Hélène Huber
email: helene.huber@univ-paris1.fr

Yves Geoffard

Myriam Khlat

Marc Perronnin

Decomposing the causes of inequalities in health care use: a micro-simulations approach

Keywords:

We propose an innovative method for the decomposition of factors associated with inequalities in the use of health care. We analyze individual data and make use of microsimulations to evaluate the effect of heterogeneity of individual behaviors on inequality in access to care. Our study employs methods that, unlike earlier work, permits evaluation of heterogeneity of individual behaviors. We provide an application of this method by decomposing inequality of health care use in France in 1998. We show that half of the inequity in access to care is due to the heterogeneity of behaviors relative to the rank of individuals in the income distribution. This approach reconciles Oaxacalike decompositions of inequality, focused on outcome gaps, with analyses involving decompositions of inequality by factors, focused on inequity indices.

Introduction

The issue of inequalities in health and health care use is regularly part of the public agenda. In European countries, the goal of public policies is not only to globally improve the health status of the population, but also to ensure equality in access to care. In most of these countries, the main concept of the health care system is egalitarian: health care is allocated according to individual need1 , and is meant to be dissociated from the ability to pay for health care. For [START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF], the literature concerning equity in access to care is strongly related to the political agenda, which could explain the great amount of European literature on this theme. For these authors, equity of the health care system is conceived as a fundamental objective even more important than its efficiency. Equity in health care use usually refers to horizontal equity, which will be the focus of this paper. Horizontal equity is defined by a situation where on average, people in the same need of treatment receive a similar treatment, irrespective of their other characteristics (notably income)2 .

While the French health care system is structured as egalitarian, covering 99% of the population (Régime Général) and with mostly regulated fees, there still exist inequalities in health and health care use [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF]. In addition, even for those covered, there still exist financial barriers to care, notably the absence of complementary insurance, or the presence of excess fees (in excess of the regulated fee amount) that some medical doctors are allowed to demand.

For example, a great number of studies [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF], VanDoorslaer, Wagstaff, Burg, Christiansen, Graeve, Duchesne, Gerdtham, Gerfin, Geurts, Gross, Hakkinen, John, Klavus, Leu, Nolan, O'Donnell, Propper, Puffer, Schellhorn, Sundberg, and Winkelhake 2000[START_REF] Vandoorslaer | Explaining income-related inequalities in doctor utilisation in Europe[END_REF] show that while health care needs are concentrated among the poor, health care use (mostly specialists visits) is concentrated among the rich. This particular feature of specialist visits can be found in many European countries. Income inequality is often depicted as a major cause for this mismatch between health care need and use of health care.

However, if all the financial barriers to care were eliminated, the health care distribution would not necessarily become totally equitable. Many factors can render the distribution of health care inequitable. For example, agents' preferences may differ ; some can prioritize health more than others. Individuals can also disagree on the benefit provided by health care use, or on the evaluation of this benefit. Heterogeneity of preferences on the one hand, and the trade-off between costs and benefit on the other, could explain the apparent inequity in health care use, for a given health status. The observed inequity would then result from rational choices. [START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF] contend that an equitable health care distribution should exactly reflect health care need in the population3 . Consequently, any deviation from this needexpected distribution is inequitable. Inequalities in health care use can thus be decomposed into a "justifiable" part, due to the distribution of need, and an "unjustifiable" part, due to all other factors. A measure of inequality in health care use (often its concentration index with respect to individual income) is usually decomposed into the sum of the different factors which have led to this inequality, labeled justifiable (e.g. differences in health care need) or unjustifiable (e.g. differences in income). However, these decompositions generally account for differences in individual characteristics and endowments (income level, health status or education), but they do not account for differences in individual behaviors.

In this article we propose an innovative method for the decomposition of inequalities in health care use. The main contribution of this work is to extend the standard methodology by proposing a decomposition that allows for the evaluation of the impact of individual preferences on inequalities in access to care. We take into account the impact of the heterogeneity of behaviors with respect to the individuals' social rank, which cannot be taken into consideration in the standard methodology.

We first describe the limitations of the standard methodology. Second, we describe our methodology and how it addresses these limitations. Third, we present an application using French data from 1998 (the Appariement developed by Irdes4 ), that decomposes factors associated with inequality in health care use.

2 The decomposition of inequalities in health care use: the standard method and its limitations

The concentration index and its decomposition

An index measuring inequality in health care use with respect to income must be able to describe observed inequality, and identify its "justifiable" and "unjustifiable" parts. The inequality index we use here is the concentration index of health care use, relative to income. This index is widely used and has convenient properties [START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF]. In particular, it can be easily decomposed in a linear way (see section 2.1). It is used in particular by Ecuity 5 , a group devoted to international comparisons in health and health care use inequalities.

The concentration index of a variable y (for example, the number of physician visits) relative to income I can be defined using the concentration curve of y with respect to I. This concentration curve links the cumulative proportion of individuals, ranked by income, to the corresponding proportion of y used by them, with respect to the total amount of y. Within this framework, a measure of inequality in health care use is given by the concentration index, i.e. twice the area between the concentration curve and the line of equality. Let there be a population of n individuals i (i ∈ [1..n]), each having a health consumption y i and whose fractional rank 6 in the income distribution is R i . Let y be the mean health care use. The concentration index C of health care use in this population can be defined as C = 2 ny n i=1 y i R i -1 [START_REF] Wagstaff | On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam[END_REF].

We should emphasize here that inequality can be measured with tools other than the concentration index. Since we do not use the standard decomposition method in our new methodology when disentangling the various factors leading to inequality, the exclusive use of the concentration index is no longer necessary. We nevertheless use it for comparability purposes.

Assume here that health care use can be explained by factors (x k ), k ∈ [1..K] within a standard linear model [START_REF] Wagstaff | On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam[END_REF], which is a rather strong assumption:

∀i ∈ [1..n], y i = α + K k=1 γ k x k,i + ε i (1)
This implies the following decomposition [START_REF] Wagstaff | On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam[END_REF] 7 :

C = K k=1 γ k x k y C k + GC ε y (2)
Where x k is the mean of the x k,i , y the mean of y i , C k the concentration index of x k with respect to income, and GC ε the generalized concentration index of

ε i (GC ε = 2 n n i=1 ε i R i ).
2.2 The Horizontal Inequity Index and its drawbacks

Computation of the Horizontal Inequity index

In expression (2), labeling M the need variables and Z all the other variables, and labeling δ and β their vectors of coefficients yields:

6 Let r i be the rank of individual i in the income distribution. The fractional rank R i is defined as R i = r i /n. 7 Originally, [START_REF] Wagstaff | On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam[END_REF] had developed this decomposition for health inequality and not health care use inequality, but their method is suitable for the decomposition of inequality of any variable y (see [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF]).

C = K1 k=1 δ k m k µ C k + K2 k=1 β k z k µ C k + GC ε µ .
(3)

The first element on the right hand side of expression (3) represents justifiable inequality, i.e.

inequality in need. The second and third elements jointly represent unjustifiable inequality, arising from factors other than need: their sum equals the Horizontal Inequity Index. Inequality in health care use with respect to income could totally be explained by differing needs: if the distribution of health care use perfectly reflects the distribution of need, the distribution of health care use can be inegalitarian but equitable.

Limitations

Linearity The decomposition as expressed in ( 2) is necessarily linear. However, a great number of explanatory models of health care use are non linear (for example, count data models). In this case, decomposition (2) is used, with parameters γ k replaced by parameters γ m k , where the γ m k are the marginal effects of each variable x k evaluated at the sample mean (WorldBank 2005). The decomposition is then an approximation. [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF] recommend the use of a standard linear model such as (1) for y, even when the estimated model does not suit the variable. Although quite convenient, this solution is conceptually unsatisfactory.

