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We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits…

Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…

Several recent works have proposed instance-dependent upper bounds on the number of episodes needed to identify, with probability $1-\delta$, an $\varepsilon$-optimal policy in finite-horizon tabular Markov Decision Processes (MDPs). These…

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…

General Bayesian updating replaces the likelihood with a loss scaled by a learning rate, but posterior uncertainty can depend sharply on that scale. We propose a simple post-processing that aligns generalized posterior draws with their…

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an…

In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convexe constraints on the solution. Through a sequence of approximating Hilbertian spaces…

Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability --…

Region-based classification of PolSAR data can be effectively performed by seeking for the assignment that minimizes a distance between prototypes and segments. Silva et al (2013) used stochastic distances between complex multivariate…

Stochastic optimization via Stochastic Gradient Descent (SGD) is a fundamental problem in statistics and optimization. This paper revisits Stochastic Gradient Descent (SGD) for strongly convex objectives, establishing tight, uniform-in-time…

Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor…

We present a family of novel block-sample MAC-Bayes bounds (mean approximately correct). While PAC-Bayes bounds (probably approximately correct) typically give bounds for the generalization error that hold with high probability, MAC-Bayes…

Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability…

In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain.…

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference.…