Amortized Variational Inference with Sequential Monte Carlo for Inclusive KL Minimization

Core Concepts

Proposing SMC-Wake as an alternative to RWS for fitting amortized variational approximations, providing consistent gradient estimators and accurate posterior approximations.

Abstract

The content introduces Sequential Monte Carlo (SMC) for inclusive KL minimization in amortized variational inference. It compares SMC-Wake to Reweighted Wake-Sleep (RWS) and discusses the challenges of minimizing the forward KL divergence. The method proposes three gradient estimators, highlighting their unbiasedness and consistency. Experimental results on simulated and real datasets demonstrate the effectiveness of SMC-Wake in fitting accurate variational distributions approximating the posterior.
1. Introduction

Training encoder network for amortized variational inference.
Challenges in minimizing forward KL divergence.
Proposal of SMC-Wake as an alternative to RWS.
2. Background

Overview of Reweighted Wake-Sleep (RWS).
Issues with biased gradients and concentrated distributions.
Proposal of SMC-Wake using likelihood-tempered SMC samplers.
3. Mass Concentration in RWS

Circular pathology leading to degenerate variational distributions.
Proposed solution: using prior as base distribution in LT-SMC.
4. SMC-WAKE

Methodology for fitting amortized encoder with sequential Monte Carlo.
Three gradient estimators proposed, emphasizing unbiasedness and consistency.
5. Related Work

Comparison with VSMC, FIVO, AESMC, MSC, NASMC, AFT, CR-AFT, NVI methods.
6. Experiments
Two moons:

Comparison of SMC-Wake with RWS on a simulated dataset.
Avoiding mode collapse in MNIST:

Illustration of wake-phase training issues on MNIST dataset.
Transformed Gaussian:

Comparison between MSC and SMC-PIMH-Wake on a hierarchical model.
Galaxy spectra emulator:

Emulator training using PROVABGS simulator and comparison with MCMC results.

Stats

"Reweighted Wake-Sleep (RWS) suffers from heavily biased gradients."
"SMC-Wake fits variational distributions accurately compared to existing methods."

Quotes

"The circular pathology can lead to degenerate mass concentration."
"SMC-Wake provides consistent gradient estimates for forward KL minimization."

Key Insights Distilled From

Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inference

by Declan McNam... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2403.10610.pdf

Deeper Inquiries

How can the circular pathology be effectively addressed in wake-phase training

循環的な病理を効果的に解決するためには、Wake-phaseトレーニング中の提案ステップでqϕが自身を更新することを避ける必要があります。具体的には、LT-SMCサンプラーを使用して事前分布から提案することで、この問題を回避します。これにより、qϕがピーク時のポステリア密度内のみ集中しないようにします。

What are the implications of biased gradient estimators on the overall performance of variational inference methods

バイアスのある勾配推定器が変分推論手法全体のパフォーマンスに与える影響は重大です。バイアスされた勾配推定器は収束性や安定性を損なう可能性があります。その結果、モデル学習やパラメータ最適化の品質が低下し、正確な結果や信頼性の高い予測値を得ることが難しくなります。

How can the concept of sequential Monte Carlo be applied to other areas beyond amortized variational inference

シーケンシャルモンテカルロ（SMC）の概念は、摂動マルコフ連鎖（PIMH）、Markovian Score Climbing（MSC）など他の領域でも活用されています。例えば、MCMC外側ループ内でSMCサンプラーを使用したり、「Annealed Flow Transport Monte Carlo」や「Variational Sequential Monte Carlo」などさまざまな手法で採用されています。これらは異常検出や画像処理など幅広い分野で利用されており、精度向上や計算効率化へ貢献しています。