Related papers: Towards Sharp Minimax Risk Bounds for Operator Lea…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected)…
It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…
High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz…
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular,…
Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…
Inspired by the recent work [28] on the statistical robustness of empirical risks in reproducing kernel Hilbert space (RKHS) where the training data are potentially perturbed or even corrupted, we take a step further in this paper to…
We study learning problems in which the underlying class is a bounded subset of $L_p$ and the target $Y$ belongs to $L_p$. Previously, minimax sample complexity estimates were known under such boundedness assumptions only when $p=\infty$.…
Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data,…
We study differentially private (DP) stochastic optimization (SO) with loss functions whose worst-case Lipschitz parameter over all data may be extremely large or infinite. To date, the vast majority of work on DP SO assumes that the loss…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
A fundamental problem in statistics and machine learning is to estimate a function $f$ from possibly noisy observations of its point samples. The goal is to design a numerical algorithm to construct an approximation $\hat f$ to $f$ in a…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…