Related papers: The Bayes cost in the binary decision problem

Fixed-budget best-arm identification (BAI) is a bandit problem where the agent maximizes the probability of identifying the optimal arm within a fixed budget of observations. In this work, we study this problem in the Bayesian setting. We…

Using the known necessary and sufficient conditions for minimum error discrimination (MED), first it is shown that a Helstrom family of ensembles is equivalent to these conditions and then by a convex combination of the initial states (the…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training…

We investigate strategies for estimating a depolarizing channel for a finite dimensional system. Our analysis addresses the double optimization problem of selecting the best input probe state and the measurement strategy that minimizes the…

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…

Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a…

Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a…

The need of discriminating between different quantum states is a fundamental issue in Quantum Information and Communication. The actual realization of generally optimal strategies in this task is often limited by the need of supplemental…

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 derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…

We derive information-theoretic lower bounds on the Bayes risk and generalization error of realizable machine learning models. In particular, we employ an analysis in which the rate-distortion function of the model parameters bounds the…

The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was…

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…

A/B testing is ubiquitous within the machine learning and data science operations of internet companies. Generically, the idea is to perform a statistical test of the hypothesis that a new feature is better than the existing platform---for…

The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest…

We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…

Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success…

We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…