相关论文: The BP Dependency Function: a Generic Measure of D…

Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…

Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…

Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…

Principal component analysis is a long-standing go-to method for exploring multivariate data. The principal components are linear combinations of the original variables, ordered by descending variance. The first few components typically…

Composite indicators aggregate a set of variables using weights which are understood to reflect the variables' importance in the index. In this paper we propose to measure the importance of a given variable within existing composite…

Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…

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…

Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random…

In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables $Y$ and $Z$ given a third variable $X$, all taking values in general topological spaces.…

In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…

Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation…

This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…

In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…

This article examines the limitations of Pearson's correlation in selecting predictor variables for linear models. Using mtcars and iris datasets from R, this paper demonstrates the limitation of this correlation measure when selecting a…

This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…

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…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…

This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…