[Paper Review] Importance Weighted Adversarial Variational Autoencoders for Spike Inference from Calcium Imaging Data

Daniel Jiwoong Im, Sridhama Prakhya+3 more|arXiv (Cornell University)|Jun 7, 2019

Generative Adversarial Networks and Image Synthesis18 references4 citations

TL;DR

This paper proposes Importance Weighted Adversarial Variational Bayes (IW-AVB) and Importance Weighted Adversarial Autoencoders (IW-AAE), which combine adversarial training with importance weighting to improve posterior approximation in latent variable models. The method enables fast, parallel sampling of correlated posterior distributions over discrete binary spike trains, significantly outperforming factorized VAE posteriors in spike inference from calcium imaging data while maintaining high speed.

ABSTRACT

The Importance Weighted Auto Encoder (IWAE) objective has been shown to improve the training of generative models over the standard Variational Auto Encoder (VAE) objective. Here, we derive importance weighted extensions to AVB and AAE. These latent variable models use implicitly defined inference networks whose approximate posterior density q_ϕ(z|x) cannot be directly evaluated, an essential ingredient for importance weighting. We show improved training and inference in latent variable models with our adversarially trained importance weighting method, and derive new theoretical connections between adversarial generative model training criteria and marginal likelihood based methods. We apply these methods to the important problem of inferring spiking neural activity from calcium imaging data, a challenging posterior inference problem in neuroscience, and show that posterior samples from the adversarial methods outperform factorized posteriors used in VAEs.

Motivation & Objective

• To address the challenge of learning accurate, correlated posterior distributions over discrete binary spike trains in neural activity inference.
• To extend importance weighting to adversarial variational autoencoders (AVB and AAE), where the posterior density is implicitly defined and intractable to evaluate.
• To improve posterior inference quality in spike inference from calcium imaging by combining adversarial training with importance weighting.
• To enable fast, parallel sampling of correlated spike posteriors, overcoming the sequential sampling bottleneck of autoregressive models.
• To provide theoretical connections between adversarial objectives and marginal likelihood-based criteria.

Proposed method

• Proposes IW-AVB and IW-AAE, which extend the importance weighted autoencoder (IWAE) objective to models with implicitly defined posteriors, such as AVB and AAE.
• Uses adversarial training to learn an inference network that maps noise to samples from the posterior, without requiring explicit evaluation of the posterior density.
• Employs multiple importance-weighted samples during training to tighten the lower bound on the log-likelihood, improving model evidence estimation.
• Applies the models to spike inference by using a biophysical generative model to map spike trains to fluorescence traces, and a convolutional neural network as the inference network.
• Trains models using adversarial objectives that match the prior and posterior distributions via a discriminator network.
• Employs non-amortized and amortized inference settings to evaluate performance and generalization across neurons.

Experimental results

Research questions

• RQ1 Can importance weighting be effectively applied to adversarial variational autoencoders (AVB and AAE) with implicitly defined posteriors?
• RQ2 Do adversarially trained inference networks with importance weighting produce better posterior approximations than standard VAEs with factorized posteriors in spike inference?
• RQ3 Can adversarial training generate correlated posterior samples over discrete spike trains that are both accurate and efficiently sampled in parallel?
• RQ4 What is the theoretical relationship between the IW-AAE and IW-AVB objectives and marginal likelihood or optimal transport criteria?
• RQ5 Does the proposed method generalize across neurons in amortized inference, and how does it compare to autoregressive baselines in speed and accuracy?

Key findings

• IW-AVB, AAE, and IW-AAE achieve posterior inference performance that lies between VIMCO-FACT (factorized) and VIMCO-CORR (autoregressive), but with significantly faster inference.
• Adversarially trained inference networks generate correlated posterior samples that outperform factorized VAE posteriors in accuracy, as measured by spike correlation with ground truth.
• The proposed methods achieve a substantial speed advantage over VIMCO-CORR, which requires sequential sampling, by enabling parallel sampling of correlated spike trains.
• In amortized inference, IW-AVB, AAE, and IW-AAE outperform even non-amortized baselines, indicating strong generalization across neurons.
• Theoretical analysis reveals connections between adversarial objectives and log-likelihood, clarifying the relationship between AAE and Wasserstein autoencoder objectives.
• Empirical results show that IW-AVB and IW-AAE produce posterior approximations with fewer false negatives than VIMCO-FACT and fewer false positives than VIMCO-CORR, indicating improved balance in detection.