arXiv subjects

Demba Ba

Publications and source records attributed to Demba Ba.

46 records · Page 3Linked to original sources

arXiv2019

Fast Convolutional Dictionary Learning off the Grid

Given a continuous-time signal that can be modeled as the superposition of localized, time-shifted events from multiple sources, the goal of Convolutional Dictionary Learning (CDL) is to identify the location of the events--by Convolutional Sparse Coding (CSC)--and learn the template for each source--by Convolutional Dictionary Update (CDU). In practice, because we observe samples of the continuous-time signal on a uniformly-sampled grid in discrete time, classical CSC methods can only produce estimates of the times when the events occur on this grid, which degrades the performance of the CDU. We introduce a CDL framework that significantly reduces the errors arising from performing the estimation in discrete time. Specifically, we construct an expanded dictionary that comprises, not only discrete-time shifts of the templates, but also interpolated variants, obtained by bandlimited interpolation, that account for continuous-time shifts. For CSC, we develop a novel computationally efficient CSC algorithm, termed Convolutional Orthogonal Matching Pursuit with interpolated dictionary (COMP-INTERP). We benchmarked COMP-INTERP to Contiunuous Basis Pursuit (CBP), the state-of-the-art CSC algorithm for estimating off-the-grid events, and demonstrate, on simulated data, that 1) COMP-INTERP achieves a similar level of accuracy, and 2) is two orders of magnitude faster. For CDU, we derive a novel procedure to update the templates given sparse codes that can occur both on and off the discrete-time grid. We also show that 3) dictionary update with the overcomplete dictionary yields more accurate templates. Finally, we apply the algorithms to the spike sorting problem on electrophysiology recording and show their competitive performance.

eess.SP↗

arXiv2019

Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach

We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.

stat.ML↗

arXiv2018

Sequential Detection of Regime Changes in Neural Data

The problem of detecting changes in firing patterns in neural data is studied. The problem is formulated as a quickest change detection problem. Important algorithms from the literature are reviewed. A new algorithmic technique is discussed to detect deviations from learned baseline behavior. The algorithms studied can be applied to both spike and local field potential data. The algorithms are applied to mice spike data to verify the presence of behavioral learning.

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arXiv2018

Scalable Convolutional Dictionary Learning with Constrained Recurrent Sparse Auto-encoders

Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.

cs.LG↗

arXiv2018

Spike Sorting by Convolutional Dictionary Learning

Spike sorting refers to the problem of assigning action potentials observed in extra-cellular recordings of neural activity to the neuron(s) from which they originate. We cast this problem as one of learning a convolutional dictionary from raw multi-electrode waveform data, subject to sparsity constraints. In this context, sparsity refers to the number of neurons that are allowed to spike simultaneously. The convolutional dictionary setting, along with its assumptions (e.g. refractoriness) that are motivated by the spike-sorting problem, let us give theoretical bounds on the sample complexity of spike sorting as a function of the number of underlying neurons, the rate of occurrence of simultaneous spiking, and the firing rate of the neurons. We derive memory/computation-efficient convolutional versions of OMP (cOMP) and KSVD (cKSVD), popular algorithms for sparse coding and dictionary learning respectively. We demonstrate via simulations that an algorithm that alternates between cOMP and cKSVD can recover the underlying spike waveforms successfully, assuming few neurons spike simultaneously, and is stable in the presence of noise. We also apply the algorithm to extra-cellular recordings from a tetrode in the rat Hippocampus.

stat.ME↗

arXiv2018

Multitaper Spectral Estimation HDP-HMMs for EEG Sleep Inference

Electroencephalographic (EEG) monitoring of neural activity is widely used for sleep disorder diagnostics and research. The standard of care is to manually classify 30-second epochs of EEG time-domain traces into 5 discrete sleep stages. Unfortunately, this scoring process is subjective and time-consuming, and the defined stages do not capture the heterogeneous landscape of healthy and clinical neural dynamics. This motivates the search for a data-driven and principled way to identify the number and composition of salient, reoccurring brain states present during sleep. To this end, we propose a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), combined with wide-sense stationary (WSS) time series spectral estimation to construct a generative model for personalized subject sleep states. In addition, we employ multitaper spectral estimation to further reduce the large variance of the spectral estimates inherent to finite-length EEG measurements. By applying our method to both simulated and human sleep data, we arrive at three main results: 1) a Bayesian nonparametric automated algorithm that recovers general temporal dynamics of sleep, 2) identification of subject-specific "microstates" within canonical sleep stages, and 3) discovery of stage-dependent sub-oscillations with shared spectral signatures across subjects.

stat.ML↗

arXiv2018

A Modularized Efficient Framework for Non-Markov Time Series Estimation

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

math.OC↗

arXiv2017

Classification of Local Field Potentials using Gaussian Sequence Model

A problem of classification of local field potentials (LFPs), recorded from the prefrontal cortex of a macaque monkey, is considered. An adult macaque monkey is trained to perform a memory-based saccade. The objective is to decode the eye movement goals from the LFP collected during a memory period. The LFP classification problem is modeled as that of classification of smooth functions embedded in Gaussian noise. It is then argued that using minimax function estimators as features would lead to consistent LFP classifiers. The theory of Gaussian sequence models allows us to represent minimax estimators as finite dimensional objects. The LFP classifier resulting from this mathematical endeavor is a spectrum based technique, where Fourier series coefficients of the LFP data, followed by appropriate shrinkage and thresholding, are used as features in a linear discriminant classifier. The classifier is then applied to the LFP data to achieve high decoding accuracy. The function classification approach taken in the paper also provides a systematic justification for using Fourier series, with shrinkage and thresholding, as features for the problem, as opposed to using the power spectrum. It also suggests that phase information is crucial to the decision making.

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arXiv2017

Wavelet Shrinkage and Thresholding based Robust Classification for Brain Computer Interface

A macaque monkey is trained to perform two different kinds of tasks, memory aided and visually aided. In each task, the monkey saccades to eight possible target locations. A classifier is proposed for direction decoding and task decoding based on local field potentials (LFP) collected from the prefrontal cortex. The LFP time-series data is modeled in a nonparametric regression framework, as a function corrupted by Gaussian noise. It is shown that if the function belongs to Besov bodies, then using the proposed wavelet shrinkage and thresholding based classifier is robust and consistent. The classifier is then applied to the LFP data to achieve high decoding performance. The proposed classifier is also quite general and can be applied for the classification of other types of time-series data as well, not necessarily brain data.

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arXiv2017

Estimating a Separably-Markov Random Field (SMuRF) from Binary Observations

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking data is the need to collapse neural activity over time or trials, which may cause the loss of information pertinent to understanding the function of a neuron or circuit. We introduce a new method that can determine not only the trial-to-trial dynamics that accompany the learning of a contingency by a neuron, but also the latency of this learning with respect to the onset of a conditioned stimulus. The backbone of the method is a separable two-dimensional (2D) random field (RF) model of neural spike rasters, in which the joint conditional intensity function of a neuron over time and trials depends on two latent Markovian state sequences that evolve separately but in parallel. Classical tools to estimate state-space models cannot be applied readily to our 2D separable RF model. We develop efficient statistical and computational tools to estimate the parameters of the separable 2D RF model. We apply these to data collected from neurons in the pre-frontal cortex (PFC) in an experiment designed to characterize the neural underpinnings of the associative learning of fear in mice. Overall, the separable 2D RF model provides a detailed, interpretable, characterization of the dynamics of neural spiking that accompany the learning of a contingency.

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