Elements of information theory
Elements of information theory
Spikes: exploring the neural code
Spikes: exploring the neural code
Causal architecture, complexity and self-organization in time series and cellular automata
Causal architecture, complexity and self-organization in time series and cellular automata
Dynamic analysis of neural encoding by point process adaptive filtering
Neural Computation
Blind construction of optimal nonlinear recursive predictors for discrete sequences
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity
Neural Computation
Observable Operator Models for Discrete Stochastic Time Series
Neural Computation
IEEE Transactions on Information Theory
Context tree estimation for not necessarily finite memory processes, via BIC and MDL
IEEE Transactions on Information Theory
Encoding through patterns: Regression tree-based neuronal population models
Neural Computation
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Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for inferring a minimal representation of that structure and for characterizing its complexity. Starting from spike trains, our approach finds their causal state models (CSMs), the minimal hidden Markov models or stochastic automata capable of generating statistically identical time series. We then use these CSMs to objectively quantify both the generalizable structure and the idiosyncratic randomness of the spike train. Specifically, we show that the expected algorithmic information content (the information needed to describe the spike train exactly) can be split into three parts describing (1) the time-invariant structure (complexity) of the minimal spike-generating process, which describes the spike train statistically; (2) the randomness (internal entropy rate) of the minimal spike-generating process; and (3) a residual pure noise term not described by the minimal spike-generating process. We use CSMs to approximate each of these quantities. The CSMs are inferred nonparametrically from the data, making only mild regularity assumptions, via the causal state splitting reconstruction algorithm. The methods presented here complement more traditional spike train analyses by describing not only spiking probability and spike train entropy, but also the complexity of a spike train's structure. We demonstrate our approach using both simulated spike trains and experimental data recorded in rat barrel cortex during vibrissa stimulation.