Related papers: Sobolev Independence Criterion
The use of machine learning models in decision support systems with high societal impact raised concerns about unfair (disparate) results for different groups of people. When evaluating such unfair decisions, one generally relies on…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the…
We introduce the Conditional Independence Regression CovariancE (CIRCE), a measure of conditional independence for multivariate continuous-valued variables. CIRCE applies as a regularizer in settings where we wish to learn neural features…
Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic…
The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion…
Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution…
In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…
We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…
A variety of indices aim to quantify the impact of input variables on a response, typically the output from a complex computer code or black-box model. Most commonly used, the Sobol' index typically measures the influence of some inputs…
Independent component analysis (ICA) is a widely used BSS method that can uniquely achieve source recovery, subject to only scaling and permutation ambiguities, through the assumption of statistical independence on the part of the latent…
In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobol's approach relies on the simplicity of…
A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
Determining conditional independence (CI) relationships between random variables is a fundamental yet challenging task in machine learning and statistics, especially in high-dimensional settings. Existing generative model-based CI testing…