The interpretation of the C k Expressions (2) and (3) involve the concentration indices of every explanatory factor, which implies that these indices make sense. Among other variables, indicators of health status are present in the explanatory model of health care use. Computing the concentration index on a continuous health variable means considering it as an "ill-health stock", that could be aggregated into a total stock of ill-health at the population level. This is obviously not the case for a categorical variable. To avoid such a misuse of the variable, one can compute a concentration index for every category of the health indicator considered (each category being coded with a dummy variable: 0/1). This option is chosen by the Ecuity group. The main drawback of such a method is that describing the distribution of an indicator of ill-health according to income becomes difficult, as there are as many concentration indices to analyze as there are categories within this indicator. The new method we propose here avoids the computation and interpretation problems of such indicators. In addition to the issue concerning health indicators, income is often introduced as its logarithm in the explanatory models ; the standard decomposition leads to the computation and interpretation of the concentration index of the log of income with respect to income itself, which makes interpretation difficult.

Accounting for preferences Disentangling inequality into its justifiable and unjustifiable parts using expression (3) assumes that an equitable distribution of health care use is the one that we would observe if every individual in the population were treated like the average individual, ac-cording to his/her health status. Indeed, to implement decompositions (2) then (3), the estimation of model ( 1) is made on the whole sample. For any indicator of health care need m k , the estimated coefficient δk represents what amount of health care society as a whole allocates on average for that need. Any deviation from this average relationship is taken into account by variables Z and their coefficients β. In the Ecuity group studies, this average behavior is taken as a norm. One cannot distinguish different δ k by income level, and presumably different preferences according to income level. Indeed, the social epidemiology literature has shown that individuals' social rank has an impact on health behaviors [START_REF] Wilkinson | Unhealthy societies: the afflictions of inequality[END_REF]. Decomposition (3) only takes into account the distribution of explanatory variables with respect to income, and does not take into account the potential heterogeneity of coefficients with respect to income.

The limitation to a single explanatory equation of health care consumption Explanatory models of health care consumption can be highly non-linear. The most relevant -and common -model specifications are two-part models, explaining the decision to consume (probit or logit) and the level of consumption conditional on the participation to the health care system (GLM truncated at zero). Another way of modeling health care consumption is the use of single equation zero-inflated models.

Whatever explanatory model is chosen, the decomposition of inequality into several factors (expression (2) or its approximation in the case of a non-linear model) can only be computed for one single equation of a model and is a linear approximation. In the works of Ecuity, we thus get separately:

• a decomposition of the probability of use (logit or probit model)

• a decomposition of the conditional consumption (GLM or OLS )

• a decomposition of unconditional consumption (zero-inflated model).

Consistency between the different steps of the reasoning is not guaranteed: two-part models and zero-inflated models are conceptually different and do not model the same processes. Consequently, this method does not ensure that the fraction of inequity due to a certain factor can be relevantly partitioned into participation and conditional consumption behaviors.

A new method using microsimulations

The new decomposition method proposed here overcomes the difficulties of the standard approach (see section 2). To allow for comparison of our results to those of the Ecuity group, we chose the widely used concentration index as the measurement of inequity.

We run convenient estimation methods of health care use first on the whole sample, then on the different income quantiles of the sample. Next, we compute counterfactual distributions of health care use, assuming various hypotheses detailed below, notably homogeneity then heterogeneity of behaviors. This computation and comparison of counterfactual health care use distributions is inspired from [START_REF] Dormont | Health expenditure growth: reassessing the threat of aging[END_REF]. For all these simulated distributions, we compute the concentration index of health care use with respect to income; we are thus able to identify the impact of each hypothesis on the value of the concentration index. This innovative method provides several advantages: it avoids the linear approximation that is imposed by the standard decomposition approach even when the explanatory model is non-linear, it avoids the limitation to one single equation and it permits the identification of the impact of heterogeneity of behaviors on the observed inequality in health care use.

While the standard decomposition expresses the health care use concentration index as a function of the concentration indices of all the explanatory factors of the model (see expression (2)), the method we propose here does not require explanatory factors of health care use whose concentration index makes sense.

We simulate health care use distributions from which we compute the concentration index instead of decomposing the concentration index of an observed distribution. Contrary to the standard method, this process allows us to disentangle the effects of participation and conditional consumption within one single explanatory model of total health care consumption.

The most innovative feature of our method is the ability to estimate a model of health care use by income quantile. We propose a horizontal inequity index that depends not only on the distribution of variables Z according to income (already provided by the standard method) but also on the heterogeneity of parameters β and δ with respect to income. We believe that this method provides a way to identify individual preferences, which is not possible with the standard decomposition described in section 2.

Modeling health care use

Let y i be the variable representing individual i's health care use within a population of N individuals. For example, y i can take the format of a number of visits, or expenditures. We choose here to use a modified two-part model: Logit for the participation equation and a GLM for the consumption equation.

As is common in the literature, explanatory variables are categorized as need (M 1 and M 2 for participation and consumption equation respectively) and non-need variables (Z 1 and Z 2 respec-tively). The explanatory model is the following:

(1)

E(P i ) = G(Z 1 b + M 1 d) (2) E(y i /P i = 1) = F (Z 2 β + M 2 δ)
A prediction of the model for every individual i is as follows:

y i = G(Z 1,i b + M 1,i d) participation * F (Z 2,i β + M 2,i δ) conditional consumption (4)
Let C be the concentration index of health care use y in the observed population. The objective here is to decompose the value of C into the unique contributions of each group of variables, using simulated distributions of health care use.

Parameter estimation

The model is estimated on the whole sample, yielding parameters b, d, β and δ. The sample is then split into Q income quantiles. The model is estimated on each quantile, and the following parameters are computed: ( b q ), ( d q ), ( β q ) and ( δ q ), q ∈ [1..Q]. Parameters δ q can differ, which would indicate the presence of different practices for a given morbidity, according to the income quantile to which the individual belongs. Parameters β q can differ as well, which would indicate a heterogenous effect of socio-economic variables on health care consumption, with respect to income level. This holds as well for parameters d q and b q . This estimation of coefficients specific to distinct subgroups of population is directly inspired from [START_REF] Oaxaca | Male-Female Wage Differentials in Urban Labor Markets[END_REF]. Income level is controlled for at every step.

For each estimated equation, the parameters represent individual behaviors. Parameters d and δ (as well as their equivalents d q and δ q for each income quantile q) represent the observed practices for a given level of morbidity, all other things equal. In the remainder of the article, we will call these parameters practices: the value of a parameter estimate represents the response in terms of health care to a given health status. These practices are individual behaviors, and can originate from the demand or supply of health goods. Parameters d correspond to practices linked to participation, which can be related to demand. Parameters δ correspond to practices linked to conditional consumption, mainly related to supply.

The simulation of distributions and the computation of their concentration indices

Once parameters are estimated, we simulate health care use distributions under various hypotheses.

We label Z 1 , M 1 , Z 2 and M 2 the sample mean of each corresponding variable. To understand the role of each factor in total observed inequality in health care use, we assume a perfectly egalitarian distribution of health care use. Then, we change one by one each explanatory factor of health care use in order to identify its contribution to the degree of inequality that is observed for variable y i .

The different steps of simulations are described hereafter.

The baseline of our microsimulations is a distribution of health care use that is perfectly egalitarian. It corresponds to a situation where all the individuals would share the same characteristics (∀i, ∀j ∈ {1, 2}, Z j,i = Z j and M j,i = M j ) and where the impact of these characteristics would be the same, regardless of the income quantile of the individual (∀q, b q = b and d q = d et ∀q, β q = β and δ q = δ). This distribution of health care use can be expressed as follows:

∀i, y 0 i = G(Z 1 b + M 1 d) * F (Z 2 β + M 2 δ) = Constant (5)
As the simulated health care use is by definition the same for everyone, its concentration index is necessarily equal to 0: CI 0 = 0.

