Related papers: Sobolev Independence Criterion
In the context of sensitivity analysis of complex phenomena in presence of uncertainty, we motivate and precise the idea of orienting the analysis towards a critical domain of the studied phenomenon. We make a brief history of related…
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…
Machine learning continues to grow in popularity in academia, in industry, and is increasingly used in other fields. However, most of the common metrics used to evaluate even simple binary classification models have shortcomings that are…
Iterated sampling importance resampling (i-SIR) is a Markov chain Monte Carlo (MCMC) algorithm which is based on $N$ independent proposals. As $N$ grows, its samples become nearly independent, but with an increased computational cost. We…
Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes…
This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been…
A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the…
Independent component analysis (ICA) is a statistical method for transforming an observable multidimensional random vector into components that are as statistically independent as possible from each other.Usually the ICA framework assumes a…
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…
In this paper, we aim to perform sensitivity analysis of set-valued models and, in particular, to quantify the impact of uncertain inputs on feasible sets, which are key elements in solving a robust optimization problem under constraints.…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
As a fundamental visual attribute, image complexity significantly influences both human perception and the performance of computer vision models. However, accurately assessing and quantifying image complexity remains a challenging task. (1)…
Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density…
We propose a two-step pseudo-maximum likelihood procedure for semiparametric single-index regression models where the conditional variance is a known function of the regression and an additional parameter. The Poisson single-index…
Our aim is to evaluate fundamental parameters from the analysis of the electromagnetic spectra of stars. We may use $10^3$-$10^5$ spectra; each spectrum being a vector with $10^2$-$10^4$ coordinates. We thus face the so-called "curse of…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case…
In this paper, we present a new algorithm for semi-supervised representation learning. In this algorithm, we first find a vector representation for the labels of the data points based on their local positions in the space. Then, we map the…