Austin J. Brockmeier

Evaluating dependence in spike train metric spaces

Assessing dependence between two sets of spike trains or between a set of input stimuli and the corresponding generated spike trains is crucial in many neuroscientific applications, such as in analyzing functional connectivity among neural assemblies, and in neural coding. Dependence between two random variables is traditionally assessed in terms of mutual information. However, although well explored in the context of real or vector valued random variables, estimating mutual information still remains a challenging issue when the random variables exist in more exotic spaces such as the space of spike trains. In the statistical literature, on the other hand, the concept of dependence between two random variables has been presented in many other ways, e.g. using copula, or using measures of association such as Spearmans ρ, and Kendalls τ. Although these methods are usually applied on the real line, their simplicity, both in terms of understanding and estimating, make them worth investigating in the context of spike train dependence. In this paper, we generalize the concept of association to any abstract metric spaces. This new approach is an attractive alternative to mutual information, since it can be easily estimated from realizations without binning or clustering. It also provides an intuitive understanding of what dependence implies in the context of realizations. We show that this new methodology effectively captures dependence between sets of stimuli and spike trains. Moreover, the estimator has desirable small sample characteristic, and it often outperforms an existing similar metric based approach.

An Association Framework to Analyze Dependence Structure in Time Series

The purpose of this paper is two-fold: first, to propose a modification to the generalized measure of association (GMA) framework that reduces the effect of temporal structure in time series; second, to assess the reliability of using association methods to capture dependence between pairs of EEG channels using their time series or envelopes. To achieve the first goal, the GMA algorithm was updated so as to minimize the effect of the correlation inherent in the time structure. The reliability of the modified scheme was then assessed on both synthetic and real data. Synthetic data was generated from a Clayton copula, for which null hypotheses of uncorrelatedness were constructed for the signal. The signal was processed such that the envelope emulated important characteristics of experimental EEG data. Results show that the modified GMA procedure can capture pairwise dependence between generated signals as well as their envelopes with good statistical power. Furthermore, applying GMA and Kendalls tau to quantify dependence using the extracted envelopes of processed EEG data concords with previous findings using the signal itself.

Adaptive Inverse Control of Neural Spatiotemporal Spike Patterns With a Reproducing Kernel Hilbert Space (RKHS) Framework

The precise control of spiking in a population of neurons via applied electrical stimulation is a challenge due to the sparseness of spiking responses and neural system plasticity. We pose neural stimulation as a system control problem where the system input is a multidimensional time-varying signal representing the stimulation, and the output is a set of spike trains; the goal is to drive the output such that the elicited population spiking activity is as close as possible to some desired activity, where closeness is defined by a cost function. If the neural system can be described by a time-invariant (homogeneous) model, then offline procedures can be used to derive the control procedure; however, for arbitrary neural systems this is not tractable. Furthermore, standard control methodologies are not suited to directly operate on spike trains that represent both the target and elicited system response. In this paper, we propose a multiple-input multiple-output (MIMO) adaptive inverse control scheme that operates on spike trains in a reproducing kernel Hilbert space (RKHS). The control scheme uses an inverse controller to approximate the inverse of the neural circuit. The proposed control system takes advantage of the precise timing of the neural events by using a Schoenberg kernel defined directly in the space of spike trains. The Schoenberg kernel maps the spike train to an RKHS and allows linear algorithm to control the nonlinear neural system without the danger of converging to local minima. During operation, the adaptation of the controller minimizes a difference defined in the spike train RKHS between the system and the target response and keeps the inverse controller close to the inverse of the current neural circuit, which enables adapting to neural perturbations. The results on a realistic synthetic neural circuit show that the inverse controller based on the Schoenberg kernel outperforms the decoding accuracy of other models based on the conventional rate representation of neural signal (i.e., spikernel and generalized linear model). Moreover, after a significant perturbation of the neuron circuit, the control scheme can successfully drive the elicited responses close to the original target responses.

Neural decoding with kernel-based metric learning

In studies of the nervous system, the choice of metric for the neural responses is a pivotal assumption. For instance, a well-suited distance metric enables us to gauge the similarity of neural responses to various stimuli and assess the variability of responses to a repeated stimulus—exploratory steps in understanding how the stimuli are encoded neurally. Here we introduce an approach where the metric is tuned for a particular neural decoding task. Neural spike train metrics have been used to quantify the information content carried by the timing of action potentials. While a number of metrics for individual neurons exist, a method to optimally combine single-neuron metrics into multineuron, or population-based, metrics is lacking. We pose the problem of optimizing multineuron metrics and other metrics using centered alignment, a kernel-based dependence measure. The approach is demonstrated on invasively recorded neural data consisting of both spike trains and local field potentials. The experimental paradigm consists of decoding the location of tactile stimulation on the forepaws of anesthetized rats. We show that the optimized metrics highlight the distinguishing dimensions of the neural response, significantly increase the decoding accuracy, and improve nonlinear dimensionality reduction methods for exploratory neural analysis.