The next step of the simulation takes into account the heterogeneity of morbidity among individuals, while keeping behaviors homogenous:

∀i, y 1 i = G(Z 1 b + M 1,i d) * F (Z 2 β + M 2,i δ) (6)
Where M 1 is replaced by M 1,i and M 2 by M 2,i in expression (7). The concentration index CI 1 computed on distribution y 1 gives the degree of inequality due to inequality in morbidity. It is close conceptually to the Need index, mentioned in section 2.2, because it represents the index of inequality that is due to diffences in need with respect to income.

Following this reasoning, every element of the right hand side of equation ( 7) (variables and parameters alike) is successively replaced in order to eventually get to the final observed distribution. The following table summarizes the whole process. The name of the concentration index computed on each counterfactual distribution is labeled next to each equation.

Baseline y

0 i = G(Z 1 b + M 1 d) * F (Z 2 β + M 2 δ) CI 0 (7) M orbidity y 1 i = G(Z 1 b + M 1,i d) * F (Z 2 β + M 2,i δ) CI 1 (8)
P ractices (part.)

y 2 i,q = G(Z 1 b + M 1,i d q ) * F (Z 2 β + M 2,i δ) CI 2 (9)
P ractices (cond. cons.)

y 2bis i,q = G(Z 1 b + M 1,i d q ) * F (Z 2 β + M 2,i δ q ) CI 2bis (10) SES indicators y 3 i,q = G(Z 1,i b + M 1,i d q ) * F (Z 2,i β + M 2,i δ q ) CI 3 (11) Impact of SES y 4 i,q = G(Z 1,i b q + M 1,i d q ) * F (Z 2,i β q + M 2,i δ q ) CI 4 (12)
Notice that accounting for the heterogeneity of practices corresponding to participation is made in equation ( 9) while the one corresponding to the conditional consumption is made in equation ( 10).

By calling C the observed concentration index computed on observed health care use, it can be easily seen that C is equal to the sum of the following 6 elements:

• ∆ 1 = CI 1 -CI 0 (= CI 1 -0 = CI 1 )

is the contribution of the inequalities in morbidity

• ∆ 2 = CI 2 -CI 1 is the contribution of the heterogeneity of practices corresponding to participation

• ∆ 2bis = CI 2bis -CI 2 is the contribution of the heterogeneity of practices corresponding to the conditional consumption

• ∆ 3 = CI 3 -C 2bis is the contribution of socio-economic inequalities • ∆ 4 = CI 4 -CI 3
is the contribution of the heterogeneity of behaviors linked to the socioeconomic variables

• ∆ 5 = C -CI 4 is the contribution of unobserved heterogeneity And C = ∆ 1 + ∆ 2 + ∆ 2bis + ∆ 3 + ∆ 4 + ∆ 5 .

Interpretation

The component of C due to the heterogeneity of needs is equal to ∆ 1 , that we will call Need in what follows, mainly in order to compare our results with the existing literature (see equation ( 3)):

N eed = ∆ 1 . ( 13
)
The The data comprise 4,336 individuals. We focus on the number of visits, divided into the number of general practitioner (GP) visits and the number of specialist visits 8 . Average number of visits is 4,8 for GPs and 3,5 for specialists. Detailed results of analyses are available upon request.

We decompose inequality in health care use using the new method we outlined in section 3, and compare our results to those yielded from the standard decomposition method.

Decomposition process

The choice of a model for health care use

We use a two-part model, which explains participation in the health care system and conditional consumption for users with two independent equations. The dependent variable is the number of visits (GPs, specialists and dentists, total). The explanatory variables of health care use are selected according to their degree of significance in a regression explaining the total number of visits. We chose a common set of variables to explain GP and specialist visits, in order to easily compare results. Since individuals are observed for a one year period, the synthetic indicators of morbidity as well as the presence of complementary insurance are likely to be endogenous in the estimated equations: only exogenous variables are kept in the analysis. This selection of variables is performed on the whole sample of individuals age 15 and above. The detailed list of selected variables is available upon request.

We model the probability of participation to consultations using a Logit model. To model the conditional number of visits we choose a GLM (Generalized Linear Model) using a log link and a Zero-Truncated Negative Binomial as the distribution. Indeed, the data show overdispersion in that the variance of the dependent variable is greater than its expected value (see [START_REF] Vandoorslaer | Explaining income-related inequalities in doctor utilisation in Europe[END_REF] or [START_REF] Grogger | Models for truncated counts[END_REF]). We categorized the sample into income

quintiles q ∈ [1..Q], with Q = 5.
8 The numbers of visits were computed by the author using Irdes data.

4.2

The analysis of inequalities in health care use in France, year 1998

Results using the new methodology

The results are presented here as tables synthesizing total inequality, decomposed into various elements. The degree of total inequality, called C, is presented as the sum of two elements: the degree of inequality due to the heterogeneity of need9 (the Need index) and the degree of inequality due to other factors than need (the inequity index HI ). The inequity index HI is in turn decomposed into the distribution of variables with respect to income, and the heterogeneity of behaviors (represented by the heterogeneity of coefficients with respect to income). This behavioral component comes from the heterogeneity of three types of coefficients, whose different effects are presented in the tables:

• the heterogeneity of practices corresponding to participation (linked to need),

• the heterogeneity of practices corresponding to conditional consumption (linked to need),

• the heterogeneity of other behaviors (linked to the other non-need variables).

The table presented hereafter provides the components of the decomposition of inequality observed on our sample, year 1998. In each row, the value written in bold is equal to the sum of the components written as plain text in that same row.

GP's Specialists All physicians

C -0,0219 0,0884 0,0252 Need -0,0047 -0,0078 -0,0065 HI -0,0172 0,0962 0,0317 HI -0,0172 0,0962 0,0317 Variables -0,0097 0,0450 0,0135 Behaviors -0,0075 0,0512 0,0182

Behaviors -0,0075 0,0512 0,0182 Participation 0,0004 0,0381 0,0257 Other 0,0281 0,0481 0,0047 Cond. consumption -0,0361 -0,0351 -0,0122 Let us recall that "participation" and "other" behaviors relate to the demand side, while "conditional consumption" behaviors relate to the supply side.

The contribution of each factor was computed using the concentration indices of the various simulated distributions of health care use. An analysis of robustness with respect to the order of introduction of the various effects was performed ; results remained essentially unchanged.

Results obtained with the standard methodology

We implemented the standard methodology on our data, using the number of GP visits as the outcome variable. As is common practice in the Ecuity research papers to take into account the mass in zero, we run Zero-Inflated regressions and computed the marginal effects of each variable in order to get the decomposition given by expression (2) using marginal effects (see section 2.2.2).

The total index of inequality C is decomposed into the sum of one part due to need (Need ) and another part due to all the non-need factors (HI ). Results are given in the following table :   Value Percentage C -0,022 Need -0,018 0,82 HI -0,004 0,18

Table 2: Decomposition of the inequality in GP visits, year 1998, using the Ecuity methodology

The order of magnitude of the indices of total inequality C is similar to other studies (see for example [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF], on Appariement data of year 2000). Although variables differ between our analysis and these authors', the order of magnitude of Need and HI contributions remains the same.

Comparison of results obtained with the standard and the new methodology

The Need index found with our method differs largely from what is found with the standard methodology, whether in [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF] or in our own calculations. For GP visits, the standard methodology generally finds on French data that the Need index amounts to almost 80% of C, while in our method Need represents roughly 20% of C.

In our results, the part of inequality due to differences in need is much smaller, and the part due to non-need variables (the unjustifiable part) is much bigger than what can be found with the standard methodology. The "unjustifiable" part of health care use inequality could thus be much larger than what the standard methodology indicates.

Interpretation of our results: the importance of the heterogeneity of behaviors in the observed inequality

We notice that C < 0 for GP visits, and C > 0 for specialist visits and the total number of visits.

