Pairwise maximum-entropy models and their Glauber dynamics: bimodality, bistability, non-ergodicity problems, and their elimination via inhibition

Abstract

Pairwise maximum-entropy models have been used in recent neuroscientific literature to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, predicts a bimodal distribution for the population-averaged activity, and for some population sizes the second mode peaks at high activities, with 90% of the neuron population active within time-windows of few milliseconds. This bimodality has several undesirable consequences: 1. The presence of two modes is unrealistic in view of observed neuronal activity. 2. The prediction of a high-activity mode is unrealistic on neurobiological grounds. 3. Boltzmann learning becomes non-ergodic, hence the pairwise model found by this method is not the maximum entropy distribution; similarly, solving the inverse problem by common variants of mean-field approximations has the same problem. 4. The Glauber dynamics associated with the model is either unrealistically bistable, or does not reflect the distribution of the pairwise model. This bimodality is first demonstrated for an experimental dataset comprising 159 neuron activities recorded from the motor cortex of macaque monkey. Using a reduced maximum-entropy model, evidence is then provided that this bimodality affects typical neural recordings of population sizes of a couple of hundreds or more neurons. As a way to eliminate the bimodality and its ensuing problems, a modified pairwise model is presented, which -- most important -- has an associated pairwise Glauber dynamics. This model avoids bimodality thanks to a minimal asymmetric inhibition. It can be interpreted as a minimum-relative-entropy model with a particular prior, or as a maximum-entropy model with an additional constraint.

References in corpus (45)

• Statistical physics of social dynamics
• Weak pairwise correlations imply strongly correlated network states in a neural population
• Statistical mechanics for natural flocks of birds
• Maximum entropy models for antibody diversity
• Searching for collective behavior in a network of real neurons
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Decorrelation of neural-network activity by inhibitory feedback
• Impact of network structure and cellular response on spike time correlations
• Pairwise maximum entropy models for studying large biological systems: when they can and when they can't work
• Statistical physics of pairwise probability models
• Small-correlation expansions for the inverse Ising problem
• Universal properties of correlation transfer in integrate-and-fire neurons
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Optimal Data-Based Binning for Histograms
• Stimulus-dependent maximum entropy models of neural population codes
• The correlation structure of local cortical networks intrinsically results from recurrent dynamics
• Maximum Entropy and Bayesian Data Analysis: Entropic Priors
• The simplest maximum entropy model for collective behavior in a neural network
• Ising models for networks of real neurons
• Bayesian Approaches to Copula Modelling
• Dynamical criticality in the collective activity of a population of retinal neurons
• Spin glass models for a network of real neurons
• Thermodynamics of natural images
• Topology of event distribution as a generalized definition of phase transitions in finite systems
• Generalized canonical ensembles and ensemble equivalence
• Faster solutions of the inverse pairwise Ising problem
• Echoes in correlated neural systems
• Time-Reversal and Entropy
• Markov processes follow from the principle of Maximum Caliber
• Cumulants of Hawkes point processes
• Network inference using asynchronously updated kinetic Ising Model
• Statistical Mechanics in the Extended Gaussian Ensemble
• Maximum entropy, fluctuations and priors
• On the inequivalence of statistical ensembles
• A derivation of the master equation from path entropy maximization
• Correlated fluctuations in strongly-coupled binary networks beyond equilibrium
• A Bayesian Characterization of Relative Entropy
• Effect of coupling asymmetry on mean-field solutions of direct and inverse Sherrington-Kirkpatrick model
• Noise Suppression and Surplus Synchrony by Coincidence Detection
• Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon Entropy
• Role of correlations in population coding
• Estimating Functions of Distributions from A Finite Set of Samples, Part 2: Bayes Estimators for Mutual Information, Chi-Squared, Covariance and other Statistics
• On the relation between plausibility logic and the maximum-entropy principle: a numerical study
• Systematic fluctuation expansion for neural network activity equations
• Inverse problems in spin models

Cited by in corpus (3)

• Maximum entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity
• Simulations Approaching Data: Cortical Slow Waves in Inferred Models of the Whole Hemisphere of Mouse
• Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties