Biology subjects

Babadi, B.

Publications and source records attributed to Babadi, B..

3 recordsLinked to original sources

bioRxiv2017

Multiplicative Updates for Optimization Problems with Dynamics

We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative deconvolution, point-process smoothing, ML estimation for Poisson Observations, nonnegative least squares and nonnegative matrix factorization (NMF). Our algorithm can also account for temporal and spatial structure and regularization. We will analyze the performance of our algorithm on simultaneously recorded neuronal calcium imaging and electrophysiology data.

neuroscience↗

bioRxiv2017

Real-Time Tracking of Selective Auditory Attention from M/EEG: A Bayesian Filtering Approach

Humans are able to identify and track a target speaker amid a cacophony of acoustic interference, which is often referred to as the cocktail party phenomenon. Results from several decades of studying this phenomenon have culminated in recent years in various promising attempts to decode the attentional state of a listener in a competing-speaker environment from non-invasive neuroimaging recordings such as magnetoencephalography (MEG) and electroencephalography (EEG). To this end, most existing approaches compute correlation-based measures by either regressing the features of each speech stream to the M/EEG channels (the decoding approach) or vice versa (the encoding approach). These procedures operate in an offline fashion, i.e., require the entire duration of the experiment and multiple trials to provide robust results. Therefore, they cannot be used in emerging applications such as smart hearing aid devices, where a single trial must be used in real-time to decode the attentional state. In this paper, we close this gap by developing an algorithmic pipeline for real-time decoding of the attentional state. Our proposed framework consists of three main modules: 1) Real-time and robust estimation of encoding or decoding coefficients, achieved by sparse adaptive filtering, 2) Extracting reliable markers of the attentional state, and thereby generalizing the widely-used correlation-based measures thereof, and 3) Devising a near real-time state-space estimator that translates the noisy and variable attention markers to robust and reliable estimates of the attentional state with minimal delay. Our proposed algorithms integrate various techniques including forgetting factor-based adaptive filtering, {ell}1-regularization, forward-backward splitting algorithms, fixed-lag smoothing, and Expectation Maximization. We validate the performance of our proposed framework using comprehensive simulations as well as application to experimentally acquired M/EEG data. Our results reveal that the proposed real-time algorithms perform nearly as accurate as the existing state-of-the-art offline techniques, while providing a significant degree of adaptivity, statistical robustness, and computational savings.

neuroscience↗

bioRxiv2016

Fast and Stable Signal Deconvolution via Compressible State-Space Models

Abstract-Objective:Common biological measurements are in the form of noisy convolutions of signals of interest with possibly unknown and transient blurring kernels. Examples include EEG and calcium imaging data. Thus, signal deconvolution of these measurements is crucial in understanding the underlying biological processes. The objective of this paper is to develop fast and stable solutions for signal deconvolution from noisy, blurred and undersampled data, where the signals are in the form of discrete events distributed in time and space. Methods: We introduce compressible state-space models as a framework to model and estimate such discrete events. These state-space models admit abrupt changes in the states and have a convergent transition matrix, and are coupled with compressive linear measurements. We consider a dynamic compressive sensing optimization problem and develop a fast solution, using two nested Expectation Maximization algorithms, to jointly estimate the states as well as their transition matrices. Under suitable sparsity assumptions on the dynamics, we prove optimal stability guarantees for the recovery of the states and present a method for the identification of the underlying discrete events with precise confidence bounds. Results: We present simulation studies as well as application to calcium deconvolution and sleep spindle detection, which verify our theoretical results and show significant improvement over existing techniques. Conclusion: Our results show that by explicitly modeling the dynamics of the underlying signals, it is possible to construct signal deconvolution solutions that are scalable, statistically robust, and achieve high temporal resolution. Significance: Our proposed methodology provides a framework for modeling and deconvolution of noisy, blurred, and undersampled measurements in a fast and stable fashion, with potential application to a wide range of biological data.

bioengineering↗