Computational Statistics seminars

Higher cortical areas carry a wide range of sensory, cognitive, and motor signals supporting complex goal-directed behavior. These signals mix in heterogeneous responses of single neurons, making it difficult to untangle underlying mechanisms. I will present two approaches for revealing interpretable circuit mechanisms from heterogeneous neural responses during cognitive tasks. First, I will show a flexible nonparametric framework for simultaneously inferring population dynamics on single trials and tuning functions of individual neurons to the latent population state. When applied to recordings from the premotor cortex during decision-making, our approach revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Second, I will show an approach for inferring an interpretable network model of a cognitive task—the latent circuit—from neural response data. We developed a theory to causally validate latent circuit mechanisms via patterned perturbations of activity and connectivity in the high-dimensional network. This work opens new possibilities for deriving testable mechanistic hypotheses from complex neural response data.

A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose to infer networks of causal relations via pairwise edge measure (PEMs) that one can easily compute from lagged correlation matrices. Motivated by contributions of process motifs to covariance and lagged variance, we formulate two PEMs that correct for confounding factors and for reverse causation. To demonstrate the performance of our PEMs, we consider network interference from simulations of linear stochastic processes, and we show that our proposed PEMs can infer networks accurately and efficiently. Specifically, for slightly autocorrelated time-series data, our approach achieves accuracies higher than or similar to Granger causality, transfer entropy, and convergent crossmapping -- but with much shorter computation time than possible with any of these methods. Our fast and accurate PEMs are easy-to-implement methods for network inference with a clear theoretical underpinning. They provide promising alternatives to current paradigms for the inference of linear models from time-series data, including Granger causality, vector-autoregression, and sparse inverse covariance estimation.