Stephen Keeley

Rabia Gondur, Usama Bin Sikandar, Evan Schaffer et al.

Characterizing the relationship between neural population activity and behavioral data is a central goal of neuroscience. While latent variable models (LVMs) are successful in describing high-dimensional time-series data, they are typically only designed for a single type of data, making it difficult to identify structure shared across different experimental data modalities. Here, we address this shortcoming by proposing an unsupervised LVM which extracts temporally evolving shared and independent latents for distinct, simultaneously recorded experimental modalities. We do this by combining Gaussian Process Factor Analysis (GPFA), an interpretable LVM for neural spiking data with temporally smooth latent space, with Gaussian Process Variational Autoencoders (GP-VAEs), which similarly use a GP prior to characterize correlations in a latent space, but admit rich expressivity due to a deep neural network mapping to observations. We achieve interpretability in our model by partitioning latent variability into components that are either shared between or independent to each modality. We parameterize the latents of our model in the Fourier domain, and show improved latent identification using this approach over standard GP-VAE methods. We validate our model on simulated multi-modal data consisting of Poisson spike counts and MNIST images that scale and rotate smoothly over time. We show that the multi-modal GP-VAE (MM-GPVAE) is able to not only identify the shared and independent latent structure across modalities accurately, but provides good reconstructions of both images and neural rates on held-out trials. Finally, we demonstrate our framework on two real world multi-modal experimental settings: Drosophila whole-brain calcium imaging alongside tracked limb positions, and Manduca sexta spike train measurements from ten wing muscles as the animal tracks a visual stimulus.

Michael Shvartsman, Benjamin Letham, Stephen Keeley

Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make each choice captures additional information about the decision process, however existing models incorporating RTs for choice prediction do so in fully parametric settings or over discrete stimulus sets. This is in part because the de-facto standard model for choice RTs, the diffusion decision model (DDM), does not admit tractable, differentiable inference. The DDM thus cannot be easily integrated with flexible models for continuous, multivariate function approximation, particularly Gaussian process (GP) models. We propose a novel differentiable approximation to the DDM likelihood using a family of known, skewed three-parameter distributions. We then use this new likelihood to incorporate RTs into GP models for binary choices. Our RT-choice GPs enable both better latent value estimation and held-out choice prediction relative to baselines, which we demonstrate on three real-world multivariate datasets covering both human psychophysics and preference learning applications.

Stephen L. Keeley, David M. Zoltowski, Yiyi Yu et al.

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 \textit{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.