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Recent successes of massively overparameterized models have inspired a new line of work investigating the underlying conditions that enable overparameterized models to generalize well. This paper considers a framework where the possibly…

Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…

Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…

A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…

We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…

We define an evolving in-time Bayesian neural network called a Hidden Markov Neural Network, which addresses the crucial challenge in time-series forecasting and continual learning: striking a balance between adapting to new data and…

This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

Let $G$ be a regular graph and $H$ a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of $H$ one expects to find in a random subgraph of $G$.

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…

Domain generalization (DG) intends to train a model on multiple source domains to ensure that it can generalize well to an arbitrary unseen target domain. The acquisition of domain-invariant representations is pivotal for DG as they possess…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…

A probability distribution allows practitioners to uncover hidden structure in the data and build models to solve supervised learning problems using limited data. The focus of this report is on Variational autoencoders, a method to learn…

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative…

Unsupervised Domain Adaptation aims to learn a model on a source domain with labeled data in order to perform well on unlabeled data of a target domain. Current approaches focus on learning \textit{Domain Invariant Representations}. It…

This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate…

Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…