This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings are now a standard tool in neuroscience research, it is important to have a measure of such network-wide behavioral coordination and information sharing, applicable to multiple neural spike train data. We propose a new statistic, informational coherence, which measures how much better one unit can be predicted by knowing the dynamical state of another. We argue informational coherence is a measure of association and shared information which is superior to traditional pairwise measures of synchronization and correlation. To find the dynamical states, we use a recently-introduced algorithm which reconstructs effective state spaces from stochastic time series.

The concept of surprise is central to sensory processing, adaptation, learning, and attention. Yet, no widely-accepted mathematical theory currently exists to quantitatively characterize surprise elicited by a stimulus or event, for observers that range from single neurons to complex natural or engineered systems. We describe a formal Bayesian definition of surprise that is the only consistent formulation under minimal axiomatic assumptions. Surprise quantifies how data affects a natural or artificial observer, by measuring the difference between posterior and prior beliefs of the observer. Using this framework we measure the extent to which humans direct their gaze towards surprising items while watching television and video games. We find that subjects are strongly attracted towards surprising locations, with 72% of all human gaze shifts directed towards locations more surprising than the average, a figure which rises to 84% when considering only gaze targets simultaneously selected by all subjects.

We consider the scaling of the number of examples necessary to achieve good performance in distributed, cooperative, multi-agent reinforcement learning, as a function of the the number of agents n. We prove a worstcase lower bound showing that algorithms that rely solely on a global reward signal to learn policies confront a fundamental limit: They require a number of real-world examples that scales roughly linearly in the number of agents. For settings of interest with a very large number of agents, this is impractical. We demonstrate, however, that there is a class of algorithms that, by taking advantage of local reward signals in large distributed Markov Decision Processes, are able to ensure good performance with a number of samples that scales as O(log n). This makes them applicable even in settings with a very large number of agents n.

The classical Bayes rule computes the posterior model probability from the prior probability and the data likelihood. We generalize this rule to the case when the prior is a density matrix (symmetric positive definite and trace one) and the data likelihood a covariance matrix. The classical Bayes rule is retained as the special case when the matrices are diagonal. In the classical setting, the calculation of the probability of the data is an expected likelihood, where the expectation is over the prior distribution. In the generalized setting, this is replaced by an expected variance calculation where the variance is computed along the eigenvectors of the prior density matrix and the expectation is over the eigenvalues of the density matrix (which form a probability vector). The variances along any direction is determined by the covariance matrix. Curiously enough this expected variance calculation is a quantum measurement where the covariance matrix specifies the instrument and the prior density matrix the mixture state of the particle. We motivate both the classical and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the classical Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices.

This paper presents a new sampling algorithm for approximating functions of variables representable as undirected graphical models of arbitrary connectivity with pairwise potentials, as well as for estimating the notoriously difficult partition function of the graph. The algorithm fits into the framework of sequential Monte Carlo methods rather than the more widely used MCMC, and relies on constructing a sequence of intermediate distributions which get closer to the desired one. While the idea of using "tempered" proposals is known, we construct a novel sequence of target distributions where, rather than dropping a global temperature parameter, we sequentially couple individual pairs of variables that are, initially, sampled exactly from a spanning tree of the variables.

A standard method to obtain stochastic models for symbolic time series is to train state-emitting hidden Markov models (SE-HMMs) with the Baum-Welch algorithm. Based on observable operator models (OOMs), in the last few months a number of novel learning algorithms for similar purposes have been developed: (1,2) two versions of an "efficiency sharpening" (ES) algorithm, which iteratively improves the statistical efficiency of a sequence of OOM estimators, (3) a constrained gradient descent ML estimator for transition-emitting HMMs (TE-HMMs). We give an overview on these algorithms and compare them with SE-HMM/EM learning on synthetic and real-life data.

We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph; the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.

Linear text classification algorithms work by computing an inner product between a test document vector and a parameter vector. In many such algorithms, including naive Bayes and most TFIDF variants, the parameters are determined by some simple, closed-form, function of training set statistics; we call this mapping mapping from statistics to parameters, the parameter function. Much research in text classification over the last few decades has consisted of manual efforts to identify better parameter functions. In this paper, we propose an algorithm for automatically learning this function from related classification problems. The parameter function found by our algorithm then defines a new learning algorithm for text classification, which we can apply to novel classification tasks. We find that our learned classifier outperforms existing methods on a variety of multiclass text classification tasks.

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

The observed physiological dynamics of an infant receiving intensive care are affected by many possible factors, including interventions to the baby, the operation of the monitoring equipment and the state of health. The Factorial Switching Kalman Filter can be used to infer the presence of such factors from a sequence of observations, and to estimate the true values where these observations have been corrupted. We apply this model to clinical time series data and show it to be effective in identifying a number of artifactual and physiological patterns.