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The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…
The paper is concerned with a class of nonlinear free boundary problems, which are usually solved by variational methods based on primal (or primal-dual) variational settings. We deduce and investigate special relations (error identities).…
In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
This PhD thesis is concerned with SDP bounds for codes: upper bounds for (non)-binary error correcting codes and lower bounds for (non)-binary covering codes. The methods are based on the method of Schrijver that uses triple distances in…
We present a device-independent (DI) self-testing protocol in a constrained prepare-measure scenario, based on the $n-$bit parity-oblivious multiplexing (POM) task. In this scenario, a parity-oblivious constraint is imposed on the…
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…
In several interesting applications one is faced with the problem of simultaneous binary hypothesis testing and parameter estimation. Although such joint problems are not infrequent, there exist no systematic analysis in the literature that…
We study the problem of approximate near neighbor (ANN) search and show the following results: - An improved framework for solving the ANN problem using locality-sensitive hashing, reducing the number of evaluations of locality-sensitive…
The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%,…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of…
The problem of publishing privacy-guaranteed data for hypothesis testing is studied using the maximal leakage (ML) as a metric for privacy and the type-II error exponent as the utility metric. The optimal mechanism (random mapping) that…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…