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Learning Coupled Subspaces for Multi-Condition Spike Data

Yididiya Y. Nadew, Xuhui Fan, Christopher J. Quinn

TL;DR

This work proposes a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner and proposes a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space.

Abstract

In neuroscience, researchers typically conduct experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analysing high-dimensional spike data is a challenging statistical problem. To this end, Gaussian process factor analysis (GPFA), a popular class of latent variable models has been proposed. GPFA extracts smooth, low-dimensional latent trajectories underlying high-dimensional spike train datasets. However, such analyses are often done separately for each experimental condition, contrary to the nature of neural datasets, which contain recordings under multiple experimental conditions. Exploiting the parametric nature of these conditions, we propose a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner. In particular, we propose a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space. Our approach not only boosts model accuracy and is faster, but also improves model interpretability compared to approaches that separately fit models for each experimental condition.

Learning Coupled Subspaces for Multi-Condition Spike Data

TL;DR

This work proposes a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner and proposes a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space.

Abstract

In neuroscience, researchers typically conduct experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analysing high-dimensional spike data is a challenging statistical problem. To this end, Gaussian process factor analysis (GPFA), a popular class of latent variable models has been proposed. GPFA extracts smooth, low-dimensional latent trajectories underlying high-dimensional spike train datasets. However, such analyses are often done separately for each experimental condition, contrary to the nature of neural datasets, which contain recordings under multiple experimental conditions. Exploiting the parametric nature of these conditions, we propose a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner. In particular, we propose a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space. Our approach not only boosts model accuracy and is faster, but also improves model interpretability compared to approaches that separately fit models for each experimental condition.

Paper Structure

This paper contains 29 sections, 59 equations, 3 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. The GPFA model
  4. Data Augmentation
  5. Tensor-based Methods for Neural Data
  6. METHOD
  7. Likelihood
  8. Weights as functions over conditions
  9. Unknown number of latent dimensions
  10. Priors over remaining variables
  11. Augmenting auxiliary variables
  12. Inference
  13. Predicting Weight Functions for Unobserved Conditions
  14. EXPERIMENTS
  15. Synthetic Experiment
  16. ...and 14 more sections

Figures (3)

  • Figure 1: Conceptual example of drifting gratings experiments with varying orientations (left) and corresponding neuronal responses (right) in terms of firing rates.
  • Figure 2: Synthetic Experiment (a) Hinton diagram showing inferred set of weights the first neuron in the synthetic datasets. Columns indicate the set of weights a given latent dimensions. Each row indicates weights for a given conditions. Sizes of the blocks represent the magnitude of weight, whereas blocks in "red" correspond to negative weights and "blue" corresponds to positive weights. (b) Firing rate plot compares the firing rate of the generative model (solid curves) with inferred by CS-GPFA (dashed curves). Each curve represents the firing rate for a given condition across time (limited to the first 5 conditions, for clarity).
  • Figure 3: MC Maze Experiment: (a)Comparison with baselines using mean test log-likelihood performance on varying number of training trials. (b) Performance of CS-GPFA(smooth) on test conditions inters of test log-likelihood (c) CS-GPFA(smooth)'s inferred latent processes and corresponding weights for the first neuron in the dataset (blue indicates positive weights; red indicates negative weights) (d) Polar plots showing the firing patterns of group of neurons along varying conditions (i.e. reaching angles in degrees).