Related papers: Testing Convex Truncation
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
Detecting out-of-distribution (OOD) data is a critical task for maintaining model reliability and robustness. In this study, we propose a novel anomaly detection algorithm that leverages the convex hull (CH) property of a dataset by…
The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…
This paper studies the problem of finding the median of N distinct numbers distributed across networked agents. Each agent updates its estimate for the median from noisy local observations of one of the N numbers and information from…
Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting…
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…
We consider the question of averaging on a graph that has one sparse cut separating two subgraphs that are internally well connected. While there has been a large body of work devoted to algorithms for distributed averaging, nearly all…
The ability of machine learning (ML) algorithms to generalize well to unseen data has been studied through the lens of information theory, by bounding the generalization error with the input-output mutual information (MI), i.e., the MI…
Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Let X Nv(0, {\Lambda}) be a normal vector in v dimensions, where {\Lambda} is diagonal. With reference to the truncated distribution of X on the interior of a v-dimensional Euclidean ball, we completely prove a variance inequality and a…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing…
We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
The vast majority of theoretical results in machine learning and statistics assume that the available training data is a reasonably reliable reflection of the phenomena to be learned or estimated. Similarly, the majority of machine learning…
Central limit theorems for the log-volume of a class of random convex bodies in $\mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $n\to\infty$. In particular, the case of random simplices pinned at the origin and…
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices…
We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…