Related papers: Can we globally optimize cross-validation loss? Qu…
Least absolute shrinkage and selection operator or Lasso is one of the widely used regularization methods in regression. Statisticians usually implement Lasso in practice by choosing the penalty parameter in a data-dependent way, the most…
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…
This paper investigates the efficiency of the K-fold cross-validation (CV) procedure and a debiased version thereof as a means of estimating the generalization risk of a learning algorithm. We work under the general assumption of uniform…
Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the…
Robust regression aims to develop methods for estimating an unknown regression function in the presence of outliers, heavy-tailed distributions, or contaminated data, which can severely impact performance. Most existing theoretical results…
Cross-Validation (CV), and out-of-sample performance-estimation protocols in general, are often employed both for (a) selecting the optimal combination of algorithms and values of hyper-parameters (called a configuration) for producing the…
We consider a general model for high-dimensional empirical risk minimization whereby the data $\mathbf{x}_i$ are $d$-dimensional Gaussian vectors, the model is parametrized by $\mathbf{\Theta}\in\mathbb{R}^{d\times k}$, and the loss depends…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
Cross validation is widely used for selecting tuning parameters in regularization methods, but it is computationally intensive in general. To lessen its computational burden, approximation schemes such as generalized approximate cross…
Estimating out-of-sample risk for models trained on large high-dimensional datasets is an expensive but essential part of the machine learning process, enabling practitioners to optimally tune hyperparameters. Cross-validation (CV) serves…
We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient…
Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…
We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean…
Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving…
This paper presents a model-free reinforcement learning (RL) algorithm to solve the risk-averse optimal control (RAOC) problem for discrete-time nonlinear systems. While successful RL algorithms have been presented to learn optimal control…
In machine learning, statistics, econometrics and statistical physics, cross-validation (CV) is used asa standard approach in quantifying the generalisation performance of a statistical model. A directapplication of CV in time-series leads…
We prove that Riemannian contraction in a supervised learning setting implies generalization. Specifically, we show that if an optimizer is contracting in some Riemannian metric with rate $\lambda > 0$, it is uniformly algorithmically…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…