Efficient Non-conjugate Gaussian Process Factor Models for Spike Count Data using Polynomial Approximations

Stephen Keeley, David Zoltowski, Yiyi Yu, Spencer Smith, Jonathan Pillow
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5177-5186, 2020.

Abstract

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-keeley20a, title = {Efficient Non-conjugate {G}aussian Process Factor Models for Spike Count Data using Polynomial Approximations}, author = {Keeley, Stephen and Zoltowski, David and Yu, Yiyi and Smith, Spencer and Pillow, Jonathan}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5177--5186}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/keeley20a/keeley20a.pdf}, url = {https://proceedings.mlr.press/v119/keeley20a.html}, abstract = {Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.} }
Endnote
%0 Conference Paper %T Efficient Non-conjugate Gaussian Process Factor Models for Spike Count Data using Polynomial Approximations %A Stephen Keeley %A David Zoltowski %A Yiyi Yu %A Spencer Smith %A Jonathan Pillow %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-keeley20a %I PMLR %P 5177--5186 %U https://proceedings.mlr.press/v119/keeley20a.html %V 119 %X Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.
APA
Keeley, S., Zoltowski, D., Yu, Y., Smith, S. & Pillow, J.. (2020). Efficient Non-conjugate Gaussian Process Factor Models for Spike Count Data using Polynomial Approximations. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5177-5186 Available from https://proceedings.mlr.press/v119/keeley20a.html.

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