Application of Statistical Techniques to Neural Data Analysis

1. Application of Statistical Techniques to Neural Data Analysis Aniket Kaloti 03/07/2006

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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.