Related papers: A Concentration Result of Estimating Phi-Divergenc…
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…
We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, goal-oriented uncertainty quantification tools that…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…
The main purpose of this paper is to present new families of test statistics for studying the problem of goodness-of-fit of some data to a latent class model for binary data. The families of test statistics introduced are based on…
The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
We elaborate on a deconvolution method, used to estimate the empirical distribution of unknown parameters, as suggested recently by Efron (2013). It is applied to estimating the empirical distribution of the 'sampling probabilities' of m…
Sampling is often a necessary evil to reduce the processing and storage costs of distributed tracing. In this work, we describe a scalable and adaptive sampling approach that can preserve events of interest better than the widely used…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
For nonlinear supervised learning models, assessing the importance of predictor variables or their interactions is not straightforward because it can vary in the domain of the variables. Importance can be assessed locally with sensitivity…
Scientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity.…
In this Note we introduce a new methodology for Bayesian inference through the use of $\phi$-divergences and the duality technique. The asymptotic laws of the estimates are established.