Related papers: Notion of information and independent component an…
Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the…
Distributed computation in artificial life and complex systems is often described in terms of component operations on information: information storage, transfer and modification. Information modification remains poorly described however,…
We study a separable design for computing information measures, where the information measure is computed from learned feature representations instead of raw data. Under mild assumptions on the feature representations, we demonstrate that a…
Identifying the origin of nonequilibrium characteristics in a generic interacting system having multiple degrees of freedom is a challenging task. In this context, information theoretic measures such as mutual information and related…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
Although G\"odel's incompleteness theorem made mathematician recognize that no axiomatic system could completely prove its correctness and that there is an eternal hole between our knowledge and the world, physicists so far continue to work…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…
Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the…
When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced…
We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis…