Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov Chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the spiking patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I-neurons dramatically overestimates synchrony among E-neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80%-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.Comment: 17 pages, 8 figure

Natural Wake-Sleep Algorithm

The benefits of using the natural gradient are well known in a wide range of optimization problems. However, for the training of common neural networks the resulting increase in computational complexity sets a limitation to its practical application. Helmholtz Machines are a particular type of generative model composed of two Sigmoid Belief Networks (SBNs), acting as an encoder and a decoder, commonly trained using the Wake-Sleep (WS) algorithm and its reweighted version RWS. For SBNs, it has been shown how the locality of the connections in the graphical structure induces sparsity in the Fisher information matrix. The resulting block diagonal structure can be efficiently exploited to reduce the computational complexity of the Fisher matrix inversion and thus compute the natural gradient exactly, without the need of approximations. We present a geometric adaptation of well-known methods from the literature, introducing the Natural Wake-Sleep (NWS) and the Natural Reweighted Wake-Sleep (NRWS) algorithms. We present an experimental analysis of the novel geometrical algorithms based on the convergence speed and the value of the log-likelihood, both with respect to the number of iterations and the time complexity and demonstrating improvements on these aspects over their respective non-geometric baselines.Comment: 19 pages, 9 figure

Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless Sensor Networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks (WSNs). We study the problem of scheduling the sleep times of the individual sensors to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation (SPSA) estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation for the Q-values) is updated in an on-policy temporal difference (TD) algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model. Our simulation results on a 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work