相关论文: How to quantify direct correlations between variab…
By the modified directed likelihood, higher order accurate confidence limits for a scalar parameter are obtained from the likelihood. They are conveniently described in terms of a confidence distribution, that is a sample dependent…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendall's $\tau$. However, the…
Predicting the collaboration likelihood and measuring cognitive trust to AI systems is more important than ever. To do that, previous research mostly focus solely on the model features (e.g., accuracy, confidence) and ignore the human…
Measuring the relatedness between scientific publications has important applications in many areas of bibliometrics and science policy. Controlled vocabularies provide a promising basis for measuring relatedness because they address issues…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…
Given an intractable distribution $p$, the problem of variational inference (VI) is to find the best approximation from some more tractable family $Q$. Commonly, one chooses $Q$ to be a family of factorized distributions (i.e., the…
Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid potential model misspecification bias or over-complicating the…
Multivariate correlation analysis plays an important role in various fields such as statistics, economics, and big data analytics. In this paper, we propose a pair of measures, the unsigned correlation coefficient (UCC) and the unsigned…
We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…
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…
The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then…
How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes…
Firstly, assuming Gaussianity, equations for the following information theory measures are presented: total correlation/coherence (TC), dual total correlation/coherence (DTC), O-information, TSE complexity, and redundancy-synergy index…
Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…