Related papers: Robust Least Squares Methods Under Bounded Data Un…
We introduce a procedure for conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This estimator minimizes a new general excess risk bound for statistical learning. On standard examples, this…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…
We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear…
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
We address the problem of learning the parameters of a mean square stable switched linear systems (SLS) with unknown latent space dimension, or \textit{order}, from its noisy input--output data. In particular, we focus on learning a good…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We study the stochastic linear bandit problem with multiple arms over $T$ rounds, where the covariate dimension $d$ may exceed $T$, but each arm-specific parameter vector is $s$-sparse. We begin by analyzing the sequential estimation…
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…
We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…
We study contextual dynamic pricing, where a decision maker posts personalized prices based on observable contexts and receives binary purchase feedback indicating whether the customer's valuation exceeds the price. Each valuation is…
Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…