Related papers: Kernel-based independence tests for causal structu…

Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we…

This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…

We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…

A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…

In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…

Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…

This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized…

We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models…

This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…

We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm…

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…

Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental data where an experimenter intervenes on a subset of correlates. One of the…

Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…

We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $\sigma$-compact groups and extends classical Haar-based approaches…

Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure…

Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the…