Related papers: Unitary-process discrimination with error margin
Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…
Non-discrimination is a recognized objective in algorithmic decision making. In this paper, we introduce a novel probabilistic formulation of data pre-processing for reducing discrimination. We propose a convex optimization for learning a…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is…
The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…
We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers and a third system, which is guaranteed to be prepared in one of…
We consider the unambiguous discrimination between two unknown qudit states in $n$-dimensional ($n\geqslant2$) Hilbert space. By equivalence of unknown pure states to known mixed states and with the Jordan-basis method, we demonstrate that…
Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad…
With the widespread adoption of machine learning in the real world, the impact of the discriminatory bias has attracted attention. In recent years, various methods to mitigate the bias have been proposed. However, most of them have not…
We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem…
Predictive mean matching (PMM) is a popular imputation strategy that imputes missing values by borrowing observed values from other cases with similar expectations. We show that, unlike other imputation strategies, PMM is not guaranteed to…
In recent years there has been a growing interest in developing "streaming algorithms" for efficient processing and querying of continuous data streams. These algorithms seek to provide accurate results while minimizing the required storage…
Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…
This article investigates unsupervised classification techniques for categorical multivariate data. The study employs multivariate multinomial mixture modeling, which is a type of model particularly applicable to multilocus genotypic data.…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.