相关论文: Convergence Rates for Empirical Estimation of Bina…

We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising…

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…

Density ratio estimation (DRE) is a core technique in machine learning used to capture relationships between two probability distributions. $f$-divergence loss functions, which are derived from variational representations of $f$-divergence,…

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

We propose a scalable divergence estimation method based on hashing. Consider two continuous random variables $X$ and $Y$ whose densities have bounded support. We consider a particular locality sensitive random hashing, and consider the…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to $N$ identical and independent detectors. The root of the tree represents a fusion center that makes the…

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a…

We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…

The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to…

We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of…

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…

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

The accuracy of binary classification systems is defined as the proportion of correct predictions - both positive and negative - made by a classification model or computational algorithm. A value between 0 (no accuracy) and 1 (perfect…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…