We study the problem of estimating ap-dimensional s-sparse vector in a linear model with Gaussian design and additivenoise.

Workinginthestandard potential outcomes framework, we propose a data-driven modification to an arbitrary (nonparametric) prior based on the propensity score that corrects for the first-orderposteriorbias,therebyimprovingperformance.Weillustrateourmethod for Gaussian process (GP) priors using (semi-)synthetic data.

Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices.

We study theregretincurred bytheagent, firstwhen sheknowsherrewardfunction but does not know the distribution of the task duration, and then when she does not knowher reward function, either.

We consider here the sparse Gaussian process regression (SGPR) approach introduced by Titsias [31], which is widely used in practice (see [1, 9] for implementations) and has been studied in many recent works [13,21,5,6,38,28,32,22,23].

We show that the matrix perspective function, which is jointly convex in the Cartesian product of a standard Euclidean vector space and a conformal space of symmetric matrices, has a proximity operator in an almost closed form.

Robust learning is a critical field that seeks to develop efficient algorithms that can recover an underlying model despite possibly malicious corruptions in the data. In recent decades, being able to deal with corrupted measurements has become of crucial importance.

Our second contribution is to introduce ensemble of clustered desparsified multi-task Lasso (ecd-MTLasso), which has two advantages compared to current methods:i)it offers statistical guarantees andii)it allows to trade spatial specificity for sensitivity, leading to a powerful adaptive method. Our third contribution is an empirical validation of the theoretical claims.