GP visits are thus concentrated among the poor, while specialist visits are concentrated among the rich. The Need index is negative for the three variables: needs are thus concentrated in the lowest part of the income distribution. The HI index, that represents the degree of horizontal inequity, is negative for the number of GP visits and positive for the number of specialist visits and the total number of visits. This means that for GP visits, the poor receive more in proportion than the rich, for a given need. Conversely, for specialists visits, the rich receive more in proportion than the poor, for a given need.

The HI index reflects both the distribution of variables and the heterogeneity of behaviors. The goal of our method is precisely to put emphasis on the behavioral component. We observe that inequality due to the heterogeneity of behaviors is far from negligible: for all type of care, it amounts to nearly half of the HI index. Having estimated the model on each one of the income quintiles, we have shown that half of the horizontal inequity index is due to the heterogeneity of behaviors with respect to income. This observation cannot be identified in studies using the standard methodology.

We find that the effect of behaviors is globally pro-poor in the case of GP visits and pro-rich in the case of specialists visits. Each one of the three components of HI have the same sign for each type of care. The heterogeneity of practices linked to participation is clearly pro-rich: for a given morbidity and given other characteristics, the poor resort less to physician care (GP or specialists) than the rich. However, the heterogeneity of behaviors linked to conditional consumption is propoor. Once the decision to consume is made, the poor receive more in proportion than the rich, for an equivalent morbidity.

For the three types of health care use we study (GP, specialists and total number of visits), the heterogeneity of practices linked to participation appears to be pro-rich. Participation behaviors for a given morbidity have a strong link to demand behaviors. This results shows the presence of a heterogeneity of access linked to the rank in the income distribution. This heterogeneity could signify the poor's lower preference for health. Indeed, the coefficients capturing practices for a given morbidity are estimated with a model where income is present, as well as many other individual characteristics. The influence of income level is thus taken into account in the explanatory model of health care use.

The heterogeneity of practices linked to conditional consumption appear to be pro-poor, for all types of health care use. Conditional consumption can be linked to the supply side. The suppliers' pro-poor behavior could compensate the pro-rich behaviors of individuals. The health care system would support equality of treatment. However, the poor's reduced participation in the health care system could induce a late recognition of their illness, and thus a degradation of health. This late participation could lead to more frequent and costly health care use once participation has been decided, and to less favorable outcomes overall.

The total number of physician visits is globally inequitable, and in favor of the rich (HI = 0, 0317). Half of this inequity arises from the heterogeneity of behaviors (0, 0182). This pro-rich inequity of behaviors is mainly due to the pro-rich heterogeneity of practices linked to participation that correspond to the demand side. The interpretation of results can be questioned: they can be interpreted as the poor's lower preference for health, or as an indication of a problem in access to care. In the case of a lower preference for health, should these preferences be followed?

As a matter of fact, the results we outline here can be strongly linked to the social epidemiology literature. The link between inequality in health and inequality in income is well recognised:

according to [START_REF] Wilkinson | Unhealthy societies: the afflictions of inequality[END_REF], the absolute level of income is less important that the relatve position of individuals in the society. From an economic point of view, this position can in some way be assessed by the rank of the individual in the income distribution. Our results showed heterogenous behaviors with respect to the individual rank in the income distribution in a model where income level is controlled. Following the social epidemiology literature, it indicates that when explaining individual behaviors, the relative place in the society is as important as the observed absolute income level. Within a public policy perspective, these results might indicate that in order to reduce inequity in health care use, one should reduce income inequality but also influence behaviors of underconsumption that can be observed in the lower part of the income distribution.

Solely reducing income inequality will indeed reduce health care use inequity, but if behaviors are linked to the relative position in the society (which in our study is represented by the rank in the income distribution), an important source of inequity will remain. This source of inequity, the heterogeneity of behaviors with respect to social rank, cannot be identified in the standard decompositions, and its effect is unjustly attributed to inequality of income (as in expression (3)).

Using the standard decomposition for policy purposes might be misleading, in the sense that it leads to neglecting an important source of inequity.

Conclusion

The method we propose for the analysis of inequality provides a synthetic analysis of the various factors that lead to the observed inequality in health care use. The micro-simulation approach avoids the computation and calculation of indices whose interpretation might be questionable, as in the standard decomposition. Our estimation by income quantile improves upon standard decompositions by providing the identification of heterogeneity of behaviors linked to the rank in the income distribution. While the standard way of testing for health care use inequity is usually done by comparing behaviors relative to various income quantiles (see [START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF]), this feature had remained absent from the standard decompositions of health care use.

The decomposition we propose here provides a link between the [START_REF] Oaxaca | Male-Female Wage Differentials in Urban Labor Markets[END_REF] style counterfactual analyses and the inequity decomposition methods.

The application we proposed enabled us to analyze the sources of inequity in physician visits in France in 1998. Our results are consistent with the previous literature in that for a given morbidity, GP use is concentrated among the poor, and specialist use is concentrated among the rich.

We adhered to the standard approach in the literature that distinguishes justifiable and unjustifiable inequality. The index of horizontal inequity that we built (HI ) was decomposed into behaviors and individual characteristics; we showed that the heterogeneity of behaviors represents nearly half of the HI index. Taking into account the heterogeneity of behaviors appears to be fundamental when trying to explain the sources of inequity in health care use. This heterogeneity of behaviors can be linked to the heterogeneity of individual preferences. The link with the social epidemiology literature improves upon the standard decomposition approaches, and further research should examine the heterogeneity of health care behaviors and its impact on inequity.

  The analysis of inequality in health care use in France: an application We use the Appariement, a survey conducted in France every other year by Irdes. We use year 1998 and restricted the analysis to people age 15 and above. The data provide detailed health care use of every individual, as well as personal characteristics such as age, household size and household income. A great number of morbidity indicators are available, such as synthetic indicators (e.g. level of disability) as well as detailed indicators corresponding to diseases (e.g. presence of diabetes).

component of C due to other factors than need, labeled HI, is equal to ∆ 2 + ∆ 2bis + ∆ 3 + ∆ 4 + ∆ 5 : 4

Table 1 :

 1 Decomposition of the inequality observed in 1998 in France

A discussion of the notion of need for care can be found in[START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF].

Vertical equity is defined by a situation where people in different need for care receive appropriately dissimilar treatments[START_REF] Wagstaff | Handbook of Health Economicsvol. 1, chap. Equity in health care finance and delivery[END_REF].

From this point of view, health inequalities are described as given, while one should keep in mind that the distribution of health is likely to be influenced by health care use.

Institute for research and information in health economics, 10 rue Vauvenargues, 75018 Paris, France -www. irdes.fr

European project whose goal is to study inequality in health, health care use and health care financing: http: //www2.eur.nl/bmg/ecuity/. Research teams come from the following countries: Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Spain, Sweden, U-K, Norway, Switzerland, USA.

In other words, due to morbidity and age.

We should emphasize that the effect of unobserved heterogeneity is contained within HI (see [START_REF] Vandoorslaer | Income-related inequality in the use of medical care in 21 OECD countries[END_REF]). This decomposition quantifies the global effect of morbidity on the degree of inequality observed (the Need indicator), and does not have the computation and interpretation issues of the C k that are found in expression (2). Moreover, whereas the heterogeneity of practices is not modeled in the standard approach, it is explicitly modeled here with the estimated parameters d q and δ q , q ∈ [1..Q]. As was mentioned earlier, the groups of variables we chose reflect the common distinction between need and non-need variables. However, our method is able to compute the contribution to inequality of any group of variables or even any isolated variable.

Index HI as defined by expression ( 14) can be decomposed into two components : one due to the distribution of the variables in the sample and one due to the heterogeneity of the coefficients corresponding to these variables. The component of inequality due to the variables is thus defined by the following expression:

While the component of HI due to the heterogeneity of behaviors can be written as:

The degree of inequality due to the heterogeneity of behaviors with respect to income can be decomposed into three effects:

• ∆ 2 : practices corresponding to participation, that can be linked to the demand side

• ∆ 2bis : practices corresponding to the conditional consumption, that can be linked mainly to the supply side

• ∆ 4 : parameters corresponding to non-need variables (socio-economic variables), that can be linked to the demand side This decomposition enables us to distinguish the degree of inequality that is due to the supply and demand of health care through the analysis of ∆ 2 and ∆ 2bis and to identify precisely the agents' preferences.


