them in final version of this paper if it is accepted3 .

Deeper RNN models

Discussion

Following are the main outcomes of our experiments:

• In general, it was observed that bidirectional RNNs are better than uni-directional RNNs.

• BGRU has much less computation time than BLSTM. So BGRU model could be more easily deployed on small devices like mobile, etc.

• GRU networks outperformed simple LSTM for all network depths and for fixed number of parameters. We also evaluated GRU networks with 5 or more recurrent layers but they did not improve the performance.

• Vanishing and exploding gradient problem is avoided by looking at threshold and clip the gradient to that threshold. On top of it, LSTM and GRU also helped to avoid such type of problems in following way:

-LSTM allows disabling of writing to a cell by turning "off" the gate to prevent any changes in the content of the cell over many cycles. It means that longer term dependencies can be learned. Similarly, when the gate is "open", the update equation does not completely replace the contents of a cell, rather maintaining a weighted average of a new value and previous value.

-In GRU, the update gate controls how much information from the previous hidden state will carry over to the current hidden state to maintain an averaged gradient. Also, when the reset gate is close to 0, the hidden state is forced to ignore the previous hidden state and reset with the current input only. Using this, the hidden state can drop any information which is irrelevant in the future.

• We will provide a github link to all our GRU scripts used, in the final version of this paper, so that other researchers can reproduce our experiments made on TED-LIUM dataset with Kaldi.

CONCLUSION AND PERSPECTIVES

Conclusion

The goal of this work was to evaluate and compare several RNN models for a large vocabulary continuous speech recognition task in English (TEDLIUM dataset). More precisely, RNN models were trained with different number of layers to compare the performance of LSTM and GRU. It was found that GRU outperforms LSTM in terms of (less) computation time and (better) WER 4 .

A novel architecture (DNN-BGRU-DNN) was also proposed which achieves better performance than its (recently proposed) DNN-BLSTM-DNN counterpart. The proposed model is easy to implement using Kaldi. It does not get overfitting due to regularization and also avoid vanishing or exploding gradient problems observed for single LSTM/GRU. 4 tested with roughly equivalent number of parameters Intensive experiments were performed with deeper and wider recurrent networks. For 3-layered BGRU model, 16.37% and 13.35% WER were achieved using 3-and 5gram language models respectively which is more than 16% relative improvement over the DNN baseline of 19.45% WER when 3-gram language model is considered. To the best of our knowledge, 13.35% WER is the best performance ever reported on dev set of this TEDLIUM experimental setup.

Perspectives

Following ideas could be proposed in future work:

• Short term: at the time of this paper submission, we were not able to complete experiments on DNN-BGRU-DNN with 3 or more BGRU layers. We expect further improvements compared to our 13.35% WER obtained with the 3-layer BGRU in Table 5. Such experiments will be included in the final version of this paper if accepted.

• Long term: other architectures such as Highway Networks [START_REF] Kumar Srivastava | Highway networks[END_REF], High order RNNs [START_REF] Soltani | Higher order recurrent neural networks[END_REF], Multi-Function Recurrent Unit (MuFuRU) [START_REF] Weissenborn | Mufuru: The multi-function recurrent unit[END_REF] could be studied and experimented on TEDLIUM. Connectionist Temporal Classification method [START_REF] Graves | Connectionist temporal classification[END_REF] is another promising approach as it does not require presegmented (forcealigned) training data, or external post-processing to extract the label sequence from the network outputs.

Combining convolutional neural networks (CNN) with deep LSTM and GRU models would be another interesting direction to explore.

Aknowledgment

Most of the computations presented in this paper were performed using the Froggy platform of the CIMENT infrastructure (https://ciment.ujf-grenoble.fr), which is supported by the Rhône-Alpes region (GRANT CPER07 13 CIRA) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d'Avenir supervised by the Agence Nationale pour la Recherche.

Fig. 1 .

 1 Fig. 1. Proposed architecture: DNN-BGRU-DNN. The model has 3 parts: ReLU DNN used to project the original fMLLR acoustic features to vectors which are then consumed by a BGRU before a final ReLU DNN uses the BGRU output for additional non linear projections before softmax classification. Figure modified from [15].

Table 1 .

 1 1 (HMM-SGMM) and Table 2 (HMM-DNN). HMM-SGMM performance on TEDLIUM devFor HMM-DNN, we experimented with deeper and wider networks, however we found that 8 layered DNN architecture was the best.

	Model	dev (WER%)
	subspace-GMM	18.64 (lm3)
		16.25 (lm5)

Table 2 .

 2 HMM-DNN performance on TEDLIUM dev

	Model	Size Layers dev (WER%) params n.
	BLSTM 128	1	23.2 (lm3)	4.6M
	LSTM	128	5	25.91 (lm3)	1.2 M
	LSTM	256	5	22.98 (lm3)	3M
	BLSTM 512	1	23.73 (lm3)	5.2M
	BGRU	512	1	22.44 (lm3)	4.8M
	GRU	256	5	21.32 (lm3)	1.8M

Table 3 .

 3 Small size LSTM and GRU performance on TEDLIUM dev. Preliminary experiments on TEDLIUM dev.

Table 4 .

 4 Proposed Model Results on TEDLIUM dev.

	Model	Size	Layers	dev (WER%)	params n.
	[Existing]
	DNN-BLSTM-DNN	1024-512-1024	2-1-2	20.24 (lm3),	12.37M
				19.11 (lm5)
	[Proposed]
	DNN-BGRU-DNN	1024-512-1024	2-1-2	20.13 (lm3),	11.12M
				16.85 (lm5)

Table 5 .

