Related papers: Scenario Reduction Revisited: Fundamental Limits a…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
Given multiple source domains, domain generalization aims at learning a universal model that performs well on any unseen but related target domain. In this work, we focus on the domain generalization scenario where domain shifts occur among…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…
This paper is concerned with minimax conditional independence testing. In contrast to some previous works on the topic, which use the total variation distance to separate the null from the alternative, here we use the Wasserstein distance.…
We present discretize_distributions, a Python package that efficiently constructs discrete approximations of Gaussian mixture distributions and provides guarantees on the approximation error in Wasserstein distance. The package implements…
We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
We study the approximation of a (finite) continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds…
Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimizing the conditional negative…
We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance…
We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…