Vân Anh Huynh‐Thu

Yann Claes, Vân Anh Huynh-Thu, Pierre Geurts

Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the obtained models are more accurate than purely data-driven models, the optimization process usually comes with sensitive regularization constraints. Furthermore, while such hybrid methods have been tested in various scientific applications, they have been mostly tested on dynamical systems, with only limited study about the influence of each model component on global performance and parameter identification. In this work, we introduce a new hybrid training approach based on partial dependence, which removes the need for intricate regularization. Moreover, we assess the performance of hybrid modeling against traditional machine learning methods on standard regression problems. We compare, on both synthetic and real regression problems, several approaches for training such hybrid models. We focus on hybrid methods that additively combine a parametric term with a machine learning term and investigate model-agnostic training procedures. Therefore, experiments are carried out with different types of machine learning models, including tree-based models and artificial neural networks. We also extend our partial dependence optimization process for dynamical systems forecasting and compare it to existing schemes.

Yann Claes, Pierre Geurts, Vân Anh Huynh-Thu

Over the last few years, there has been an increased interest in making machine learning models more interpretable. Although a great deal of effort goes into developing techniques for interpreting the interactions learned by a given model, fewer studies focus on assessing the quality of such explanations. Even fewer focus on how to adjust the model to produce explanations faithful to prior knowledge, a process known as explanation-guided learning. Furthermore, most approaches in this area focus on classification problems and usually assume prior knowledge about which input features or regions are most important. In this work, we introduce a new approach to steering neural networks based on partial dependence, such that their average response to certain features aligns with specific functional domain knowledge about the problem. We empirically demonstrate on a range of regression problems, including dynamical systems forecasting, that models whose training has been controlled using our method perform better than unconstrained models and are more data-efficient. Moreover, we highlight that interpretations obtained from the former actually align with the user-provided knowledge, whereas those obtained from the latter do not.

Antonio Sutera, Gilles Louppe, Van Anh Huynh-Thu et al.

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems.

Vân Anh Huynh-Thu, Pierre Geurts

This paper presents a model-agnostic ensemble approach for supervised learning. The proposed approach is based on a parametric version of Random Subspace, in which each base model is learned from a feature subset sampled according to a Bernoulli distribution. Parameter optimization is performed using gradient descent and is rendered tractable by using an importance sampling approach that circumvents frequent re-training of the base models after each gradient descent step. The degree of randomization in our parametric Random Subspace is thus automatically tuned through the optimization of the feature selection probabilities. This is an advantage over the standard Random Subspace approach, where the degree of randomization is controlled by a hyper-parameter. Furthermore, the optimized feature selection probabilities can be interpreted as feature importance scores. Our algorithm can also easily incorporate any differentiable regularization term to impose constraints on these importance scores.

Antonio Sutera, Gilles Louppe, Vân Anh Huynh-Thu et al.

In many cases, feature selection is often more complicated than identifying a single subset of input variables that would together explain the output. There may be interactions that depend on contextual information, i.e., variables that reveal to be relevant only in some specific circumstances. In this setting, the contribution of this paper is to extend the random forest variable importances framework in order (i) to identify variables whose relevance is context-dependent and (ii) to characterize as precisely as possible the effect of contextual information on these variables. The usage and the relevance of our framework for highlighting context-dependent variables is illustrated on both artificial and real datasets.