Related papers: Codivergences and information matrices
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
Data processing inequalities for $f$-divergences can be sharpened using constants called "contraction coefficients" to produce strong data processing inequalities. For any discrete source-channel pair, the contraction coefficients for…
Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial…
Recalibration of binary probabilistic classifiers to a target prior probability is an important task in areas like credit risk management. However, recalibration of a classifier learned on a training dataset to a target on a test dataset in…
We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…
For many applications of probabilistic classifiers it is important that the predicted confidence vectors reflect true probabilities (one says that the classifier is calibrated). It has been shown that common models fail to satisfy this…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
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…
Networks represent how the entities of a system are connected and can be partitioned differently, prompting ways to compare partitions. Common approaches for comparing network partitions include information-theoretic measures based on…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
Comparing the ranking of candidates by different voters is an important topic in social and information science with a high relevance from the point of view of practical applications. In general, ties and pairs of incomparable candidates…
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities…
This paper investigates a statistical procedure for testing the equality of two independently estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…
Scholars frequently employ relatedness measures to estimate the similarity between two different items (e.g., documents, authors, and institutes). Such relatedness measures are commonly based on overlapping references ($\textit{i.e.}$,…