 5 Experiments on deeper and wider RNNs (LSTM and GRU) evaluated on TEDLIUM dev.

as well as the HMM-SGMM baseline

Based on results observed in Tables

and

[START_REF] Hochreiter | Long short-term memory[END_REF], we believe that WER should be further reduced.


Benjamin Lecouteux

Laurent Besacier

Use of auxiliary translation for improving decoding in statistical machine translation

Keywords: Driven Decoding Algorithm, System Combination, Machine Translation

Recently, the concept of driven decoding (DD), has been sucessfully applied to the automatic speech recognition (speech-to-text) task: an auxiliary transcription guide the decoding process. There is a strong interest in applying this concept to statistical machine translation (SMT). This paper presents our approach on this topic. Our first attempt in driven decoding consists in adding several feature functions corresponding to the distance between the current hypothesis decoded and the auxiliary translations available. Experimental results done for a french-to-english machine translation task, in the framework of the WMT 2011 evaluation, show the potential of the DD approach proposed.

Introduction

The concept of Driven Decoding Algorithm (DDA), introduced by [START_REF] Lecouteux | Integrating imperfect transcripts into speech recognition systems for building high-quality corpora[END_REF] has been successfully applied to the automatic speech recognition (speechto-text) task. This idea is to use an auxiliary transcription (manual or automatic) to guide the decoding process. There is a strong interest in applying this concept to Statistical Machine Translation (SMT). The potential applications are: system combination, multi-source translation (from several languages, from several ASR outputs in the case of speech translation), use of an online system (like Google translate) as auxiliary translation, on-line hypothesis re-calculation in a post-edition interface, etc.

This paper presents some explorations on this topic and must be seen as a proofof-concept, illustrated by a few experiments. We used machine translation systems (LIA and LIG french-to-english systems -presented in [START_REF] Potet | The LIGA machine translation system for WMT[END_REF]) based on the standard phrase-based approach [START_REF] Koehn | Statistical machine translation[END_REF]. In such an approach, the likelihood score of a candidate translation in target language, given a source sentence, is evaluated as a log-linear combination of several feature functions.

Our first attempt in DDA consists in adding several feature functions corresponding to the distance between the current hypothesis decoded (called H) and the auxiliary translation available (T) : d(T,H). We started to experiment in a re-scoring framework for which N-Best hypotheses from the baseline MT system are re-ordered after adding the new distance functions.

The outline of this paper is as follows: Section 2 is dedicated to the works that can be considered as related to this paper proposal. Section 3 presents our approach and describes the baseline SMT systems used in our experiments further presented in Section 4. Section 6 presents a deeper analysis of the DD behavior while Section 7 proposes a validation of the DD concept for a speech translation task. Finally, last Section concludes this work and gives some perspectives.

Related Work

Unlike speech recognition, system combination in SMT involves systems based on potentially different standards such as phrasal, hierarchical and syntax based. This introduces new issues such as breaking up of phrases and alterations of word order. We first propose a description of the application of DDA in ASR systems. Then, various system combination attempts in MT are presented.

Imperfect transcript driven speech recognition

In the paper introduced by [START_REF] Lecouteux | Integrating imperfect transcripts into speech recognition systems for building high-quality corpora[END_REF], the authors use auxiliary transcripts associated with speech signals to improve ASR performance. It is demonstrated that those imperfect transcripts could actually be taken advantage of. Two methods were proposed. First method involved the combination of generic language model (LM) and a LM estimated on the imperfect transcript resulting in cutting down the linguistic space. Second method involved modifying the decoding algorithm by rescoring the estimate function. The probability of the current hypothesis which results from partial exploration of the search graph is dynamically rescored based on the alignment (with imperfect transcript) scores (done using DTW). The experimental results which used both dynamic synchronization and linguistic rescoring displayed interesting gains. Another kind of imperfect transcript that can be used is the output hypothesis of another system, leading to an integrated approach for system combination [START_REF] Lecouteux | Dynamic combination of automatic speech recognition systems by driven decoding[END_REF]. The principle proposed is that firstly, one-best hypothesis is generated from the auxiliary system and a confidence score is evaluated for each word. Then these informations are used to dynamically rescore the linguistic probabilities. The method allows substantial gains compared to ROVER approaches. More details on this approach applied to ASR can be found in [START_REF] Lecouteux | Integrating imperfect transcripts into speech recognition systems for building high-quality corpora[END_REF][START_REF] Lecouteux | Dynamic combination of automatic speech recognition systems by driven decoding[END_REF].

System Combination for Machine Translation

Confusion Network (CN) Decoding. There are important issues to address for MT system combination using confusion network (CN) decoding. An important one is the presence of errors in the alignment of hypotheses which lead to ungrammatical combination outputs. (Rosti, Matsoukas, & Schwartz, 2007) proposed arbitrary features that can be added log-linearly into the objective function in this method. This adding of new features is the core idea we followed in our proposal.