A tensor-product-kernel framework for multiscale neural activity decoding and control

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brains motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation.

Learning Recurrent Waveforms Within EEGs

Goal: We demonstrate an algorithm to automatically learn the time-limited waveforms associated with phasic events that repeatedly appear throughout an electroencephalogram. Methods: To learn the phasic event waveforms we propose a multiscale modeling process that is based on existing shift-invariant dictionary learning algorithms. For each channel, waveforms at different temporal scales are learned based on the assumption that only a few waveforms occur in any window of the time-series, but the same waveforms reoccur throughout the signal. Once the waveforms are learned, the timing and amplitude of the phasic event occurrences are estimated using matching pursuit. To summarize the waveforms learned across multiple channels and subjects, we analyze their frequency content, their similarity to Gabor-Morlet wavelets, and perform shift-invariant k-means to cluster the waveforms. A prototype waveform from each cluster is then tested for differential spatial patterns between different motor imagery conditions. Results: On multiple human EEG datasets, the learned waveforms capture key characteristics of signals they were trained to represent, with a consistency in waveform morphology and frequency content across multiple training sections and initializations. On multichannel datasets, the spatial amplitude patterns of the waveforms are also consistent and can be used to distinguish different modalities of motor imagery. Conclusion: We explored a methodology that can be used for modeling the recurrent waveforms in EEG traces. Significance: The methodology automatically identifies the most frequent phasic event waveforms in EEG, which could then be used as features for automatic evaluation and comparison of EEG during sleep, pathology, or mentally engaging tasks.

Tensor completion throughmultiple Kronecker product decomposition

We propose a novel decomposition approach to impute missing values in tensor data. The method uses smaller scale multiway patches to model the whole data or a small volume encompassing the observed missing entries. Simulations on color images show that our method can recover color images using only 5-10% of pixels, and outperforms other available tensor completion methods.

An Electric Field Model for Prediction of Somatosensory (S1) Cortical Field Potentials Induced by Ventral Posterior Lateral (VPL) Thalamic Microstimulation

Microstimulation (MiSt) is used experimentally and clinically to activate localized populations of neural elements. However, it is difficult to predict-and subsequently control-neural responses to simultaneous current injection through multiple electrodes in an array. This is due to the unknown locations of neuronal elements in the extracellular medium that are excited by the superposition of multiple parallel current sources. We, therefore, propose a model that maps the computed electric field in the 3-D space surrounding the stimulating electrodes in one brain region to the local field potential (LFP) fluctuations evoked in a downstream region. Our model is trained with the recorded LFP waveforms in the primary somatosensory cortex (S1) resulting from MiSt applied in multiple electrode configurations in the ventral posterolateral nucleus (VPL) of the quiet awake rat. We then predict the cortical responses to MiSt in “novel” electrode configurations, a result that suggests that this technique could aid in the design of spatially optimized MiSt patterns through a multielectrode array.

Information-theoretic metric learning: 2-D linear projections of neural data for visualization

Intracortical neural recordings are typically high-dimensional due to many electrodes, channels, or units and high sampling rates, making it very difficult to visually inspect differences among responses to various conditions. By representing the neural response in a low-dimensional space, a researcher can visually evaluate the amount of information the response carries about the conditions. We consider a linear projection to 2-D space that also parametrizes a metric between neural responses. The projection, and corresponding metric, should preserve class-relevant information pertaining to different behavior or stimuli. We find the projection as a solution to the information-theoretic optimization problem of maximizing the information between the projected data and the class labels. The method is applied to two datasets using different types of neural responses: motor cortex neuronal firing rates of a macaque during a center-out reaching task, and local field potentials in the somatosensory cortex of a rat during tactile stimulation of the forepaw. In both cases, projected data points preserve the natural topology of targets or peripheral touch sites. Using the learned metric on the neural responses increases the nearest-neighbor classification rate versus the original data; thus, the metric is tuned to distinguish among the conditions.

Locating spatial patterns of waveforms during sensory perception in scalp EEG

The spatio-temporal oscillations in EEG waves are indicative of sensory and cognitive processing. We propose a method to find the spatial amplitude patterns of a time-limited waveform across multiple EEG channels. It consists of a single iteration of multichannel matching pursuit where the base waveform is obtained via the Hilbert transform of a time-limited tone. The vector of extracted amplitudes across channels is used for classification, and we analyze the effect of deviation in temporal alignment of the waveform on classification performance. Results for a previously published dataset of 6 subjects show comparable results versus a more complicated criteria-based method.