Application of Statistical Signal Processing （统计信号处理中的应用）.pptVIP

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 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 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 Optimization Algortihm and Results 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. 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.) 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 EEG and ERP analysis Infomax