~~I am giving two talks in Bristol next week about (not so coincidentally) my
two latest papers.~~

- "The Computational Structure of Spike Trains"
- Bristol Centre for Complexity Sciences,
~~SM2 in the School of Mathematics, 2 pm on Tuesday 9 February~~ *Abstract:*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.- Joint work with Rob Haslinger and Kristina Lisa Klinkner.
- "Dynamics of Bayesian updating with dependent data and misspecified models"
- Statistics seminar, Department of Mathematics,
~~Seminar Room SM3, 2:15pm on Friday 20 February~~ *Abstract*: Much is now known about the consistency of Bayesian non-parametrics with independent or Markovian data.. Necessary conditions for consistency include the prior putting enough weight on the right neighborhoods of the true distribution; various sufficient conditions further restrict the prior in ways analogous to capacity control in frequentist nonparametrics. The asymptotics of Bayesian updating with mis-specified models or priors, or non-Markovian data, are far less well explored. Here I establish sufficient conditions for posterior convergence when all hypotheses are wrong, and the data have complex dependencies. The main dynamical assumption is the asymptotic equipartition (Shannon-McMillan-Breiman) property of information theory. This, plus some basic measure theory, lets me build a sieve-like structure for the prior. The main statistical assumption concerns the compatibility of the prior and the data-generating process, bounding the fluctuations in the log-likelihood when averaged over the sieve-like sets. In addition to posterior convergence, I derive a kind of large deviations principle for the posterior measure, extending in some cases to rates of convergence, and discuss the advantages of predicting using a combination of models known to be wrong.

~~I'll also be lecturing
about prediction, self-organization
and filtering to the BCCS
students.~~

~~I presume that I will not spend the ~~
*whole* week talking about
statistics, or working on the next round of papers and lectures; is there, I
don't know, someplace in Bristol to hear music or something?

**Update**, 8 February: canceled at the last minute,
unfortunately; with some hope of rescheduling.

Self-centered; Enigmas of Chance; Complexity; Minds, Brains, and Neurons

Posted by crshalizi at February 04, 2010 13:48 | permanent link