Statistical analysis of neural data

Spring 2009


This is a Ph.D.-level topics course in statistical analysis of neural data. Students from statistics, neuroscience, and engineering are all welcome to attend.

Time: W 2:40-4:40
Place: Rm 1025, 1255 Amsterdam Ave (Stat Dept building)
Professor: Liam Paninski; Office: 1255 Amsterdam Ave, Rm 1028. Email: liam at stat dot columbia dot edu

Prerequisite: A good working knowledge of basic statistical concepts (likelihood, Bayes' rule, Poisson processes, Markov chains, Gaussian random vectors), including especially linear-algebraic concepts related to regression and principal components analysis, is necessary. No previous experience with neural data is required.
Evaluation: Final grades will be based on class participation and a student project. The project can involve either the implementation and justification of a novel analysis technique, or a standard analysis applied to a novel data set. Students can work in pairs or alone (if you work in pairs, of course, the project has to be twice as impressive). See this page for some links to available datasets.
Course goals: We will introduce a number of advanced statistical techniques relevant in neuroscience. Each technique will be illustrated via application to problems in neuroscience. The focus will be on the analysis of single and multiple spike train data, with a few applications to analyzing intracellular voltage and dendritic imaging data; however, we will not cover any topics in the analysis of fMRI data (for those interested in fMRI data, see this course by Martin Lindquist instead). A brief list of statistical concepts and corresponding neuroscience applications is below.

Statistical concept / technique Neuroscience application
Point processes; conditional intensity functions Neural spike trains; Poisson images
Time-rescaling theorem for point processes Fast simulation of network models
Bias, consistency, principal components Spike-triggered averaging; spike-triggered covariance
Generalized linear models Neural encoding models including spike-history effects; inferring network connectivity
Regularization; shrinkage estimation Maximum a posteriori estimation of high-dimensional neural encoding models
State-space models; sequential Monte Carlo / particle filtering Decoding spike trains; optimal voltage smoothing
Optimization and convexity techniques Spike-train decoding; ML estimation of encoding models
Quadratic programming / nonnegative least-squares Biophysical model fitting; inference of subthreshold voltage given spike trains
Markov chain Monte Carlo: Metropolis-Hastings and hit-and-run algorithms Firing rate estimation and spike-train decoding
Markov processes; first-passage times; Fokker-Planck equation Integrate-and-fire-based neural models
Kalman filter; extended/unscented Kalman filter; EM algorithm Inferring common-input from multineuronal spike-train data; analysis of behavioral learning experiments
Mixture models; Dirichlet processes Spike-sorting / clustering
Laplace approximation; Fisher information Model-based decoding and information estimation; adaptive design of optimal stimuli

For those new to neuroscience: While we will cover all the necessary background as we go, for those who want to explore the material in greater depth, there are a bunch of good computational neuroscience resources. Four good books (each of which emphasize different topics, albeit with some overlap) are: Theoretical Neuroscience, by Dayan and Abbott; Biophysics of Computation: information processing in single neurons, by Koch; Spiking Neuron Models, by Gerstner and Kistler; and Spikes: exploring the neural code, by Rieke et al. The first chapter of the Spikes book has been kindly made available online - this makes a nice overview of some of the questions we will address in this course. Even more kindly, the full text of the Gerstner-Kistler book is online; for our purposes, the key sections are Chapter 1 and Part I. Another good online tutorial is available here. Finally, many of our examples will be drawn from the visual system: see the book Eye, Brain, and Vision (again, very kindly provided online) by David Hubel for an excellent introduction.

For those new to statistics: See this page for some introductory notes on probability and statistics (central limit theorem, Neyman-Pearson hypothesis testing, asymptotic theory for maximum likelihood estimation, sufficient statistics, etc.). Also, here is an excellent online book on convex optimization.

This page also has some useful background material on neural data analysis.

Schedule

Date Topic Reading Notes
Jan 21-28 Introduction; background on neuronal biophysics, regression, MCMC Spikes introduction; Kass et al '05; Brown et al. '04 Neuroscience review by Max Nikitchenko
Feb 4-11 Spike-triggered averaging; spike-triggered covariance; Poisson regression Simoncelli et al. '04; Chichilnisky '01; Paninski '03; Sharpee et al. '04; Paninski '04; Weisberg and Welsh, '94 notes
Feb 18-25 Point processes: Poisson process, renewal process, self-exciting process, Cox process; time-rescaling: goodness-of-fit, fast simulation of network models Brown et al. '01 Uri Eden's point process notes; supplementary notes. 1st problem set posted on courseworks.
Feb 18-25 Generalized linear models (GLM) including spike-history effects Paninski et al. '07; Truccolo et al '05; Kass et al. '01; Ahrens et al '08 notes. 2nd problem set posted on courseworks.
Feb 25 The expectation-maximization (EM) algorithm for maximum likelihood given indirect measurements / hidden data; mixture models; spike sorting Neal and Hinton '98; Lewicki '98; Salakhutdinov et al '03; Shoham et al '03; Pouzat et al '04 notes
Mar 4 Dirichlet process mixture models for spike sorting Teh's notes on Dirichlet processes; Neal's TR on sampling methods for Dirichlet process mixture models; Wood and Black '08 Guest lecture by Frank Wood; slides
Mar 11, 25 Bayesian decoding of spike trains; Markov chain Monte Carlo (MCMC) Warland et al '97; Pillow+Paninski '06 Guest lectures by Yashar Ahmadian; notes
Mar 18 Spring break
Apr 1 Hidden Markov models (HMM) in discrete space; multistate GLMs for neurons with bistable firing properties; ion channel models Rabiner tutorial; Jordan review of graphical models; Gat et al '97; Colquhoun and Hawkes '82 notes
Apr 8-15 Log-concave, smooth state space models; autoregressive models; Kalman filter; extended Kalman filter; fast tridiagonal methods. Applications in neural prosthetics, optimal smoothing of voltage/calcium traces, fitting common-input models for population spike train data, and analysis of nonstationary spike train data Kalman filter notes by Minka; Roweis and Ghahramani '99; Huys et al '06; Paninski et al '04; Jolivet et al '04; Beeman's notes on conductance-based neural modeling; Wu et al '05; Brown et al '98; Smith et al '04; Yu et al '05. Additional useful papers collected by Minka here. notes (second half to appear shortly). 3rd problem set posted on courseworks.
Apr 22 Particle filter; stratified resampling; deconvolution of spike times from noisy calcium traces Doucet et al '00; Douc et al '05; Brockwell et al '04; Huys and Paninski '09; Vogelstein et al '09. Guest lecture by Joshua Vogelstein: slides