CN decoding for MT system combination has been proposed in [START_REF] Bangalore | Computing consensus translation from multiple machine translation systems[END_REF]. The hypotheses have to be aligned using Levenshtein alignment to generate the CN. One hypothesis is chosen as skeletal hypothesis and others are aligned against it. In (Rosti, Matsoukas, & Schwartz, 2007), 1-best output from each system is used as the skeleton to develop the CN and the average of the TER scores between the skeleton and other hypotheses were used to evaluate the prior probability. Finally a joint lattice is generated by aggregating all the CN parallely. Through this work it is shown that arbitrary features could be added log-linearly by evaluating log-posterior probabilities for each CN arc. In CN decoding, the word order of the combination is affected by the skeletal hypothesis. Hence the quality of the output from the combination also depends on the skeletal hypothesis. The hypothesis with the minimum average TER-score on aligning with all other hypothesis is proposed as an improved skeletal hypothesis: E s = arg min E∈Ei Ns j=1 T ER(E j , E i ) where N s is the number of systems and E s is the skeletal hypothesis.

In [START_REF] Rosti | Combining outputs from multiple machine translation systems[END_REF] system specific confidence scores are also introduced. The better the confidence score the higher the impact of that system. In the experimental part of this same work, three phrase-based (A,C,E), two hierarchical (B,D) and one syntax based (F) systems are combined. All of them are trained on the same data. The decoder weights are tuned to optimize TER for systems A and B and BLEU for the remaining systems. Decoder weight tuning is done on the NIST MT02 task. The results of the combination system were better than single system on all the metrics but for only TER and BLEU tuning. The experiments were performed on Arabic and Chinese NIST MT tasks.

N-Best Re-ranking. Another paper [START_REF] Hildebrand | Combination of machine translation systems via hypothesis selection from combined n-best lists[END_REF] presents a slightly different method where N-Best hypotheses are re-scored instead of building a synthesis CN of the MT outputs (as described in previous sub-section). The N-Best lists from all input systems are combined and then the best hypothesis is selected according to feature scores. Three types of features are: LM features, lexical features, N-Best list based features. The feature weights are modified using Minimum Error Rate Training (MERT). Experiments are performed to find the optimal size for N-Best list combination. Four systems are used and analysed on combination of two best systems and all the systems. 50-best list was found to be optimal size for both cases. The authors showed that the impact of gradually introducing a new system for combination becomes lower as the number of systems increases. Anyway the best result is obtained when all the systems are combined.

Approach based on N-best re-ranking is presented in [START_REF] Li | Collaborative decoding: Partial hypothesis re-ranking using translation consensus between decoders[END_REF] using different way. The authors propose a method allowing to improve machine translation accuracy by leveraging translation consensus between MT systems: the hypothesis are re-ranked using augmented log-linear models with translation consensus based features.

The next Section presents the Driven Decoding concept were only the 1-bests provided by auxiliary systems are used in order to improve a primary system. An important issue to highlight is that, in the DD concept, auxiliary transcripts may be provided by black-box systems.

3 Overview of the Driven Decoding Concept

Driven Decoding

As said in the introduction part, our DDA implementation consists in adding several feature functions to the log-linear model before N-Best list re-ordering. Practically, after N-Best lists are generated by a primary system, additional scores are added to each line of the N-Best list file. Theses additional scores correspond to the distance between the current hypothesis decoded (called H) and the auxiliary translation available (T) : d(T,H). Let's say that for the LIA primary system, 2 auxiliary translations are available (from LIG and GOOGLE); in that case, 2 distance scores are added. The distance metric used in our experiments is described in the next Section and then N-Best reordering and combination processes are detailed.

Distance Metric used

We propose to use the BLEU as distance between systems. The BLEU score is the geometric mean of n-gram precision. Higher BLEU score suggest better translation quality. BLEU is used as evaluation metric and allows one to provide informations on the similarity between multiple systems. For DDA at sentence level we use a smoothed BLEU as presented in [START_REF] Lin | Orange: a method for evaluating automatic evaluation metrics for machine translation[END_REF]) in order to get meaningful BLEU scores. For future experiments, additional scores related to other metrics could be used.

N-Best Reordering and Combination

The system combination is based on the 500-best outputs generated by the LIA primary system. Each N-best list is associated with a set of 14 scores: 1 LM score, 5 translation model scores, 1 distance-based reordering score, 6 lexicalized reordering scores and the word penalty. In addition we introduce distance metric scores for each sentence.

The score combination weights are optimized in order to maximize the BLEU score at the sentence level by using Margin Infused Relaxed Algorithm (MIRA) [START_REF] Hasler | Margin infused relaxed algorithm for moses[END_REF]. We used the tool kbmira provided in the Moses package. The choice of MIRA against MERT (Minimum Error Rate Training) is motivated by a greater stability during our preliminary experiments. The MIRA parameters used are 100 iterations with a 0.001 C-parameter. For decoding, a global score is computed for each sentence (i.e. the log-linear score combination) and sentences are reordered according to the final combined score.

Baseline Systems

Used data

Both LIG and LIA systems were built using all the French and English data supplied for the WMT 2011 workshop, apart from the Gigaword monolingual corpora released by the LDC. translation models: news-c, euro, UN and giga, while three were employed to train language models (LMs). Two bilingual corpora were devoted to model tuning: tuningmt-LIG-LIA was used for the development of our two systems (Minimum Error Rate Training process [START_REF] Och | Minimum error rate training in statistical machine translation[END_REF] for LIG and LIA systems), whereas dev was used to tune the weights for driven decoding. test10 and test11 were finally put aside to evaluate the driven decoding method.

