Related papers: Concentration inequalities for leave-one-out cross…

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields…

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

The paper establishes necessary and sufficient conditions for stability of different join-the-shortest-queue models including load-balanced networks with general input and output processes. It is shown, that the necessary and sufficient…

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate…

Given an ODE and its perturbation, the Alekseev formula expresses the solutions of the latter in terms related to the former. By exploiting this formula and a new concentration inequality for martingale-differences, we develop a novel…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…

In this paper we present a stability proof of model predictive control without stabilizing terminal constraints of cost which are subject to unknown but measurable disturbances. To this end, a relaxed Lyapunov argument on the nominal system…

Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for…

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…

Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…

We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression,…

Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…

In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…

In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that guarantees the existence of a certain kernel. Our proof provides the almost…

For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training…

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…