Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps

2025-03-16

AI Summary

Optimal Transport Filters (OTFs) for real-time Bayesian filtering in non-Gaussian dynamic systems suffer from prohibitively high computational overhead due to online training at every time step. Method: This paper proposes the Amortized Optimal Transport Filter (A-OTF), the first framework to decouple optimal transport map learning into two phases: offline clustering-based pretraining and online weighted fusion. Integrating optimal transport theory, Bayesian filtering, K-means clustering, and mixture-of-experts modeling, A-OTF establishes an end-to-end amortized mapping learning architecture. Contribution/Results: Experiments demonstrate that A-OTF preserves the non-Gaussian modeling capability and filtering accuracy of standard OTFs while accelerating online inference significantly and reducing training computation cost by over 90%. It achieves a synergistic optimization of estimation accuracy and computational efficiency, enabling scalable deployment in real-time applications.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

Problem

• Reduces computational cost of real-time optimal transport filters
• Enables efficient non-Gaussian Bayesian updates in filtering
• Uses pre-trained maps and clustering for faster online inference

Innovation

• Amortized Optimal Transport Filter reduces computational cost
• Clustering algorithms select pre-trained maps subsets
• Weighted average of maps enhances online inference efficiency