LIA system characteristics

LIA system uses phrase-based translation models. All the data were provided by WMT 2011 campaign and data was tokenized with the tokenizer provided. Kneser-Ney discounted LMs were built from monolingual corpora using the SRILM toolkit [START_REF] Stolcke | SRILM -an extensible language modeling toolkit[END_REF], while bilingual corpora were aligned at the word-level using Giza++ [START_REF] Och | A systematic comparison of various statistical alignment models[END_REF] or its multi-threaded version MGiza++ [START_REF] Gao | Parallel implementations of word alignment tool[END_REF] for the large corpora UN and giga. Phrase Table and lexicalized reordering models were built with Moses [START_REF] Koehn | Moses: Open source toolkit for statistical machine translation[END_REF]. Finally, 14 features were used in the phrase-based models: 5 translation model scores, 1 distance-based reordering score, 6 lexicalized reordering score, 1 LM score and 1 word penalty score. Score weights were optimized on the WMT newstest2009 corpus (2525 sentences) according to BLEU thanks to the MERT method. More details on LIA system can be found in [START_REF] Potet | The LIGA machine translation system for WMT[END_REF].

Baseline Performances

Table 2 summarizes the baseline results obtained by LIA system using case-insensitive BLEU for scoring (used everywhere in this paper). The evaluation performance is given on 3 corpora : dev refers to WMT newstest2008 + newssyscomb2009 (2553 sentences in total) ; tst10 refers to WMT newstest2010 (2489 sent.) and tst11 refers to newstest2011 (3005 sent.). For comparison purpose, we also scored the hypotheses given by LIG system and GOOGLE Translate (online system available in February 2012) on the same data sets. Each 1-best hypothesis of these systems will be used as auxiliary translations in the DD experiments. We are aware that there is a risk that the Google system, used in 2012, may actually contain WMT 2011 data in its MT models. This is, however, something we cannot control (but the performance obtained by Google Translate makes us think that this is not the case) ; this is why we use another auxiliary system (LIG) which we control totally. We also propose a combination baseline based on the MANY [START_REF] Barrault | Many: Open source machine translation system combination[END_REF] combination tool. MANY use a LM in order to decode a CN based on the input hypothesis. We present results based on target LM used in the LIA MT system. The MIRA algorithm is used to optimize the new set of log-linear weights that includes the driven decoding (DD) features (tuning is done on our dev set).

Experiments and Results

The DD approach described before was used on LIA primary system from which N-Best lists of size 500 (using the -uniq Moses option) were generated. As auxiliary translations, we used the 1-best hypotheses from the 2 systems (LIG and GOOGLE) whose performance are given in Table 2 . This We observe that while the single LIA system is significantly better than the single LIG system, it can be improved using the 1-best from a weaker one (LIG). We observe a cumulative improvement when two systems are used in the DDA process. DDA applied to LIA system improved approximately BLEU by 1 point compared to the best individual system. When DDA 1-best is added into the oracle, the score is significantly better which shows that DDA brings MT output variety. The results obtained by the DD approach are slightly better to the state of the art MANY combination while being fully different in concept. Moreover, the method presented in this paper is less expensive in terms of computations that the MANY system (which uses a LM while our method does not).

Deeper analysis of the DDA behavior

The Table 4 and Figure 1, show the distances between (DDA LIG+GOOGLE), (DDA LIG), (DDA GOOGLE) and all baseline systems. The similarities have been computed on test11 set. However they are very stable between dev, tst10 and tst11. We observe both for LIG and GOOGLE systems that DD increases the BLEU similarity. When DD uses only the GOOGLE system the result deviates from the LIG system. But when DD uses only the LIG system the deviation against the GOOGLE system is negligeable. This behavior can be explained by the fact that LIG and LIA systems are trained on similar data: the hypotheses are similar while those of GOOGLE differ more. The Figure 1 explicits the behavior introduced by the DDA: DD allows to move the space of the hypotheses relatively to the auxiliary systems. It is interesting to note that even the LIG system (worst system a priori) is close to the DDA hypothesis. The use of a BLEU similarity between systems allows one to find a consensus between hypothesis.

In the case of a full DDA (LIG + GOOGLE) we observe that the DD result is close to both LIG and GOOGLE.

By comparing the Oracle performance between the 3 single systems (ORACLE 1best) with the performance obtained when combining the 3 systems + DDA (ORACLE 1-bests+DDA), we observe that DDA finds new hypotheses , originally not included in the 3 original systems. 7 Further validation on a speech translation task

In order to validate the DD approach, we present another set of experiments on a speech translation task (translation of TED talks). In this case, 4 individual speech recogni-Fig. 1. Similarity between all the systems. The used metric is BLEU: for each vertex the associated system is used as reference compared to the others systems.

tion systems were available to provide their transcription (named systems 0, 1, 2 and 3 further). We propose to apply the DD method to a multiple source translation task (the multiple sources being the multiple ASR outputs) in order to improve final translation. Experiments are carried out on IWSLT 2011 data for the English-to-French speech translation task. We used four ASR and a ROVER between these four ASR. More details on the experimental setup (MT training data, MT systems) are provided in (Lecouteux, Besacier, & Blanchon, 2011). For the IWSLT 2011 evaluation [START_REF] Lecouteux | Lig english-french spoken language translation system for iwslt[END_REF], we experimented two types of SLT combination: source combination (combine ASR outputs before translation) and target combination (combining MT outputs after translation). We propose here a third method using DD concept presented in this paper. The new system combination is based on the 500-best translated outputs generated from each ASR source system (the -distinct option of Moses is used to ensure that the hypotheses produced for a given sentence are all different inside a N-best list). All N-best lists are merged in a single one and for each hypothesis line, a BLEU distance score is computed against 1-best translation outputs of systems 0,1,2,3 and ROVER. So, in this case, driven decoding (DD) consists in introducing 5 additional scores before N-best re-ranking. The score combination weights are then optimized as presented in Section 3.3.

