Related papers: Detecting Weak Distribution Shifts via Displacemen…

This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

The concentration of a distribution toward a lower bound is a conceptually simple property that closely relates to concepts of rarity and poverty, but that lacks a global descriptive statistic. We term this property 'shift' and define it as…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…

Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed and not well-studied. Existing inference procedures for penalized estimators are mainly focused on strong…

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…

Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…

This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle…

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…

Distribution shifts remain a fundamental problem for the safe application of machine learning systems. If undetected, they may impact the real-world performance of such systems or will at least render original performance claims invalid. In…

To address the issue of inaccurate distributions in practical stochastic systems, a minimax linear-quadratic control method is proposed using the Wasserstein metric. Our method aims to construct a control policy that is robust against…

We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…