Related papers: An Optimal Transport Formulation of Bayes' Law for…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials ("flatness") implies a Ruelle-Perron-Frobenius Theorem and a decay of the transfer…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
This paper describes recent results obtained in collaboration with M. Huesmann and F. Otto on the regularity of optimal transport maps. The main result is a quantitative version of the well-known fact that the linearization of the…
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…
This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…
Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…
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…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…