Application of Statistical Techniques to Neural Data Analysis

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Application of Statistical Techniques to Neural Data Analysis

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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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.