Thierry Desot
email: thierry.desot@univ-grenoble-alpes.fr

François Portet
email: francois.portet@imag.fr

Michel Vacher
email: michel.vacher@imag.fr

Towards End-to-End spoken intent recognition in smart home 1 st

on clean transcriptions whereas ASR transcriptions contain errors reducing the overall performance. Although the pipeline approach is widely adopted, there is a rising interest for end-toend (E2E) SLU which combines ASR and NLU in one model, avoiding the cumulative ASR and NLU errors of the pipeline approach [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF], [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF]. The main motivation for applying the E2E approach is that word by word recognition is not needed to infer intents. On top of that, the phoneme dictionary and language model (LM) of the ASR become optional. However, E2E approaches are highly dependent on large training data sets which are difficult to acquire, limiting the applicability to new domains where data is scarce which is the case for smart homes.

The main contributions of this paper are: 1) the first work on E2E SLU for voice command in a smart home environment; 2) a comparison of a state-of-the-art pipeline approach that predicts intents from the ASR hypothesis and an E2E SLU model; 3) experiments performed with realistic non-English and synthetic data to deal with the paucity of domain specific data sets. Both approaches are positioned with respect to the state-of-the-art in Section II and are outlined in Section III. We tackle the lack of domain-specific data by using Natural Language Generation (NLG) and text-to-speech (TTS) to generate French voice command training data. An overview of these processes and data sets is given in Sections III and IV. Section V presents the results of experiments on a corpus of real smart home voice commands followed by a discussion, conclusion and outlook on future work.

II. RELATED WORK

SLU is typically seen as a slot-filling task in order to predict the speaker's intent on the one side and entities in a spoken utterance (slots and values) on the other side [START_REF] Wang | Semantic frame-based spoken language understanding[END_REF]. The most common approach is a pipeline of an ASR and an NLU module. The ASR system outputs the hypothesis transcriptions from a speech utterance that are analyzed by the NLU module to extract the meaning. While the slot-filling task is most often Abstract-Voice based interaction in a smart home has become a feature of many industrial products. These systems react to voice commands, whether it is for answering a question, providing music or turning on the lights. To be efficient, these systems must be able to extract the intent of the user from the voice command. Intent recognition from voice is typically performed through automatic speech recognition (ASR) and intent classification from the transcriptions in a pipeline. However, the errors accumulated at the ASR stage might severely impact the intent classifier. I n t his p aper, w e p ropose a n End-to-End (E2E) model to perform intent classification directly from the raw speech input. The E2E approach is thus optimized for this specific task and avoids error propagation. Furthermore, prosodic aspects of the speech signal can be exploited by the E2E model for intent classification (e.g., question vs imperative voice). Experiments on a corpus of voice commands acquired in a real smart home reveal that the state-of-the art pipeline baseline is still superior to the E2E approach. However, using artificial d ata generation techniques we show that significant i mprovement t o t he E2E model can be brought to reach competitive performances. This opens the way to further research on E2E Spoken Language Understanding.

Index Terms: spoken language understanding, automatic speech recognition, natural language understanding, ambient intelligence, voice-user interface I. INTRODUCTION Voice based interaction in a smart home has become a feature of many industrial products. To be efficient, these systems must be able to extract the intent of the user from the voice command. Intent recognition is a subtask of Spoken Language Understanding (SLU). Its aim is to extract the meaning contained in an utterance [START_REF] Wang | Semantic frame-based spoken language understanding[END_REF]. Voice based intent recognition is typically performed through automatic speech recognition (ASR) and intent classification from the transcriptions in a pipeline. However, the intent classifier i s trained This work is part of the ANR VocADom project (ANR-16-CE33-0006) funded by the french Agence Nationale pour la Recherche.

978-1-7281-0984-8/19/$31.00 addressed as a sequence labelling task, intent recognition is generally approached as a classification task over the overall transcription.

To address the cascading error effect of classical pipeline SLU models, such approaches used confidence measures and N-best lists. For instance, weighted voting strategies combining ASR output confidence measures and N-best list hypotheses were used in a Named Entity Recognition (NER) task [START_REF] Zhai | Using n-best lists for named entity recognition from Chinese speech[END_REF] to take uncertainty into account. Since the n th hypothesis tends to contain more character errors than the n-1 th hypothesis, a named entity (NE) label is considered correct if it occurs in more than 30% of the n-best candidates. This brought an improvement over the baseline F-measure (1-best) with 1.7%. Another method is to learn NLU models on noisy ASR transcriptions. In [START_REF] Sudoh | Incorporating speech recognition confidence into discriminative named entity recognition of speech data[END_REF], manual and ASR output transcriptions with word ASR confidence measures were used for a NER task, to learn a support vector machine-based (SVM) NER system. This increased precision by 2% as compared to the baseline.

More recently, to improve ASR error handling, acoustic word embeddings for ASR error detection were trained through a convolutional neural network (CNN) based ASR model to detect erroneous words. Output of this ASR model is fed to conditional random fields (CRF) and an attentionbased RNN NLU model [START_REF] Simonnet | ASR error management for improving spoken language understanding[END_REF]. The CRF outperformed the RNN approach and the concept error rate (CER) decreased by 1% integrating confidence measures. Previous approaches of SLU especially focused on tuning the ASR model or using N-best hypotheses. [START_REF] Hatmi | Incorporating named entity recognition into the speech transcription process[END_REF] modified the ASR dictionary and language model to directly generate transcriptions with NE labels. This led to a significant increase of slot recognition.

Only recently some E2E work integrates deep neural networks (DNN): in [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF], intents were directly inferred from audio MFCC features training a sequence-to-sequence (seq2seq) model on clean and noisy speech data. This gave an accuracy of 74.1% on an in-house corpus (35 types of intent), while a seq2seq NLU model fed with the ASR outputs gave 80.9%. A similar E2E approach was applied in [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF]. The author trained the Baidu Deep Speech ASR system [START_REF] Hannun | Deep speech: Scaling up end-to-end speech recognition[END_REF] on NE annotated transcriptions. The training set was increased by performing NER on a large speech data set. Their system exhibited a better identification of NER labels than a pipeline system (69 vs 65% F-measure) but was less performing with NE values extraction (47 vs 50% F-measure). This overview shows that E2E SLU models generate high expectations for joint ASR and NLU optimization but their performances have not superseded those of the pipeline approach yet. A common outcome is that data augmentation is the key factor for bringing the E2E model to superior performance. [START_REF] Li | Training neural speech recognition systems with synthetic speech augmentation[END_REF] used TTS to improve speech recognition. Gadde et al. used an ASR E2E convolutional NN model with connectionist temporal classification (CTC) and report optimal ASR performances with 50% synthetic and 50% natural speech data in the acoustic model [START_REF] Li | Training neural speech recognition systems with synthetic speech augmentation[END_REF]. This aspect supports the data augmentation strategy that is used in this paper which is developed in section V-B. The baseline pipeline method follows the diagram of Figure 1. It is composed of a first stage of ASR that extracts the transcription hypotheses from speech which are fed to an NLU module that selects the most probable intent from the hypotheses.

The ASR model is based on the ASR open source hybrid HMM-DNN Kaldi tool that uses speaker adapted features from the Gaussian mixture model (GMM) [START_REF] Povey | The Kaldi speech recognition toolkit[END_REF]. We used the nnet2 version which supports using multiple GPUs [START_REF] Povey | Parallel training of deep neural networks with natural gradient and parameter averaging[END_REF].

