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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…
Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…
Conditional independence testing is an important problem, yet provably hard without assumptions. One of the assumptions that has become popular of late is called "model-X", where we assume we know the joint distribution of the covariates,…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
Mutual Information (MI) and Conditional Mutual Information (CMI) are multi-purpose tools from information theory that are able to naturally measure the statistical dependencies between random variables, thus they are usually of central…
This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…
Conditional independence (CI) constraints are critical for defining and evaluating fairness in machine learning, as well as for learning unconfounded or causal representations. Traditional methods for ensuring fairness either blindly learn…
Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
How much explicit guidance is necessary for conditional diffusion? We consider the problem of conditional sampling using an unconditional diffusion model and limited explicit guidance (e.g., a noised classifier, or a conditional diffusion…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…