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We extend the duality between exponential integrals and relative entropy to a variational formula for exponential integrals involving the Renyi divergence. This formula characterizes the dependence of risk-sensitive functionals and related…
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…
This paper discusses an application of Shapley values in the causal inference field, specifically on how to select the top confounder variables for coarsened exact matching method in a scalable way. We use a dataset from an observational…
Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved…
We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [2004, Influence diagnostics…
In this paper, we study the adaptivity gap of the influence maximization problem under independent cascade model when full-adoption feedback is available. Our main results are to derive upper bounds on several families of well-studied…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
We propose to study quantile oriented sensitivity indices (QOSA indices) and quantile oriented Shapley effects (QOSE). Some theoretical properties of QOSA indices will be given and several calculations of QOSA indices and QOSE will allow to…
Deep neural networks have gained momentum based on their accuracy, but their interpretability is often criticised. As a result, they are labelled as black boxes. In response, several methods have been proposed in the literature to explain…
We investigate the significance of change-points within fully nonparametric regression contexts, with a particular focus on panel data where data generation processes vary across units, and error terms may display complex dependency…
Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…
In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we define and study a new sensitivity index based on the…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…
Bounding causal effects analytically, rather than numerically, is appealing for its interpretability and conceptual clarity. Existing sharp methods rely on optimization-based approaches such as the Balke-Pearl framework, whose computational…
Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$…
Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate…
We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…
Influence diagnostics such as influence functions and approximate maximum influence perturbations are popular in machine learning and in AI domain applications. Influence diagnostics are powerful statistical tools to identify influential…
In a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this…
Explainable artificial intelligence promises to yield insights into relevant features, thereby enabling humans to examine and scrutinize machine learning models or even facilitating scientific discovery. Considering the widespread technique…