Related papers: Coupling-Informed Transport Maps for Bayesian Filt…

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…

Multitarget Tracking (MTT) is the problem of tracking the states of an unknown number of objects using noisy measurements, with important applications to autonomous driving, surveillance, robotics, and others. In the model-based Bayesian…

Continued great efforts have been dedicated towards high-quality trajectory generation based on optimization methods, however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly,…

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…

This paper proposes a novel approach to map-based navigation system for unmanned aircraft. The proposed system attempts label-to-label matching, not image-to-image matching, between aerial images and a map database. The ground objects can…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…

Aiming at the prediction problem of transport capacity risk caused by the mismatch between the carrying capacity of rail transit network and passenger flow demand, this paper proposes an explainable prediction method of rail transit network…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

Drift-free localization is essential for autonomous vehicles. In this paper, we address the problem by proposing a filter-based framework, which integrates the visual-inertial odometry and the measurements of the features in the pre-built…

For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

Discovering human mobility patterns with geo-location data collected from smartphone users has been a hot research topic in recent years. In this paper, we attempt to discover daily mobile patterns based on GPS data. We view this problem…

We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation.…

Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from…

It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…

We propose an efficient Bayesian MCMC algorithm for estimating cosmological parameters from CMB data without use of likelihood approximations. It builds on a previously developed Gibbs sampling framework that allows for exploration of the…

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…