The Intent Classifier is a seq2seq attention-based PyTorch model. Recently, such models have been successfully used for the NLU slot-filling task [START_REF] Mesnil | Using recurrent neural networks for slot filling in spoken language understanding[END_REF]- [START_REF] Huang | Improving slot filling performance with attentive neural networks on dependency structures[END_REF] and supersede the previous state-of-the-art CRF model [START_REF] Jeong | Triangular-chain conditional random fields[END_REF]. An important factor that explains the improvement of NLU models (including the CRF ones) is the application of multitask learning. Intent recognition is performed jointly with slot recognition [START_REF] Liu | Attention-based recurrent neural network models for joint intent detection and slot filling[END_REF], [START_REF] Jeong | Triangular-chain conditional random fields[END_REF] which boosts performances for both tasks. Hence, many intent classifiers are trained within a framework that considers both tasks together. For that reason we propose a seq2seq model that encodes the sequence of words and decodes a sequence of symbols representing the global intent and each slot contained in the sequence to support the intent classification. For the example utterance "Turn on the light" the model generates the sequence intent[set_device], action[TURN_ON], device [light]. In this case, the intent is to set a device and the slots action and device provide information about which entities are concerned with the voice command.

The approach we propose has several advantages. First, contrary to most NLU methods that approach slot-filling as a sequence labelling task, we define the problem as a generation task. State-of-the-art approaches depend on aligned data. A sequence labelling task requires that each word in the transcription is assigned one unique slot label (e.g., the BIO NE labeling scheme). However, since our ultimate aim is to extract the intent directly from the raw speech signal, a sequence labelling approach is not adequate. It would require either to label each word in every n-best ASR hypothesis or to annotate each speech frame with a slot label. Our approach does not need aligned data and is thus more adapted to E2E intent classification from speech than the sequence labelling one.

The intent classifier we propose is close to the one of Liu et al. [START_REF] Liu | Attention-based recurrent neural network models for joint intent detection and slot filling[END_REF]. Both classifiers have shown close performances on a voice command task [START_REF] Desot | Towards a French Smart-Home Voice Command Corpus: Design and NLU Experiments[END_REF], [START_REF] Mishakova | Learning Natural Language Understanding Systems from Unaligned Labels for Voice Command in Smart Homes[END_REF]. Although the classifier of Liu et al. [START_REF] Liu | Attention-based recurrent neural network models for joint intent detection and slot filling[END_REF] has shown slightly better performances, it relies on aligned data while our intent classifier is independent from aligned data. Furthermore, since ASR errors reduce the performance of the NLU model, using unaligned data provides the flexibility to infer slot labels and values from imperfect transcriptions in order to recognize the intent. In summary, the ASR (Kaldi based) and the intent classifier (seq2seq) components represent together a strong pipeline baseline.

B. E2E SLU

The E2E approach is based on ESPnet [START_REF] Watanabe | Espnet: End-to-end speech processing toolkit[END_REF]. It integrates the KALDI data preparation, extracts Mel filter-bank features and combines Chainer and PyTorch deep learning tools [START_REF] Tokui | Chainer: a next-generation open source framework for deep learning[END_REF], [START_REF] Paszke | Automatic differentiation in PyTorch[END_REF]. The default PyTorch encoder is a pyramidal subsampling bi-LSTM [START_REF] Chan | Listen, attend and spell: A neural network for large vocabulary conversational speech recognition[END_REF], whereas the chainer back-end supports CNNs. Mapping from acoustic features to character sequences is performed by a trade-off hybrid multitask learning that combines CTC [START_REF] Amodei | Deep speech 2: End-to-end speech recognition in English and Mandarin[END_REF] and an attention-based encoder-decoder. As the attention mechanism alone allows too flexible alignments, CTC guides attention alignment to be monotonic.

logp hyb (y n |y 1:n-1 , h 1:T ) = α logp ctc (y n |y 1:n-1 , h 1:T ) + (1 -α) logp att (y n |y 1:n-1 , h 1:T ), (1)
where y n is a hypothesis of output label at position n given y 1:n-1 and the encoder output h 1:T . The score combination (logp hyb ) for the hybrid CTC/attention architecture, with attention p att and CTC p ctc log probabilities is performed during beam search. The weight α can be set manually in order to give more importance to attention or CTC. To leverage a possible text corpus, a character RNN language model can be provided for the decoding. The log probability p lm of the RNN LM can be fused with the CTC attention hybrid output by:

logp(y n |y 1:n-1 , h 1:T ) = logp hyb (y n |y 1:n-1 , h 1:T ) + β logp lm (y n |y 1:n-1 ). (2)
Since ESPnet models the ASR task at the character level, our approach to predict intents from the input signal was inspired by [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF] and [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF]. The output target of the ESPnet process was speech transcriptions augmented with characters (e.g., @, #. . . ) symbolizing the intent of the utterance. Hence, the ESPnet model is trained to predict enriched transcriptions where each hypothesis is contextualized by its global intent. This task is described in section V-B.

IV. DATA COLLECTION AND AUGMENTATION

The pipeline and E2E intent recognition methods described above have been applied to the case of voice commands in a smart home. The application context is illustrated Figure 2. Each time a dweller utters a command, this utterance is captured and analyzed by an SLU module. If the intent is to control the house (in the example, to turn on the light), the semantics extracted from the utterance are sent to the home automation system. Otherwise, the utterance is ignored. Hence, the intent recognition information is of primary importance for the decision-making module to make the home automation system activate a command or not.

SLU Home Automation

"Vocadom allume la lumière du salon"

Sound Acquisition

Fig. 2. Activation of the light by the Home Automation system after SLU analysis and intent recognition (VocADom turn on the light in the living-room).

voice based commands is a spreading feature of many IoT devices, there is a lack of speech based domainspecific corpora, especially for non-English languages such as French. To this end we collected a corpus in a real smart home with several users that is made available to the community 1 . Despite this corpus, the amount of data is far too low to train a DNN. For that reason we tackled this data scarcity problem using data generation. The next subsections outline the realistic data corpora available and the artificial training data generation.

A. Realistic Smart home data sets

Few French real domain-specific corpora are available. One can cite the SWEET-HOME corpus [START_REF] Vacher | The Sweet-Home speech and multimodal corpus for home automation interaction[END_REF] which was recorded by participants enacting activities of daily living in a smart home equipped with home automation sensors and actuators. Continuous speech was mainly composed of voice commands. However it was recorded with only single user settings with a simple set of commands respecting a strict grammar and it is not sufficient to cover a large set of intents with a lot of syntactic and lexical variation.

Hence, we also used the VocADom@A4H corpus [START_REF] Portet | Context-Aware Voice-based Interaction in Smart Home -VocADom@A4H Corpus Collection and Empirical Assessment of its Usefulness[END_REF] which includes about twelve hours of audio signal and was acquired in realistic conditions in the two-storey Amiqual4Home smart home2 (Fig. 3, 4 and5). This 87m 2 smart-home with a kitchen, living room, bedroom and bathroom, is equipped with home automation systems, multimedia devices, and microphone arrays. More than 150 sensors and actuators were set in the house to acquire speech, control light, set the heating etc. Eleven participants uttered voice commands while performing activities of daily living for about one hour. Out-ofsight experimenters reacted to participants' voice commands following a wizard-of-Oz strategy to add naturalness to the corpus. The resulting speech data was semi-automatically transcribed, then humanly double-checked and resulted in 6,747 utterances, annotated with 8 different intents, including the none intent (for sentences without intent) and slot labels. Fourteen different slot labels were defined such as the action to perform, the device to act on, the location of the device or action, the person or organization to be contacted, a device component, a device setting and the property of a location, device, or world. This corpus has been annotated by three annotators. Table I provides representative examples of voice commands with intent, slot and slot value labels. For each utterance the global intent is given with the slots between brackets. For the example "are the lights upstairs on", CHECK_DEVICE means that the lights (DEVICE) on the upper floor (LOCATION-FLOOR) should be checked whether they are on (DEVICE-SETTING) or not.

