Related papers: Notes on Forr\'e's Notion of Conditional Independe…

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…

This note provides additional interpretation for the counterfactual outcome distribution and corresponding unconditional quantile "effects" defined and estimated by Firpo, Fortin, and Lemieux (2009) and Chernozhukov, Fern\'andez-Val, and…

Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to…

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically…

The use of machine learning (ML) in high-stakes societal decisions has encouraged the consideration of fairness throughout the ML lifecycle. Although data integration is one of the primary steps to generate high quality training data, most…

Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional…

Causal structure learning with data from multiple contexts carries both opportunities and challenges. Opportunities arise from considering shared and context-specific causal graphs enabling to generalize and transfer causal knowledge across…

We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…

Understanding causal mechanisms in complex systems requires evaluating path-specific effects (PSEs) in multi-mediator models. Identification of PSEs traditionally relies on the demanding cross-world independence assumption. To relax this,…

This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…

A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model…

This work presents a conceptual synthesis of causal discovery and inference frameworks, with a focus on how foundational assumptions -- causal sufficiency, causal faithfulness, and the causal Markov condition -- are formalized and…

We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…

Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible…

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…

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…