IntroductionMotivationBackgroundHow are spike trains estimated from data?Spike Train VariabilityMinimizing variability by seeking a ``best'' answer: automated approachesA Different ApproachAccount for variability in spike train analysesModel Selection/AveragingFinite Mixture ModelsDirichlet DistributionsVisualizing Dirichlet ProcessesDefinitionExistencePosterior Dirichlet ProcessBlackwell-MacQueen Urn SchemeChinese Restaurant ProcessPosterior Estimation ResultsApplicationsExample ApplicationsApplication 1: Data Exploration; Getting The Most From Ambiguous DataApplication 2: Error bars for neural decodingDiscussionReferencesHow To Use The ModelStatistical Analysis of Neural Data Lecture 6:Nonparametric Bayesian mixture modeling:with an introduction to the Dirichlet process,a brief Markov chain Monte Carlo review,and a spike sorting applicationGuest Lecturer: Frank WoodGatsby Unit, UCLMarch, 2009Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 1 / 89Motivation: Spike Train AnalysisWhat is a spike train?Cell 1Cell 2Cell 3TimeSpikeFigure: Three spike trainsAction potentials or “spikes” are assumed to be the fundamental unit ofinformation transfer in the brain [Bear et al., 2001]Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 2 / 89Motivation: The ProblemPrevalenceSuch analyses are quite common in the neuroscience literature.Potential problemsEstimating spike trains from a neural recording (“spike sorting”) issometimes difficult to doDifferent experts and algorithms produce different spike trainsIt isn’t easy to tell which one is rightDifferent spike trains can and do produce different analysis outcomesWorryHow confident can we be about outcomes from analyses of s pike trains?Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 3 / 89Approach:Goal of today’s classPresent all the tools you need to understand a novel nonparametricBayesian spike train model thatAllows spike sorting uncertainty to be reprensented and propagatedthrough all levels of spike train analysisMaking modeling assumptions cle arIncreasing the amount and kind of data that can be utilizedAccounting for spike train variability in analysis outcomesMakes “online” spike sorting possibleRoadmapSpike SortingInfinite Gaussian mixture modeling (IGMM)Dirichlet processMCMC reviewGibbs sampler for the IGMMExperimentsWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 4 / 89Goal: philosophy and procedural understanding...Figure: Dirichlet process mixture modelingWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 5 / 89Spike SortingSpike Sorting SchematicPremotorPrimary MotorCell 1Cell 2Cell 3TimeSpikeFigure: Illustration of spike train estimationWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Spike SortingSteps1Eliminate noise2Detect action potentials3Deconvolve overlapping action potentials4Identify the number of neurons in the recording5Attribute spikes to neurons6Track changes in action potential waveshape7Detect appearance and disappearance of neuronsWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Spike SortingSteps1Eliminate noise2Detect action potentials3Deconvolve overlapping action potentials4Identify the number of neurons in the recording5Attribute spikes to neurons6Track changes in action potential waveshape7Detect appearance and disappearance of neuronsWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Spike SortingFigure: Single channel, all detected action p ote ntials.Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Spike SortingPCA 1PCA 2Figure: Projection of waveforms onto first 2 PCA basis vectors.Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Spike SortingPCA 1PCA 2Figure: Spike train variability arising from clustering ambiguity.Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 6 / 89Depth of Potential ProblemsAmount of ambiguity?Depends on experimental parameters – recording device, procedure, etc.Significance for analyses?Depends on the analysis – not well studied.Two studies of spike train variabilityQualititative [Wood et al., 2004a]Quantitative [Harris et al., 2000]Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 7 / 89How Variable Are Spike Trains Produced By Experts?Qualitative variabilitySubject A B C D ESpikes 99,160 50,796 150,917 77,194 202,351Neurons 28 32 27 18 35Table: Sorting results for 20 channels of primate motor cortical data recordedusing a chronically implanted microelectrode array [Cyberkinetic NeurotechnologySystems, Inc.] from five expert subjects [Wood et al., 2004a]. Spike counts arethe total number of waveforms lab e led (deemed unambiguous).Data from the Donoghue Laboratory with thanks to Matthew Fellows and CarlosVargas-Irwin.Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 8 / 89How Variable Are Spike Trains Produced By Experts?Figure: Two experts’ manual sortings of the same data.Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 8 / 89Quantitative Spike Train VariabilityNot just chronically implanted microarray dataIn Harris et al. [2000] six small simultaneous intra- and extra-cellularrecordings were studied (tetrode).FindingsMean (FP + FN) human error around 20%Mean (FP + FN) automated error around 10%Non-zero best ellipsoid error rateWood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 9 / 89Impact of Spike Train VariabilityNot well studiedNoted as a concern for the field by Brown et al. [2004].An example: impact on decodingSubject Neurons Spikes MSE (cm2)A 107 757,674 11.45 ± 1.39B 96 335,656 16.16 ± 2.38C 78 456,221 13.37 ± 1.52D 88 642,422 12.37 ± 1.22Ave. Human 92 547,993 13.46 ± 2.54Random 288 860,261 13.28 ± 1.54None 96 860,261 12.78 ± 1.89Deco ding result variability as a function of sorting [Wood et al., 2004a]Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 10 / 89Impact of Spike Train VariabilityNot well studiedNoted as a concern for the field by Brown et al. [2004].An example: impact on decodingSubject Neurons Spikes MSE (cm2)A 107 757,674 11.45 ± 1.39B 96 335,656 16.16 ± 2.38C 78 456,221 13.37 ± 1.52D 88 642,422 12.37 ± 1.22Ave. Human 92 547,993 13.46 ± 2.54Random 288 860,261 13.28 ± 1.54None 96 860,261 12.78 ± 1.89Deco ding result variability as a function of sorting [Wood et al., 2004a]Wood (Gatsby Unit) Dirichlet Process Mixture Modeling March 2009 10 /