Approximate Inference for Time-varying Interactions and Macroscopic Dynamics of Neural Populations

Abstract

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

28 pages, 7 figures

References in corpus (6)

• Searching for collective behavior in a network of real neurons
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• Small-correlation expansions for the inverse Ising problem
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Cited by in corpus (8)

• A unifying framework for mean-field theories of asymmetric kinetic Ising systems
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Inverse Ising problem in continuous time: A latent variable approach
• Nonequilibrium physics of brain dynamics
• State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal dynamics
• The principles of adaptation in organisms and machines II: Thermodynamics of the Bayesian brain
• Online Estimation of Multiple Dynamic Graphs in Pattern Sequences
• State-space analysis of an Ising model reveals contributions of pairwise interactions to sparseness, fluctuation, and stimulus coding of monkey V1 neurons