Table 7 shows the results for speech translation (for 3 different test sets of the IWSLT evaluation campaign for speech translation -see more in [START_REF] Lecouteux | Lig english-french spoken language translation system for iwslt[END_REF]) of:

-Single ASR system outputs (ASR-Sys0, ASR-Sys1, ASR-Sys2, ASR-Sys3) -ROVER between single systems (ROVER 0123) -Target combination, using CN decoding method explained in [START_REF] Lecouteux | Lig english-french spoken language translation system for iwslt[END_REF]) -Driven Decoding as explained above (DD Sys0123R)

We observe a slight but significant improvement provided by DD, while this method only rerank N-best lists (the target combination method explained in (Lecouteux et al., 2011) is more complex and is based on the building of a confusion network from translation N-best lists). Another benefit of DD is the simplicity to perfuse auxiliary informations into the N-bests which are further rescored according to all the systems.

Conclusion and perspectives

We have proposed a preliminary adaptation of driven decoding (DD) for machine translation. This method allows an efficient combination of machine translation systems, by rescoring the log-linear model at the N-best list level according to auxiliary systems: the basis technique is essentially guiding the search using previous system outputs. Different configurations were evaluated on the WMT 2011 evaluation corpus. The results show that the approach allows a significant improvement in BLEU score. Moreover the proposed approach yields similar (and even slightly better) results than state of the art combination methods. A validation of DD for a multisource (speech) translation task was also presented at the end of this paper. Also, the DD approach was recently validated "live" for two more evaluation campaigns (results not reported here):

-An Arabic-to-French SMT evaluation campaign (TRAD campaign) where the use of a Google auxiliary translation significantly improved the performance of the primary LIG system.

-The IWSLT 2012 SMT evaluation campaign (english-to-french task) where, again, the use of an auxiliary translation significantly improved the performance of the primary system. More experimental details can be found in [START_REF] Besacier | The LIG English to French Machine Translation System for IWSLT[END_REF].

Our future work will focus on a DD integrated into the machine translation decoder: the interest is to perfuse all information sources into the primary search algorithm and to enable the evaluation of competing hypotheses while taking into account all the constraints and knowledge available.

Finally, another track will be the use of confidence measures generated for auxiliary systems to weight their contribution to the driven decoding.

Table 1 .

 1 Table1sums up the used data and introduces designations that we follow in the remainder of this paper to refer to corpora. Four corpora were used to build Used corpora to design LIA and LIG systems (from WMT 2011 evaluation campaign)

	CORPORA	DESIGNATION	SIZE (SENTENCES)
	English-French Bilingual training
	News Commentary v6	news-c	116 k
	Europarl v6	euro	1.8 M
	UN corpus	UN	12 M
	10 9 corpus	giga	23 M
	English Monolingual training
	News Commentary v6	mono-news-c	181 k
	Shuffled News Crawl corpus (from 2007 to 2011) news-s	25 M
	Europarl v6	mono-euro	1.8 M
	Development
	newstest2008 + newssyscomb2009	dev	2,553
	newstest2009	tuning-mt-LIG-LIA	2,525
	Test
	newstest2010	test10	2,489
	newstest2011	test11	3,005

Table 2 .

 2 Table shows the results obtained for DD of LIA system using LIG and GOOGLE 1-best hypotheses. Baseline performances measured for LIA, LIG and GOOGLE systems, as well as baseline system combination using MANY (open-source sys. combination toolkit) and performances for DDA of LIA System Using LIG and/or GOOGLE 1-best hypotheses

	system	dev	tst10	tst11
	LIA (1)	25.45	29.30	29.30
	LIG (2)	24.38	27.64	28.54
	GOOGLE (3)	24.62	28.38	29.83
	MANY LIG GOOGLE LIA	26.3	30.46	30.6
	DDA GOOGLE	26.37	30.16	30.52
	DDA LIG	25.71	29.57	29.51
	DDA LIG GOOGLE (4)	26.41	30.44	30.91
	ORACLE between 1,2,3	29.5	34.0	34.63
	ORACLE between 1,2,3,4	30.0	34.7	35.2

Table 3 .

 3 Similarities (using BLEU metric) intersystems.

	system	LIA	DDA full	DDA LIG	DDA GOOGLE
	LIG	63.13	66.14	72.8	61.02
	LIA	100	77.2	83.6	77.19
	GOOGLE	51.01	66.29	51.76	65.93
	DDA full	77.2	100	79.68	90.96

Table 4 .

