Related papers: Optimal partition of feature using Bayesian classi…

For many data-intensive tasks, feature selection is an important preprocessing step. However, most existing methods do not directly and intuitively explore the intrinsic discriminative information of features. We propose a novel feature…

The original formulation of BEAMS - Bayesian Estimation Applied to Multiple Species - showed how to use a dataset contaminated by points of multiple underlying types to perform unbiased parameter estimation. An example is cosmological…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

In this work we present a method to classify a set of rock textures based on a Spectral Analysis and the extraction of the texture Features of the resulted images. Up to 520 features were tested using 4 different filters and all 31…

We study the problem of fair binary classification using the notion of Equal Opportunity. It requires the true positive rate to distribute equally across the sensitive groups. Within this setting we show that the fair optimal classifier is…

Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes' probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction.…

Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson…

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…

This paper introduces an innovative method for conducting conditional independence testing in high-dimensional data, facilitating the automated discovery of significant associations within distinct subgroups of a population, all while…

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

In discriminative settings such as regression and classification there are two random variables at play, the inputs X and the targets Y. Here, we demonstrate that the Variational Information Bottleneck can be viewed as a compromise between…

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

We introduce the Conditional Independence Regression CovariancE (CIRCE), a measure of conditional independence for multivariate continuous-valued variables. CIRCE applies as a regularizer in settings where we wish to learn neural features…

For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection…

Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density…

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…

We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for…