Related papers: Geometric Estimation of Multivariate Dependency
Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an…
The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
Use of copula for the purpose of modeling dependence has been receiving considerable attention in recent times. On the other hand, search for multivariate copulas with desirable dependence properties also is an important area of research.…
A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking…
Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Several methods to estimate MI, from samples of two random variables with unknown underlying probability distributions have been…
With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
The Gibbs-Boltzmann distribution offers a physically interpretable way to massively reduce the dimensionality of high dimensional probability distributions where the extensive variables are `features' and the intensive variables are…
The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
Feature selection and reducing the dimensionality of data is an essential step in data analysis. In this work, we propose a new criterion for feature selection that is formulated as conditional information between features given the labeled…
Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with…
Mutual Information (MI) is a fundamental metric for quantifying dependency between two random variables. When we can access only the samples, but not the underlying distribution functions, we can evaluate MI using sample-based estimators.…
In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$.…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…