Related papers: Penalized least squares approximation methods and …
We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…
We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent samples. Our procedures are based on model selection by minimization of a…
This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov…
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…
We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…
We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…
We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to…
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Penalty functions are widely used to enforce constraints in optimization problems and reinforcement leaning algorithms. Softplus and algebraic penalty functions are proposed to overcome the sensitivity of the Courant-Beltrami method to…
In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for…
We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…