arXiv subjects

Rakesh Malladi

Publications and source records attributed to Rakesh Malladi.

3 recordsLinked to original sources

arXiv2018

Mutual Information in Frequency and its Application to Measure Cross-Frequency Coupling in Epilepsy

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramer's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in- frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.

q-bio.NC↗

arXiv2017

Data-Driven Estimation Of Mutual Information Between Dependent Data

We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The main novelty of our solution lies in transforming the data to frequency domain to make the problem tractable. We define a novel metric--mutual information in frequency--to detect and quantify the dependence between two random processes across frequency using Cramér's spectral representation. Our solution calculates mutual information as a function of frequency to estimate the mutual information between the dependent data over time. We validate its performance on linear and nonlinear models. In addition, mutual information in frequency estimated as a part of our solution can also be used to infer cross-frequency coupling in the data.

cs.IT↗

arXiv2016

Identifying Seizure Onset Zone from the Causal Connectivity Inferred Using Directed Information

In this paper, we developed a model-based and a data-driven estimator for directed information (DI) to infer the causal connectivity graph between electrocorticographic (ECoG) signals recorded from brain and to identify the seizure onset zone (SOZ) in epileptic patients. Directed information, an information theoretic quantity, is a general metric to infer causal connectivity between time-series and is not restricted to a particular class of models unlike the popular metrics based on Granger causality or transfer entropy. The proposed estimators are shown to be almost surely convergent. Causal connectivity between ECoG electrodes in five epileptic patients is inferred using the proposed DI estimators, after validating their performance on simulated data. We then proposed a model-based and a data-driven SOZ identification algorithm to identify SOZ from the causal connectivity inferred using model-based and data-driven DI estimators respectively. The data-driven SOZ identification outperforms the model-based SOZ identification algorithm when benchmarked against visual analysis by neurologist, the current clinical gold standard. The causal connectivity analysis presented here is the first step towards developing novel non-surgical treatments for epilepsy.

q-bio.NC↗