Related papers: HiMAP: Hilbert Mass-Aligned Parameterization for M…
High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the…
Ensuring that generative AI systems align with human values is essential but challenging, especially when considering multiple human values and their potential trade-offs. Since human values can be personalized and dynamically change over…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…
Constructing flexible probability models that respect constraints on key functionals -- such as the mean -- is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while…
BART (Bayesian Additive Regression Trees) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear…
The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances…
In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through…
Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is…
A fundamental problem in statistics is to compare the outcomes attained by members of subpopulations. This problem arises in the analysis of randomized controlled trials, in the analysis of A/B tests, and in the assessment of fairness and…
The rapid growth of intelligent connected vehicles (ICVs) and integrated vehicle-road-cloud systems has increased the demand for accurate, real-time HD map updates. However, ensuring map reliability remains challenging due to…
For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
Discrimination mitigation within machine learning (ML) models could be complicated because multiple factors may be interwoven hierarchically and historically. Yet few existing fairness measures can capture the discrimination level within ML…
The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…