Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flows

TL;DR

This paper introduces a new amortized inference method using likelihood-weighted normalizing flows for efficient, high-dimensional, multi-modal posterior estimation without posterior training samples, highlighting the importance of base distribution topology.

Contribution

The paper proposes a novel likelihood-weighted normalizing flow approach for amortized inference that effectively captures multi-modal posteriors and emphasizes the role of base distribution topology.

Findings

Standard unimodal base distributions fail to model disconnected support.

Initializing with a Gaussian Mixture Model improves posterior reconstruction.

The method performs well on 2D and 3D benchmark tasks.

Abstract

We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional inverse problems without the need for posterior training samples. We implement the method on multi-modal benchmark tasks in 2D and 3D to check for the efficacy. A critical observation of our study is the impact of the topology of the base distributions on the modelled posteriors. We find that standard unimodal base distributions fail to capture disconnected support, resulting in spurious probability bridges between modes. We demonstrate that initializing the flow with a Gaussian Mixture Model that matches the cardinality of the target modes significantly improves reconstruction fidelity, as measured by some distance and divergence metrics.