 4 WER and BLEU for each ASR systems and DD system, in the framework of IWSLT 2011 evaluation (Speech Translation of TED Talks)

	system	WER (test 2010) BLEU (dev) BLEU (tst2010)	BLEU (tst2011)
		1664 sent	934 sent	1664 sent	818 sent
	ASR-Sys0	17.1	18.94	21.95	26.41
	ASR-Sys1	18.2	18.2	21.17	25.51
	ASR-Sys2	17.4	19.36	22.08	25.83
	ASR-Sys3	15.3	19.86	22.67	26.48
	ROVER 0123	14.1	20.24	23.27	26.89
	Target Combination	-	20.55	23.49	27.27
	DDA Sys0123R	-	20.7	23.73	27.4


Bilel Moulahi
email: bilel.moulahi@lirmm.fr

Jérôme Azé

Sandra Bringay

DARE to Care: A Context-Aware Framework to Track Suicidal Ideation on Social Media

Keywords: Social Media, Suicide, Emotional states, CRFs, Context

The abundance and growing usage of social media has given an unprecedented access to users' social accounts for studying people's thoughts and sentiments. In this work, we are interested in tracking individual's emotional states and more specifically suicidal ideation in microblogging services. We propose a probabilistic framework that models user's online activities as a sequence of psychological states over time and predicts the emotional states by incorporating the context history. Based on Conditional Random Fields, our model is able to provide comprehensive interpretations of the relationship between the risk factors and psychological states. We evaluated our approach within real case studies of Twitter' users that have demonstrated a serious change in their emotional states and online behaviour. Our experiments show that the model is able to identify suicidal ideation with high precision and good recall with substantial improvements on state-of-the-art methods.

Introduction

In the last decade, social media platforms has been increasingly used by mental health professionals and clinicians with myriad purposes ranging from the detection and diagnosis of major depressive disorders to predicting flu epidemics and symptoms spread [START_REF] Gunn | Twitter postings and suicide: An analysis of the postings of a fatal suicide in the 24 hours prior to death[END_REF][START_REF] Homan | Toward macro-insights for suicide prevention: Analyzing fine-grained distress at scale[END_REF][START_REF] Sueki | The association of suicide-related twitter use with suicidal behaviour: A cross-sectional study of young internet users in japan[END_REF]. Recent studies have shown that people are more likely to seek support from informal resources in social media, rather than seeking formal treatment from professionals. In order to better understand the information being shared, a developing body of literature have examined references to depression and suicidal ideation in open social network such as Twitter and Facebook [START_REF] Burnap | Machine classification and analysis of suicide-related communication on twitter[END_REF]. The current state of the art mainly focuses on assigning a polarity (positive, negative, neutral) describing the emotions conveyed by users. As such, most approaches are based on keyword matching mechanisms and static analysis of documents that ignore the whole user' behaviour. However, from a psychological perspective, suicidal ideation are perceived as a continuum of sequence of events and different mental states that may lead or not to real suicide. Given the stream nature of individual's online content in social media, this representation may be exploited to better study the mind of suicidal users over time by taking into account the whole context and online activity. To tackle this challenge, we leverage the Conditional Random Fields to track suicidal ideation in social media. We enhance our model using risk factors derived from the psychological literature and features based on the document content as well as previous shared posts. We evaluated our approach on a manually annotated corpus of tweets, published by users that demonstrated serious signs of suicidal ideation. The collection of users is validated by a professional with expertise in mental health research to retain only users with real symptoms. Experimental results show that the predicted sequences of emotional states achieve good results when compared to conventional approaches.

In the remainder of the paper, we first summarize related work, then describe our framework for suicidal ideation detection. We present and discuss the results, then conclude with future work.

Related Work

According to the Centers for Disease Control and Prevention [START_REF] Murphy | Mortality in the united states[END_REF], more than 40,000 suicides were reported in the United States in 2012. Suicide is now the 10th leading cause of death in the country. With the advent of social media, at-risk individuals are using the Internet to post suicidal communications on emerging services such as Facebook, Twitter and Reddit. Recent work demonstrated that evaluating suicidal risk factors in social networks can be used to prevent suicide and detect suicidal ideation in its early stages [START_REF] Gunn | Twitter postings and suicide: An analysis of the postings of a fatal suicide in the 24 hours prior to death[END_REF][START_REF] Homan | Toward macro-insights for suicide prevention: Analyzing fine-grained distress at scale[END_REF][START_REF] Sueki | The association of suicide-related twitter use with suicidal behaviour: A cross-sectional study of young internet users in japan[END_REF]. Gunn and Lester [START_REF] Gunn | Twitter postings and suicide: An analysis of the postings of a fatal suicide in the 24 hours prior to death[END_REF] analysed the Twitter posts of a person who had recently died through suicide. They studied the posts sent in the twenty-four hours prior to her death, finding an increase in positive emotions and a change in focus from the self to others as the time of death approached. The authors used the Linguistic Inquiry and Word Count (LIWC) software3 to identify parts of speech, emotional words and cognitive processes among other concepts. LIWC was also used in [START_REF] Homan | Toward macro-insights for suicide prevention: Analyzing fine-grained distress at scale[END_REF] as a sampling technique to identify "sad" Twitter posts that were subsequently classified using a machine learning into levels of distress on an ordinal scale, with around 64% accuracy in the best-case. In the same line of research, Sueki [START_REF] Sueki | The association of suicide-related twitter use with suicidal behaviour: A cross-sectional study of young internet users in japan[END_REF] used an online panel of young (early 20s) Twitter user to examine the association between suicide-related tweets and suicidal behaviour. The authors investigated the linguistic features of suicidal ideation and identified the most important markers of future suicide. For example, phrases such as "want to commit suicide" were found to be strongly associated with lifetime suicide attempts, while phrases that suggest suicidal intent, such as "want to die", were found to be less strongly associated. Despite the solid foundation, the current literature is missing potential key factors in the effort to track suicide related symptoms and ideation. Currently, few works analysed the evolution of an individual's online behaviour. Rather, the analysis is static and may take into consideration one post at a time while ignoring the whole context and the sequential nature of data streams.

