Gaussian process based nonlinear latent structure discovery in multivariate spike train data
A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes-one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes). To learn the model from data, we introduce the decoupled Laplace approximation, a fast approximate inference method that allows us to efficiently optimize the latent path while marginalizing over tuning curves. We show that this method outperforms previous Laplace-approximation-based inference methods in both the speed of convergence and accuracy. We apply the model to spike trains recorded from hippocampal place cells and show that it compares favorably to a variety of previous methods for latent structure discovery, including variational auto-encoder (VAE) based methods that parametrize the nonlinear mapping from latent space to spike rates with a deep neural network.
Summary
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The authors propose a gaussian process latent variable model with poisson observations (P-GPLVM). The demonstrate how to perform inference using a decoupled Laplace approximation. They apply the model to simulated data as well as rat hippocampal data.
The paper is well written and clearly presented. I appreciated the nice summary of the model structures in Table 1.
I would have liked to see more applications of the technique, and/or a larger improvement on real data compared to previous methods.
Questions/concerns
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- The performance benefit of the P-GPLVM is quite small over PLDS and the GPLVM on real data. For example, in Figure 2C, there is only a weak improvement over these methods (especially given the fact that the y-scale in Fig 2C shows a small range, and lack error bars), lessening the overall impact of the results.
- How does the algorithm scale with the size of the latent dimension, the number of neurons, and the length of the recording? The examples in the paper have latent dimension <= 2, on the order of tens of neurons, and 500 time points (50s binned at 100ms). Is the technique feasible for larger datasets?
- The authors ran multiple simulations and show the mean across repeats--the authors should also show the variability (standard error or deviation) across repeats, both for the r^2 performance (error bars) as well as estimated trajectories (error bands).
- If I understand correctly, the estimated latent trajectory in both the simulation and hippocampal data tracked the animal's position? That seems surprising--what if you set the latent dimension to 3? or 4, or 1?
Minor comments
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- line 103: remove the 'as' in "our model is as a doubly nonlinear ..."