Here we briefly consider why introducing a prior over the factor matrix enables automatic relevance determination. These ideas reflect results by Bishop [1] and our experiments in Section 3.1. For simplicity, we will first consider the case of factor analysis where p(X) = Q d,tN(xdt; 0,1).

Note that this is the case in the present work sinceT 30 minutes is much larger than the longest timescales learned by bGPFA(τ 2s).

Additionally,bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization.

Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional'latent' spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible incorporation of prior knowledge and uncertainty estimation, but which typically do not scale to large datasets; and (ii) highly parameterized methods without explicit priors that scale better but often struggle in the low-data regime. Here, we bridge this gap by developing a fully Bayesian yet scalable version of Gaussian process factor analysis (bGPFA), which models neural data as arising from a set of inferred latent processes with a prior that encourages smoothness over time. Additionally, bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization. To enable the analysis of continuous recordings without trial structure, we introduce a novel variational inference strategy that scales near-linearly in time and also allows for non-Gaussian noise models appropriate for electrophysiological recordings.

Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional'latent' spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible incorporation of prior knowledge and uncertainty estimation, but which typically do not scale to large datasets; and (ii) highly parameterized methods without explicit priors that scale better but often struggle in the low-data regime. Here, we bridge this gap by developing a fully Bayesian yet scalable version of Gaussian process factor analysis (bGPFA), which models neural data as arising from a set of inferred latent processes with a prior that encourages smoothness over time. Additionally, bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization. To enable the analysis of continuous recordings without trial structure, we introduce a novel variational inference strategy that scales near-linearly in time and also allows for non-Gaussian noise models appropriate for electrophysiological recordings.