Related papers: SURE-tuned Bridge Regression
The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to…
We study reinforcement learning in stochastic path (SP) problems. The goal in these problems is to maximize the expected sum of rewards until the agent reaches a terminal state. We provide the first regret guarantees in this general problem…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to…
An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
Spatiotemporal matrix-valued data arise frequently in modern applications, yet performing effective regression analysis remains challenging due to complex, dimension-specific dependencies. In this work, we propose a regularized framework…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Regression, the task of predicting a continuous scalar target y based on some features x is one of the most fundamental tasks in machine learning and statistics. It has been observed and theoretically analyzed that the classical approach,…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we…
We develop a penalized two-pass regression with time-varying factor loadings. The penalization in the first pass enforces sparsity for the time-variation drivers while also maintaining compatibility with the no-arbitrage restrictions by…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
New procedures for detecting a change in the cross-sectional mean of panel data are proposed. The procedures rely on estimating nuisance parameters using certain cross-sectional means across panels using a weighted least squares regression.…
We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or…