Diffeomorphic Measure Matching with Kernels for Generative Modeling

• URL: http://arxiv.org/abs/2402.08077v1
• Date: Mon, 12 Feb 2024 21:44:20 GMT
• Title: Diffeomorphic Measure Matching with Kernels for Generative Modeling
• Authors: Biraj Pandey, Bamdad Hosseini, Pau Batlle, and Houman Owhadi
• Abstract summary: This article presents a framework for transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs) A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification.
• Score: 1.2058600649065618
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration. A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification. An extensive suite of numerical experiments further highlights the properties, strengths, and weaknesses of the method and extends its applicability to other tasks, such as conditional simulation and inference.

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