Related papers: Bridging Maximum Likelihood and Optimal Transport …

Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite…

Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of…

This work deals with uncertainty quantification for a generic input distribution to some resource-intensive simulation, e.g., requiring the solution of a partial differential equation. While efficient numerical methods exist to compute…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…

Optimal transport is a powerful framework for computing distances between probability distributions. We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis…

Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…

We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…

Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a…

Black-Box Variational Inference (BBVI) typically relies on Stochastic Gradient Descent (SGD) to optimize the Evidence Lower Bound (ELBO). However, the stochastic gradients in BBVI inherently exhibit unbounded variance, violating standard…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

We present Sequential Neural Variational Inference (SNVI), an approach to perform Bayesian inference in models with intractable likelihoods. SNVI combines likelihood-estimation (or likelihood-ratio-estimation) with variational inference to…

Gromov-Wasserstein (GW) transport is inherently invariant under isometric transformations of the data. Having this property in mind, we propose to estimate dynamical systems by transfer operators derived from GW transport plans, when merely…

We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…

We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…

We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because…