Related papers: Neyman-Pearson classification, convexity and stoch…
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…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
Anomaly detection is a challenging task that frequently arises in practically all areas of industry and science, from fraud detection and data quality monitoring to finding rare cases of diseases and searching for new physics. Most of the…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
Feature selection aims to select the smallest subset of features for a specified level of performance. The optimal achievable classification performance on a feature subset is summarized by its Receiver Operating Curve (ROC). When infinite…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
The Bayesian learning rule is a natural-gradient variational inference method, which not only contains many existing learning algorithms as special cases but also enables the design of new algorithms. Unfortunately, when variational…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Classification is a fundamental problem in machine learning and data mining. During the past decades, numerous classification methods have been presented based on different principles. However, most existing classifiers cast the…
A significant limitation of one-class classification anomaly detection methods is their reliance on the assumption that unlabeled training data only contains normal instances. To overcome this impractical assumption, we propose two novel…
Common imaging techniques for detecting structural defects typically require sampling at more than twice the spatial frequency to achieve a target resolution. This study introduces a novel framework for imaging structural defects using…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…