Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains (1604.03053v5)

Abstract: When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded population of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent trajectories, particularly from single-trial population recordings, may help us understand the dynamics that drive neural computation. However, due to the biophysical constraints and noise in the spike trains, inferring trajectories from data is a challenging statistical problem in general. Here, we propose a practical and efficient inference method, called the variational latent Gaussian process (vLGP). The vLGP combines a generative model with a history-dependent point process observation together with a smoothness prior on the latent trajectories. The vLGP improves upon earlier methods for recovering latent trajectories, which assume either observation models inappropriate for point processes or linear dynamics. We compare and validate vLGP on both simulated datasets and population recordings from the primary visual cortex. In the V1 dataset, we find that vLGP achieves substantially higher performance than previous methods for predicting omitted spike trains, as well as capturing both the toroidal topology of visual stimuli space, and the noise-correlation. These results show that vLGP is a robust method with a potential to reveal hidden neural dynamics from large-scale neural recordings.

• The paper introduces the Variational Latent Gaussian Process (vLGP), significantly enhancing single-trial neural dynamics inference.
• It employs a history-dependent point process observation model combined with a Gaussian process prior for robust, scalable analysis.
• Experimental results on simulated and V1 data show vLGP outperforms GPFA and PLDS, accurately reconstructing latent states and stimulus topologies.

Variational Latent Gaussian Process for Neural Dynamics Inference

In their paper, Zhao and Park introduce the Variational Latent Gaussian Process (vLGP) as an innovative approach to infer latent neural dynamics from population spike train data recorded in single trials. This methodology is built on a generative framework that utilizes a history-dependent point process observation model augmented by a Gaussian process prior. The authors argue that vLGP offers significant improvements over existing methods like Gaussian Process Factor Analysis (GPFA) and Poisson Linear Dynamical Systems (PLDS), particularly in capturing neural dynamics that are not effectively characterized by linear models or inappropriate point process observation models.

Methodology

The vLGP is formulated as a scalable and computationally efficient model combining the flexibility of Gaussian processes with the structure of point process models, offering a robust approach for neural data analysis. The latent dynamics are modeled with a Gaussian process prior that integrates smoothness constraints to capture complex temporal dependencies in the data. The observation model is designed to handle both non-linear dynamics and realistic neural firing rates through a variational inference framework. By employing a non-parametric Bayesian approach, the authors elegantly sidestep the limitations of linear assumptions prevalent in PLDS and ensure relevance to millisecond-scale neural signals, which GPFA's Gaussian observation model fails to address.

Validation and Results

To evaluate the performance of vLGP, Zhao and Park apply it to both simulated datasets and real-world recordings from the primary visual cortex (V1). Their simulations demonstrate that the proposed method consistently outperforms traditional PLDS and GPFA in reconstructing latent states, as evidenced by improved rank correlations with known latent processes and higher predictive log-likelihood across various parameter settings. When applied to V1 data, the vLGP proficiently extracts the toroidal topology of the visual stimulus space and captures the noise correlations, which are critical in characterizing the variability and structures present in neural populations.

Implications and Applications

The potential applications of vLGP are vast, given its proven ability to infer latent neural dynamics accurately. Its flexibility in incorporating external covariates and accommodating various kernel structures makes it a powerful tool for exploring neural computation in diverse settings, from cortical oscillations to sensorimotor integration. Theoretical implications extend to enhancing our understanding of neural code dimensionality and the fundamental computational roles of complex network dynamics. Practical applications could include novel insights into cognitive processes such as decision-making, attention modulation, and motor planning, where the traditional trial-averaged methods fall short.

Future Directions

Looking forward, extensions of vLGP could explore more sophisticated prior structures for GP kernels or integrate additional biophysical constraints for even higher fidelity in modeling neural dynamics. The methodology opens pathways for integrating neural encoding with behavioral outputs, providing a comprehensive understanding of neural circuit function and dysfunction.

In conclusion, the paper by Zhao and Park provides a significant methodological advancement in the field of neural data analysis, bridging the gap between theoretical flexibility and practical applicability in recovering hidden neural dynamics. This paves the way for more nuanced interrogation of neural processes, pushing the boundaries of how researchers can decode the intricate dance of neuronal ensembles from spike train data.