A Context-Aware Framework to Track Suicidal Ideation on Social Media

In this section, we formulate the problem and describe our DARE4 framework to suicidal ideation tracking, and then introduce the feature extraction process.

Problem Description

Let P = < p 1 , p 2 , ..., p N > be a continuous stream of user' posts that arrive in chronological order in a given time window W . The problem consists in predicting an output vector Y = < y 0 , y 1 , ..., y N > of emotional states given the observed sequence of posts P . The input of observations P represent the feature vectors, where each observation p j contains various information about the post at time t j , and each variable y j is an emotional state inferred from p j . A natural way to represent the sequential emotional state changes is provided by the Markov network models. An interesting generalization of this framework is given by graphical models such as Conditional Random Fields (CRF) [START_REF] Lafferty | Conditional random fields: Probabilistic models for segmenting and labeling sequence data[END_REF].

Conditional Random Fields Model

CRF is a type of undirected probabilistic graphical model that has been successfully applied in many text processing and computer vision problems [START_REF] Sutton | An introduction to conditional random fields[END_REF]. One of the main strengths of this conditional model lies in its ability to encompass complex dependencies between the observations, in addition to the comprehensive interpretations of the relationship between the features it provides. In our context, this property is very important given that a transition from an emotional state to another is heavily dependent on the previous observed emotions.

Given a sequence of posts P = < p 1 , p 2 , ..., p N > and a sequence of hidden emotions Y = < y 0 , y 1 , ..., y N >, CRF models the conditional probability as follows:

p(Y |P ) = 1 Z(P ) exp( N i=1 F k=1 w k f k (y i-1 , y i , P, i)) (1)
Where Z is a normalization factor (also called the partition function) to make p(Y |P ) a valid probability over all label sequences. Z is defined as the sum of exponential number of sequences:

Z(P ) = P exp( N i=1 F k=1 w k f k (y i-1 , y i , P, i)) (2)
The scalar w k is the weight of feature f i and w k 's are the parameters of the CRF model, and are learned by numerical optimizations techniques such as gradient based approaches. The feature functions f k (y i-1 , y i , P, N ) look at a pair of adjacent (emotional) states y i-1 , y i , the whole sequence of posts P , and the current position of the sequence i. Note that the use of CRFs allows us to define a large number of dependent or independent features without worrying about the complex statistical relationship between these features. The use of each feature depends on the weight w k which acts as an activation factor of the feature. In our setting, we consider that a set of posts are included in the same sequence if they are published by the same user within the same time window T . For clarity, the online behavioural activity of a user is partitioned into sequences namely sessions. Each session S T can be thought of as a sequence of observations (posts) spanning the same time period T . During a single session, we assume that the behavioural activity of the user may be modelled by a sequence of emotional states inferred from the posts published during T . The time interval between two sessions of activity is set to a boundary threshold θ to demarcate the users mental states at different granularity. This threshold parameter is typically set to one day hours (i.e., the time a user may potentially start with a new day).

In the experiments, we tuned this parameter and also set it to 7h and 12h.

Feature Extraction

Suicidal ideation expressed by users on social media depends upon the context of the posts. In order to train and test our model, we used the text of posts as the main marker for mental health. After cleaning the posts (ie., lower case, strip punctuation, remove special characters, mentions and URLs, etc), we derive three sets of features.

The first set of features includes lexical characteristics of the text. We use Parts of Speech (POS) to capture reference to self (first personal pronouns "I", "my", "me"), nouns, verbs and adverbs. In fact, literature in the field of sociolinguistics has shown that the use of first personal singular or plural in social media posts may reveal mental well-being [START_REF] De Choudhury | Predicting postpartum changes in emotion and behavior via social media[END_REF]. Examples of Twitter posts may include: "I just wanna be left alone, I'm at the end of my rope I don't know what to do at this point" , etc. The second set of features includes Psychological and emotional lexicon features. This set refers to linguistic themes and terms that are commonly used by at-risk individuals in social media. Examples include reference to negative emotions, depression, self-harm, sadness, mental health and suicide5 [START_REF] De Choudhury | Predicting postpartum changes in emotion and behavior via social media[END_REF]. We enrich the lexicons by including other terms that refer to swear words. These features have been shown to carry important information in the context of sentiment analysis [START_REF] De Choudhury | Predicting postpartum changes in emotion and behavior via social media[END_REF]. The last set of features are Contextual features, which are related to the posts observed during previous sessions. For a given post published at time t, we use information about the characteristics of posts observed at time t -1, t -2 and even t + 1 (t + 1 informations are only available in the training phase). For instance, we check whether we observed symptoms terms in previous posts at the same user session.

