Related papers: Exploiting Chain Rule and Bayes' Theorem to Compar…

Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…

We research relations between optimal transport theory (OTT) and approximate Bayesian computation (ABC) possibly connected to relevant metrics defined on probability measures. Those of ABC are computational methods based on Bayesian…

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

Effective understanding of the environment and accurate trajectory prediction of surrounding dynamic obstacles are critical for intelligent systems such as autonomous vehicles and wheeled mobile robotics navigating in complex scenarios to…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…

Many problems ask a question that can be formulated as a causal question: "what would have happened if...?" For example, "would the person have had surgery if he or she had been Black?" To address this kind of questions, calculating an…

We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…

Trajectory prediction (TP) plays an important role in supporting the decision-making of Air Traffic Controllers (ATCOs). Traditional TP methods are deterministic and physics-based, with parameters that are calibrated using aircraft…

We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…

This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational perception of risks associated with uncertain spatial costs. Our proposed method employs the Cumulative Prospect Theory…

Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…

We introduce LatentTrack (LT), a sequential neural architecture for online probabilistic prediction under nonstationary dynamics. LT performs causal Bayesian filtering in a low-dimensional latent space and uses a lightweight hypernetwork to…

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…

We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…

The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal CAPM model we built a general sampling model suitable in…

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…

We approach the problem of constructing a quantum analogue of the immensely fruitful classical transport cost theory of Monge from a new angle. Going back to the original motivations, by which the transport is a bilinear function of a mass…

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and…

Variable-length Markov chains (VLMCs) are a flexible class of higher-order Markov models that admit a natural representation as context trees. Existing Bayesian methods for specifying prior distributions on tree structures rely on branching…