Related papers: Kullback-Leibler Divergence for Bayesian Nonparame…
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs…
We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…
This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…
It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…
Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed…
In this work we introduce a family of transformations, named \textit{divergence transformations}, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole…
In this paper, we propose some estimators for the parameters of a statistical model based on Kullback-Leibler divergence of the survival function in continuous setting. We prove that the proposed estimators are subclass of "generalized…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…
We establish a connection between distributionally robust optimization (DRO) and classical robust statistics. We demonstrate that this connection arises naturally in the context of estimation under data corruption, where the goal is to…
Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…
$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses…
We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…