REGULARIZED BRAIN READING WITH SHRINKAGE AND SMOOTHING.

Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for regularization.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network.

Predictive PAC Learning and Process Decompositions.

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not decay at the same rate. In this paper, we argue that it is natural in predictive PAC to condition not on the past observations but on the mixture component of the sample path.

Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction.

We introduce , an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data.

Homophily and Contagion Are Generically Confounded in Observational Social Network Studies.

The authors consider processes on social networks that can potentially involve three factors: homophily, or the formation of social ties due to matching individual traits; social contagion, also known as social influence; and the causal effect of an individual's covariates on his or her behavior or other measurable responses. The authors show that generically, all of these are confounded with each other. Distinguishing them from one another requires strong assumptions on the parametrization of the social process or on the adequacy of the covariates used (or both).

Philosophy and the practice of Bayesian statistics.

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory.

Comment on "Why and When 'Flawed' Social Network Analyses Still Yield Valid Tests of no Contagion".

VanderWeele et al.'s paper is a useful contribution to the on-going scientific conversation about the detection of contagion from purely observational data. It is especially helpful as a corrective to some of the more extreme statements of Lyons (2011).

Estimating beta-mixing coefficients.

The literature on statistical learning for time series assumes the asymptotic independence or "mixing" of the data-generating process. These mixing assumptions are never tested, and there are no methods for estimating mixing rates from data. We give an estimator for the beta-mixing rate based on a single stationary sample path and show it is L1-risk consistent.

Approximate Methods for State-Space Models.

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow.

The computational structure of spike trains.

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.

Automatic filters for the detection of coherent structure in spatiotemporal systems.

Most current methods for identifying coherent structures in spatially extended systems rely on prior information about the form which those structures take. Here we present two approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems.

Quantifying self-organization with optimal predictors.

Despite broad interest in self-organizing systems, there are few quantitative, experimentally applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely, an internally generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics.