Related papers: Conditional Dependence via Shannon Capacity: Axiom…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
We present a method for conditional sampling for pre-trained normalizing flows when only part of an observation is available. We derive a lower bound to the conditioning variable log-probability using Schur complement properties in the…
We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…
Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression…
Using the fact that the Shannon capacity C of a Raleigh model of wireless channels is a linear statistic of the channel matrix, we calculate its variance var[C]. We find that the expected value <C> of the Shannon capacity is typical in the…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…
Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this…
To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…
Testing for causation, defined as the preceding impact of the past values of one variable on the current value of another one when all other pertinent information is accounted for, is increasingly utilized in empirical research of the…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…
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…
Adjusting for covariates is a well established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study there may be different adjustment…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence,…