Related papers: Extropy-Based Generalized Divergence and Similarit…
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
Binary density ratio estimation (DRE), the problem of estimating the ratio $p_1/p_2$ given their empirical samples, provides the foundation for many state-of-the-art machine learning algorithms such as contrastive representation learning…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…
Data holders can produce synthetic versions of datasets when concerns about potential disclosure restrict the availability of the original records. This paper is concerned with methods to judge whether such synthetic data have a…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
Clustered and longitudinal data are pervasive in scientific studies, from prenatal health programs to clinical trials and public health surveillance. Such data often involve non-Gaussian responses--including binary, categorical, and count…
There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
In this communication, we introduce a new statistical model and study its various mathematical properties. The expressions for hazard rate, reversed hazard rate, and odd functions are provided. We explore the asymptotic behaviors of the…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
This paper proposes a goodness of fit test for the generalized Pareto distribution (GPD). Firstly, we provide two characterizations of GPD based on Stein's identity and dynamic survival extropy. These characterizations are used to test GPD…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
This paper presents and discusses the use of a new feature for PolSAR imagery: the Generalized Statistical Complexity. This measure is able to capture the disorder of the data by means of the entropy, as well as its departure from a…
Probabilistic generative models provide a powerful framework for representing data that avoids the expense of manual annotation typically needed by discriminative approaches. Model selection in this generative setting can be challenging,…
We study the geometry of probability distributions with respect to a generalized family of Csisz\'ar $f$-divergences. A member of this family is the relative $\alpha$-entropy which is also a R\'enyi analog of relative entropy in information…
Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing,…
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…