Related papers: Sobolev Independence Criterion
The Naive Bayesian classifier is a popular classification method employing the Bayesian paradigm. The concept of having conditional dependence among input variables sounds good in theory but can lead to a majority vote style behaviour.…
Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero…
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…
In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…
Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence…
Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as,…
Recent contributions of semantic information theory reveal the set-element relationship between semantic and syntactic information, represented as synonymous relationships. In this paper, we propose a synonymous variational inference (SVI)…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
Given a high-dimensional data set we often wish to find the strongest relationships within it. A common strategy is to evaluate a measure of dependence on every variable pair and retain the highest-scoring pairs for follow-up. This strategy…
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…