B. Data augmentation via artificial data generation

Since the amount of real data is too small for training, the corpus generator of Desot et al. [START_REF] Desot | Towards a French Smart-Home Voice Command Corpus: Design and NLU Experiments[END_REF] was used to produce training data automatically labeled with intents, slot and value labels for the SLU experiments. On top of that several syntactic variants per sentence are provided (table II). It was built using the open source NLTK python library to which featurerespecting top-down grammar generation was added. Semantic constraints prohibit the production of nonsensical utterances. In each produced voice command a keyword is used to activate the Smart Home. Most keywords (such as "Ichefix") are proper nouns of at least 3 syllables long to enable sufficient duration for detection. "Ichefix call a doctor" activates the Home Automation system whereas "Call a doctor" should not trigger any reaction. With this generator more than 77k voice commands were produced for training purpose. A complete overview of intents is presented in table III. As shown in this overview, the data set is imbalanced.

Although the current trend for data augmentation is to use constrained RNN language models [START_REF] Hou | Sequence-to-sequence data augmentation for dialogue language understanding[END_REF], such systems still need a set of initial sentences for bootstrapping and are difficult to control and to make them generalize to unseen concepts. This is why standard expert-based NLG was used in this work [START_REF] Gatt | Survey of the state of the art in natural language generation: Core tasks, applications and evaluation[END_REF].

Finally, the ESLO2 corpus utterances (126h) of conversational French speech [START_REF] Serpollet | A large reference corpus for spoken French: Eslo 1 and 2 and its variations[END_REF] was considered in the study. This corpus does not contain any voice commands but shares similarities with VocADom@A4H since it contains frequent disfluencies, repetitions, revisions and restarts [START_REF] Rangarajan | Analysis of disfluent repetitions in spontaneous speech recognition[END_REF]. ESLO2 was used to model the none intents in the training set. To extract a set of none intent utterances, an n-gram model was learned on the artificial corpus. Every utterance too close to the n-gram model was detected as a command-related utterance. All the detected sentences containing a token in a predefined list of domestic-related tokens were manually checked and put aside if they truly contained a domestic-related intent: e.g., "You should open the door" was set aside as it is actually a Set_device intent.

C. Summary of the data sets

V. EXPERIMENTS AND RESULTS

A. Pipeline Intent Recognition Baseline Approach

Baseline ASR transcriptions were generated using Kaldi. We compared two acoustic models. The first one was trained on 90% randomly selected speakers of the corpora ESTER1 (100h) and 2 (100h), REPERE (60h), ETAPE (30h), SWEET-HOME (2.5h), BREF120 (120h) [START_REF] Tan | A French non-native corpus for automatic speech recognition[END_REF], VOIX-DETRESSE (0.5h) [START_REF] Aman | Etude de la performance des modèles acoustiques pour des voix de personnes âgées en vue de l'adaptation des systèmes de RAP (assessment of the acoustic models performance in the ageing voice case for ASR system adaptation)[END_REF] and CIRDOSET (2h) [START_REF] Vacher | The CIRDO corpus: comprehensive audio/video database of domestic falls of elderly people[END_REF]. For the second one we added 90% of the speakers of 126 hours of ESLO2 speech data [START_REF] Serpollet | A large reference corpus for spoken French: Eslo 1 and 2 and its variations[END_REF], 10% being kept as development (DEV) set. The ASR dictionary consisted of 305k phonetic transcriptions of words based on the BD-LEX lexicon [START_REF] Perennou | A data and cognition base of spoken French[END_REF] to which phonetic variants were added with the LIA grapheme-to-phoneme conversion tool LIA_Phon 3 . For decoding, we used a 3-gram LM, based on the artificial corpus combined with the SWEET-HOME 3 http://lia.univ-avignon.fr corpus. A generic LM was trained on 3,323M words, using EU bookshop, TED2013, Wit3, GlobalVoices, Gigaword, Europarl-v7, MultiUN, OpenSubtitles2016, DGT, News Commentary, News WMT, LeMonde, Trames, Wikipedia and our training data. The final LM resulted from an interpolation of the specific LM (weight = 0.6) with the generic LM (weight = 0.4).

The acoustic features are MFCC and were used to train a speaker-dependent triphone GMM model with speaker adapted transformation linear maximum likelihood regression (SAT+fMLLR). The final model was a hybrid HMM-DNN, mapping the transformed fMLLR characteristics to the corresponding HMM states. Word error rates (WER) in table V show that the fMLLR and HMM-DNN models with the ESLO2 data slightly outperform the acoustic models without it. The NLU seq2seq model was composed of a bi-directional LSTM encoder and decoder. The input words were first passed to a 300-unit embedding layer. The encoder and decoder were each a single layer of 500 units. Adam optimizer was used with a batch size of 10, using gradient clipping at a norm of 2.0. Dropout was set to 0.2 and training continued for 10,000 steps with a learning rate of 0.0001. Input sequence length was set to 50 and output sequence length to 20. Beam search of size 4 was used. The NLU model was implemented using the LIG PyTorch seq2seq library 4 . The training data was 90% of the combined artificial and the filtered ESLO2 data, the remaining 10% being the DEV set. The test data was the VocADom@A4H corpus. Both sets are described in section IV. F1-score at intent level on VocADom@A4H is shown in table VI. Results analysis shows a strong tendency towards none intent predictions due to the majority none intent class (unweighted manual).

We handled this imbalanced data problem by modifying the weight assignment in the cross entropy loss function of the PyTorch Seq2seq model. This was calculated on the complete training data and the resulting class weights were summed per batch. The total sum was multiplied with the cross entropy loss calculated per batch following equation ( 3):

weight_class_i = total_instances instances_class_i (3)
The loss for majority intent classes dropped faster as compared to the loss for intent classes less represented in the training data. Consequently training increased for the minority intent classes. This method clearly improved performances (weighted manual).

NLU performances for intent predictions on the Vo-cADom@A4H ASR output (weighted ASR) are worse than for the manual transcription predictions (weighted manual).

B. End-to-End Approach for Intent Recognition

For the E2E experiments, we used ESPnet default settings. The encoder was a very deep convolutional neural network (VGG) followed by six bidirectional (BLSTM) layers with 320 units. The decoder was a single LSTM layer with 300 units. The attention-CTC multi-task learning weight was set to 0.5. The optimizer was Adadelta with a batch size of 30. Training continued for 20 epochs. Beam size of 20 was used for decoding.

In this section, we describe the performance of ESPnet on a typical ASR task followed by the E2E intent prediction using an enriched transcription approach. ESPnet was first trained for an ASR task using the same training set as the Kaldi model in the pipeline approach (section V-A) and evaluated on the VocADom@A4H data set. The results reported in table VII show that ESPnet exhibits a higher Word Error Rate and Character Error Rate (CER) (real_data) as compared to Kaldi. However, when using the same LM data as in the Kaldi setup (section V-A) for training and applying the character-based LM with ESPnet, the WER and character error rate (CER) improved (real_data+LM).

Addition of synthetic speech data for an ASR task has proven to be beneficial to the ASR performance [START_REF] Li | Training neural speech recognition systems with synthetic speech augmentation[END_REF]. To compensate the lack of a large amount of domain-specific speech training data, the ASR training set described in Section V-A was augmented with TTS data generated on the complete artificial corpus using the open source French female SVOX voice 5 and represents 14.67% of the total acoustic model data. As shown in the third raw (real_data+LM+TTS), the addition of the TTS generated data brought significant improvement. Although far from perfect, the results obtained on our DEV set (25.7% WER) are comparable to those obtained by Ghannay et al. [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF] on their DEV set (20.70% WER) using the Baidu Deep Speech E2E ASR system. Moreover, Ghannay et al. [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF] used a real corpus of newswire with similar conditions in training and test data, while in this paper, we deal with noisy domestic speech in the test data that is not present in our training set.

