Related papers: Tractable Fully Bayesian Inference via Convex Opti…

In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

In analyses with severe data-limitations, augmenting the target dataset with information from ancillary datasets in the application domain, called source datasets, can lead to significantly improved statistical procedures. However, existing…

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…

We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…

We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…

Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other.…

Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space $(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is…

Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…

Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…

We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning,…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…

In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…

The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…

This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…