Experiments

Data Preparation and Evaluation Setting

Due to the absence of publicly available datasets for the evaluation of suicide detection methods in social media, we used the Twitter streaming API6 to collect tweets containing references to themes such as self-mutilation and suicide. We exploit a list of key phrases generated from the American Psychological Association 7 (APA) list of suicide risk factors and keywords from the American Association of Suicidology8 (AAS) list of warning signs. Within all the collected tweets, we only considered users that demonstrated serious suicide symptoms in their online behaviour. To ascertain the source of the tweets, the Twitter accounts are validated by a professional with expertise in mental health research, which resulted in 60 users. As an attempt to avoid over-fitting, we also included 60 Twitter accounts of normal users with the same keywords. Table 1 shows the statistics of dataset used in the experiments. We also show in Figure 1 The most challenging task of an experimental evaluation is the data labelling. To solve this problem, eight researchers and a mental health professional manually annotated and assessed a random subset of tweets to determine the class of tweets. We define three levels of mental states:: (i) No distress: in which the post discusses everyday occurrences such as work, going out, weekend activities, etc. (ii) Minimal/Moderate distress: which refers to post expressing distress and that could be considered common for most individuals (i.e., exam, presentation for work, etc.), and (iii) Severe distress: that refers to posts that include mentions of self-harm, suicidal thoughts, apologies, feelings of worthlessness, self-hate, guilt, etc.

Each tweet was reviewed by at least two annotators. The annotated data had a Cohen's kappa statistic of 69.1%, which is considered as a substantial agreement among the annotators. The weighted kappa statistic, which takes into account different levels of disagreement, was around 71.5%.

Results and Discussion

We present our results in two phases. We start by exploring the emotional states dynamics on Twitter, then we present and discuss the results of the predictions given by our Framework.

Analysis of the Emotional States Change

In this section, we explore the users behavioural changes over time. We analyse the shifts between the emotional states. Table 2 shows the transitions between the 3 emotional states that we considered in our setting. Table 2: Users emotion changes according to the three mental states. Bold values correspond to the most likely transitions. Each row may be interpreted by the transition from a state to another.

It is interesting to note from Table 2, that the most likely transitions between two different states led from the No distress to the Minimal distress state, with a lower probability value for the opposite transition. This is natural given that users shifting to a more risky emotional state are unlikely to return to the normal state. Interestingly enough, we also observe that users on the No distress and Severe distress states tend to remain in the same state with values of 0.54 and 1.41, respectively. The probability obtained for the Severe distress state is unexceptional and may be interpreted by the fact that this mental state is generally reached when the individual is focusing on suicide and usually ends by a suicide attempt [START_REF] Adler | A mixed methods approach to identify cognitive warning signs for suicide attempts[END_REF], which also explains the very low probability value for the transition from Severe distress to Minimal distress.

Evaluation of the DARE Framework

To examine the effectiveness of the proposed approach, we perform a comparative evaluation against a set of representative machine learning methods. We also compare our model against a configuration of CRFs that do not consider the sequences of observations (i.e., each post is considered as a session). All the models are trained and tested using a 5-fold cross-validation approach. In the training phase, the models are built using the default WEKA9 parameter settings. To train our CRF, we exploit the Gradient descent using the L-BFGS method. The coefficients for L1 and L2 regularization are set by defaults to 0.1 and 0.1, respectively. The threshold parameter θ representing the time interval between two sessions of activity is set to 12 hours (7 and 24 hours led to the same results). We perform all experiments within a fair setting, using the same training and test data with a 5-fold cross validation. Table 3 reports the results by means of average Precision, Recall and F1-score measures. We start by noting that both configurations of our CRFs frameworks outperform the tested baselines in terms of F1-score. These gains are more expressive for the DARE approach, which confirm the benefits of modelling the user's activity as a sequence of dependent observations (context), which in turn, are modelled as a sequence of emotional states over time. The results achieved by the baselines are rather similar with a slight advantage of SVM, Neural Network and the Bagging algorithm. The low values may be related to the training phase in which we didn't considered feature selection, which may be considered as a disadvantage in text classification tasks. In addition, we considered three emotional states instead of two as used in most of sentiment analysis tasks. The analysis of results obtained by DARE for the individual emotional states are found to be better for the No distress (0.828) and Severe distress states (0.711) according to the F1-score. In fact, we found that the high rate of false negatives for Minimal distress state may be explained by the fact that: (i) the latter stands in two emotional states; and (ii) the self-transition for this state is very low (0.01) compared to the ingoing and outgoing transitions (see Table 2), especially from/to the No distress state.

Conclusion and Future Work

In this paper, we proposed an approach for suicidal ideation tracking based on the Conditional Random Fields framework. Our model outshines the traditional machine learning methods in input features, flexibility and extensibility to other settings involving data streams.

This study has some limitations that can be explored in future work. We plan to further consider a more fine-grained classification to include emotional states such as anger, sadness, fear, etc., instead of considering only three level of distress states. The impact of the models parameters can also be investigated, eg., long-term user behaviour (θ parameter) and size of data. Another interesting perspective is to personalize the predictions by generating distinct users behaviour models based on their online activities. Additionally, we would also like to test the impact of sentiment-specific word embedding on our model.

Fig. 1 :

 1 Fig. 1: Temporal distribution of all tweets over a 24-hour day (from midnight to 23H). Most of the tweets are published late at night.

Table 1 :

 1 the temporal distribution of the time creation of the tweets over the hours of the day. Summary of statistics of data collected form Twitter. A session is a sequence of observations.

	Users	120
	Tweets	29887
	Sessions	8421
	Avg. of #tweets per session	5
	Max of #tweets per session 200
	Min of #tweets per session	1

Table 3 :

 3 Evaluation results of the DARE framework.

https://liwc.wpengine.com

DARE stands for conDitionAl Random fiElds

https://github.com/sbma44/begin_anew

https://dev.twitter.com/streaming/overview

http://www.apa.org/topics/suicide/

http://www.suicidology.org

www.cs.waikato.ac.nz/ml/weka/