Application of statistical techniques to neural data analysis
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Application of Statistical Techniques to Neural Data Analysis. Aniket Kaloti 03/07/2006. Introduction. Levels of Analysis in Systems and Cognitive Neuroscience Spikes: primary neural signals Single cells and receptive fields Multiple electrode recordings fMRI EEG and ERPs.

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Application of Statistical Techniques to Neural Data Analysis

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Application of statistical techniques to neural data analysis

Application of Statistical Techniques to Neural Data Analysis

Aniket Kaloti

03/07/2006


Introduction

Introduction

  • Levels of Analysis in Systems and Cognitive Neuroscience

    • Spikes: primary neural signals

    • Single cells and receptive fields

    • Multiple electrode recordings

    • fMRI

    • EEG and ERPs

Retinal Ganglion Cell

Receptive Field

Visual Cortical (V1) Cell

Receptive Field


Receptive field estimation a new information theoretic method sharpee et al 2004

Receptive Field Estimation: A New Information Theoretic Method (Sharpee et al, 2004)

  • V1 cells of primary concern

  • Linear-Nonlinear Model: estimate the Wiener filter, estimate non-linearity graphically

  • Classically, white noise stimuli were used

  • Works best for Gaussian stimulus ensembles

  • Natural Stimuli: non-Gaussian

From Simoncelli et al, 2003


The model

The Model

  • Receptive field as a special dimension in the high-dimensional stimulus space

  • Hence, reduce dimensionality of the stimulus space conditioned on the neural response

  • To formulate this, define the density

  • Ispike defines the mutual information between the entire stimulus ensemble and the spike

  • In practice, use the time average equation

Sharpee et al, 2004


Optimization algortihm and results

Optimization Algortihm and Results

  • Finding “most informative” dimensions:

    • Ispike: total mutual information;

    • If only a few dimensions in the stimulus space are relevant, then Ispike should be equal to mutual information between spike and the relevant subspace in the direction of the vector v

    • Find the pdfs of the projections onto the relevant subspace v

    • Maximize Iv with respect to v to obtain the relevant dimension, i.e., the receptive field

  • Figure: the comparison of the standard method with the present method applied on model in last slide


Independent component analysis ica

Independent Component Analysis (ICA)

  • Blind source separation

  • Blind: input and transfer function unknown

  • Very ill-posed without further assumptions

    • f linear A, usually symmetric

    • s are independent (hence ICA)

    • Most commonly: n is zero

  • Independece: joint density factorizes

  • Independence: mutual information is zero

  • The problem: estimate independent sources through inversion of the matrix A.

Observed signals

Unknown sources

Additive/observational noise

Unknown function


Ica estimation techniques

ICA Estimation Techniques

  • Basic idea: minimize mutual information between the components of s.

  • Maximum likelihood (ML) method

    • Likelihood definition

    • Log-likelihood

    • Batch of T samples

    • Use W = A-1

  • Maximize L; equivalent to minimizing mutual information


Ica estimation contd

ICA estimation (contd.)

  • Cumulant (moment) based methods: kurtosis = fourth central moment; mutual information approximations involving kurtosis

  • Negentropy: difference of entropies between Gaussian vector and the vector of interest; measure of non-Gaussianity

  • Infomax ICA: maximize information transmission in a neural network


Applications of ica

Applications of ICA

  • EEG and ERP analysis

    • Infomax ICA most commonly applied technique; gives rise to temporally independent EEG signals

    • Independent components: can they tell us anything about the brain activity?

  • fMRI: spatially independent processes (?)

  • Speech separation

  • Natural images: independent components give V1 like receptive fields

Source: www.bnl.gov/neuropsychology/ERPs_al.asp


Other techniques applicable to neural science

Other techniques applicable to neural science

  • Point process analysis of neural coding

  • Information theoretic analysis of information coding in the neural system

  • Principal components analysis to neural recordings and spike sorting

  • Recently developed nonlinear dimensionality reduction techniques like Isomap, Hessian eigenmaps, Laplacian eigenmaps etc in face and object recognition.


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