To perform intent recognition using ESPnet, we added intent labels (symbols) in the manual transcriptions of the corpus in sentence initial and final positions as follows:

set_device: "@ VOCADOM switch on the light please @". For none intent sentences without voice command, no symbol was inserted. To study the impact of the synthetic data, different proportions of TTS data were used. For the creation of the character-based LM, we added the artificial corpus data with the intents injected as symbols into the data of the LM used with Kaldi in section V-A.

Table VIII mentions the hours of combined real and TTS training data (+tts) per model (TRAIN) and the percentage of the number of hours of TTS generated data in the acoustic model (SYNTH in TRAIN). Intent classes are not well predicted for the VocADom@A4H test set (+tts). These results pinpoint a too large distance between the acoustic features of the TTS data, and the VocADom@A4H natural speech data. This seems confirmed as performances increased when moving 1k sentences from the test set to the training set. Analysis showed that intent class prediction benefits more from the SWEET-HOME real data and the 1k test sentences added to the acoustic model, combined with the TTS data (+tts+VocADom@A4H_1k). (+tts+VocADom@A4H_1k+inc). Reducing the impact of the utterances without voice-command, by leaving only 11k utterances with a none class label in the acoustic model, slightly improved performance (+tts+VocADom@A4H_1k+dec).

Decoding with the character-based LM including artificial corpus data augmented with the symbolic intent class labels, using our two best models, significantly increased the F1-score (+tts+VocADom@A4H_1k+inc+LM, +tts+VocADom@A4H_1k+dec+LM). The maximal E2E SLU performance was reached using an attention-CTC multi-task learning weight of 0.5.

For a fair comparison we also retrained the pipeline SLU ASR and NLU modules using the same reduced training data. Table IX (E2E SLU) recalls the best E2E performance from table VIII (+tts+VocADom@A4H_1k+dec+LM) and compares intent classification performance with he pipeline SLU model, trained on the reduced data set. With such a small training data set the E2E model is able to supersede the baseline pipeline approach for intent prediction. However this time the pipeline ASR (Kaldi) exhibited a WER of >90%. With an E2E ASR (ESPnet) training on the same reduced data a WER of 60.6% was obtained. Hence we used the resulting ESPnet ASR transcriptions as input for the NLU subcomponent which did not outperform the E2E SLU model in table IX. Analysis showed that the character-based ASR E2E approach made better use of a reduced amount of data than the pipeline wordbased approach for which more data is needed. It also trains better on combined natural and artificial speech. This also demonstrates that a high ASR performance is not mandatory for an E2E SLU approach, different from the pipeline SLU.

VI. DISCUSSION

E2E SLU is only partially dependent on ASR performance, and intent prediction can benefit from a well-balanced attention-CTC multi-task learning (optimal results were obtained with multi-task learning weight of 0.5). The attention mechanism combined with the bi-LSTM allows a more flexible alignment, which focuses on the important parts (the intent label symbols) in the sequence and models longterm dependencies from which intent prediction can benefit. However erroneous ASR transcriptions have an impact on intent prediction. For E2E ASR frequent errors occur for the keyword proper noun predictions (10% of the total ASR errors), different from pipeline ASR with a lexicon. Mispronunciations in the artificial speech data partially explain these errors but have their impact on intent classification as each command contains a keyword. Hence by moving a small portion of real domain-specific data to the training data these errors decreased.

To reduce the impact of imbalanced data, in the pipeline approach, a weighting majority class strategy was used successfully in the cross entropy loss function. In the E2E SLU model, data over-and sub-sampling of the minority and majority classes was applied to the training data, improving performances. Although the ASR performance must be improved, it shows that E2E spoken intent recognition is feasible with imperfect ASR transcriptions, if the ratio between natural and artificial speech in a small unaligned training data set is optimal. The E2E spoken intent recognition approach did not outperform the pipeline approach. However, the best model still obtains a 70.21% F1-score for intent prediction without using the slot label information, contrary to the pipeline approach using the named entity information at the same time as the intents in a multitask setting. On top of that the pipeline approach was outperformed by the E2E SLU approach with both systems trained on the same small-sized training data (61.35% vs 70.21% F1-score).

VII. CONCLUSION AND FUTURE WORK

This study shows that E2E intent prediction is possible in a data scarce context combining NLG and TTS augmentation. Furthermore it is portable to new domains, providing there is a small amount of domain-specific data. These aspects have not been investigated in the closest related work to ours [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF], [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF]. E2E intent prediction is a promising way to reach similar or higher performances than a pipeline approach. Further work to achieve this includes extending our intent recognition approach with slot label and slot value information also by using transcription augmentation. On top of that, multi-task [START_REF] Ghannay | End-to-end named entity and semantic concept extraction from speech[END_REF] and transfer learning with models trained on similar or far larger domain-specific data sets should be investigated.

Fig. 3 .

 3 Fig. 3. Instrumented kitchen.

Fig. 4 .

 4 Fig. 4. Ground floor: kitchen and living room.

Fig. 5 .

 5 Fig. 5. First floor: bedroom and bath room.

  , '#' (check_device), ']' (get_world_property), '{' (get_room_property), '[' (contact).

TABLE I EXAMPLES

 I OF NLU ANNOTATED VOICE COMMANDS

	Sentence + NLU annotation
	are the lights upstairs on?
	CHECK_DEVICE(DEVICE=light="lights",
	LOCATION-FLOOR=1="upstairs",
	DEVICE-SETTING=on="on")
	call the doctor
	CONTACT(PERSON-OCCUPATION=doctor="doctor")
	what time is it?
	GET_WORLD_PROPERTY(WORLD_PROPERTY=time="time")
	open the blind
	SET_DEVICE(ACTION=open="open",
	DEVICE=blind="blind")
	increase the volume of the radio
	SET_DEVICE_PROPERTY(ACTION=turn_up="increase",
	DEVICE-COMPONENT=volume="the volume",
	DEVICE=radio="of the radio")

  Table IV summarizes the statistics for all corpora. The ESLO2 set is the largest one, without voice commands. The

TABLE III ARTIFICIAL

 III CORPUS (ARTIF.) AND VOCADOM@A4H (REAL.): EXAMPLES AND FREQUENCY OF INTENTS

	Intent	Example (French)	English translation	Frequency
				Artif.	Real.
	Contact	Appelle un médecin	Call a doctor	567	114
	Set_device	Ouvre la fenêtre	Open the window	63,288	2178
	Set_device_property	Diminue le volume de la télé	Decrease the TV volume	7290	9
	Set_room_property	Diminue la température	Decrease the temperature	3564	21
	Check_device	Est-ce que la fenêtre est ouverte?	Is the window open?	2754	284
	Get_room_property	Quelle est la température?	What's the temperature?	9	3
	Get_world_property	Quelle heure est-il?	What's the time?	9	3
	None	La fenêtre est ouverte	The window is open	-	4135

artificial data set contains the highest frequency of voice commands but has a smaller vocabulary than the VocADom@A4H corpus. The SWEET-HOME data set has a smaller size and less syntactic variation than the VocADom@A4H corpus that was used as test corpus in all the experiments (unless otherwise specified).

TABLE IX PIPELINE

 IX AND E2E SLU PERFORMANCES (%) WITH VOCADOM@A4H SUBSET (1K.) IN TRAINING AND SUB-SAMPLING

	Training	Hours	(%) TTS	Intent
	set (reduced) of speech in train F1-score
	Pipeline SLU 84.69	94.39	61.35
	E2E SLU	84.69	94.39	70.21

https://vocadom.imag.fr

https://amiqual4home.inria.fr

https://gricad-gitlab.univ-grenoble-alpes.fr/getalp/seq2seqpytorch

https://launchpad.net/ubuntu/+source/svox

VIII. ACKNOWLEDGEMENTS

We thank Dr. Raheel Qader and Dr. Benjamin Lecouteux for their support using the PyTorch seq2seq library and Kaldi.