相关论文: Closed-Form Gaussian Estimators for Multi-Source P…

In this paper, we define a new measure of the redundancy of information from a fault tolerance perspective. The partial information decomposition (PID) emerged last decade as a framework for decomposing the multi-source mutual information…

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate…

Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…

We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI…

The Partial Information Decomposition (PID) framework has emerged as a powerful tool for analyzing high-order interdependencies in complex network systems. However, its application to dynamic processes remains challenging due to the…

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(\mu,\Sigma)$ in $\mathbb{R}^d$. All previous estimators are either…

We study methods for simultaneous analysis of many noisy experiments in the presence of rich covariate information. The goal of the analyst is to optimally estimate the true effect underlying each experiment. Both the noisy experimental…

A reaction-coordinate--resolved information-theoretic analysis of chemical reactivity is developed using mutual information and partial information decomposition (PID). Along an intrinsic reaction coordinate (IRC), a local empirical…

A new ensemble forecast algorithm, named as the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the time evolution of the probability density functions (PDFs) of complex…

The partial information decomposition (PID) and its extension integrated information decomposition ($\Phi$ID) are promising frameworks to investigate information phenomena involving multiple variables. An important limitation of these…

We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique…

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique.…

Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…

Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique…

Partial Information Decomposition (PID) seeks to disentangle how information about a target variable is distributed across multiple sources, separating redundant, unique, and synergistic contributions. Despite extensive theoretical…

Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…