Related papers: A unified minimax result for restricted parameter …
We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
The quality of the narrow-width approximation is examined for partonic and convolved cross sections of sample processes. By comparison with accurate predictions significant limitations are revealed.
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
In this paper, we study a class of problems where the sum of truncated convex functions is minimized. In statistical applications, they are commonly encountered when $\ell_0$-penalized models are fitted and usually lead to NP-Hard…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing…
This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems…
The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of…
Inspired by logistic regression, we introduce a regression model for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model we also develop a…