Related papers: Constrained Denoising, Empirical Bayes, and Optima…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or…
We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph…
In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
This manuscript proposes a novel empirical Bayes technique for regularizing regression coefficients in predictive models. When predictions from a previously published model are available, this empirical Bayes method provides a natural…
Systematics contaminate observables, leading to distribution shifts relative to theoretically simulated signals-posing a major challenge for using pre-trained models to label such observables. Since systematics are often poorly understood…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
We study the problem of denoising observations \(Y_i=X_i+Z_i\), where the latent variables \(X_i\) are sampled from a low-dimensional manifold in \(\mathbb{R}^n\) and the noise variables \(Z_i\) are isotropic Gaussian. We propose a…
Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…
We propose an empirical Bayes estimator for two-way effects in linked data sets based on a novel prior that leverages patterns of assortative matching observed in the data. To capture limited mobility we model the bipartite graph associated…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…