37 citations · 151 across the 27 of their papers we have counts for
33 papers
Generative models for simulation based filtering: Formulations and Empirical Comparisons
Mohammad Al-Jarrah, Wei Deng, Bamdad Hosseini +1
This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analy…
Error Analysis of Bayesian Inverse Problems with Generative Priors
Bamdad Hosseini, Ziqi Huang
Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns t…
Error Analysis of Triangular Optimal Transport Maps for Filtering
Mohammad Al-Jarrah, Bamdad Hosseini, Niyizhen Jin +2
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…
Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps
Mohammad Al-Jarrah, Bamdad Hosseini, Amirhossein Taghvaei
In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport f…
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
The article presents a systematic study of the problem of conditioning a Gaussian random variable on nonlinear observations of the form where $ϕ: \mathcal{X} \to…
Data-Driven Approximation of Stationary Nonlinear Filters with Optimal Transport Maps
Mohammad Al-Jarrah, Bamdad Hosseini, Amirhossein Taghvaei
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of par…
Diffeomorphic Measure Matching with Kernels for Generative Modeling
Biraj Pandey, Bamdad Hosseini, Pau Batlle +1
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equation…
Conditional Optimal Transport on Function Spaces
Bamdad Hosseini, Alexander W. Hsu, Amirhossein Taghvaei
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian…
Nonlinear Filtering with Brenier Optimal Transport Maps
Mohammad Al-Jarrah, Niyizhen Jin, Bamdad Hosseini +1
This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy…
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
Pau Batlle, Yifan Chen, Bamdad Hosseini +2
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assump…
Kernel Methods are Competitive for Operator Learning
Pau Batlle, Matthieu Darcy, Bamdad Hosseini +1
We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neu…
Optimal Transport Particle Filters
Mohammad Al-Jarrah, Bamdad Hosseini, Amirhossein Taghvaei
This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). Th…
Bayesian Posterior Perturbation Analysis with Integral Probability Metrics
Alfredo Garbuno-Inigo, Tapio Helin, Franca Hoffmann +1
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the rob…
An Approximation Theory Framework for Measure-Transport Sampling Algorithms
Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki +2
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algo…
A Kernel Approach for PDE Discovery and Operator Learning
Da Long, Nicole Mrvaljevic, Shandian Zhe +1
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy…
Intrinsic Sparsity of Kantorovich Solutions
Bamdad Hosseini, Stefan Steinerberger
Let be two finite sets of points having and points with and being the associated unifo…
An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms
Amirhossein Taghvaei, Bamdad Hosseini
This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation bet…
Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identificat…
Posterior Consistency of Semi-Supervised Regression on Graphs
Andrea L. Bertozzi, Bamdad Hosseini, Hao Li +2
Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. Th…
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki +1
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular tra…
Model Reduction and Neural Networks for Parametric PDEs
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki +1
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of…
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Franca Hoffmann, Bamdad Hosseini, Assad A. Oberai +1
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a cen…
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Franca Hoffmann, Bamdad Hosseini, Zhi Ren +1
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data. This paper is concerned wi…
Geometric structure of graph Laplacian embeddings
Nicolas Garcia Trillos, Franca Hoffmann, Bamdad Hosseini
We analyze the spectral clustering procedure for identifying coarse structure in a data set , and in particular study the geometry of graph Laplacian embeddings wh…