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Cunle Qian
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2020) 32 (10): 1863–1900.
Published: 01 October 2020
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Modeling spike train transformation among brain regions helps in designing a cognitive neural prosthesis that restores lost cognitive functions. Various methods analyze the nonlinear dynamic spike train transformation between two cortical areas with low computational eficiency. The application of a real-time neural prosthesis requires computational eficiency, performance stability, and better interpretation of the neural firing patterns that modulate target spike generation. We propose the binless kernel machine in the point-process framework to describe nonlinear dynamic spike train transformations. Our approach embeds the binless kernel to eficiently capture the feedforward dynamics of spike trains and maps the input spike timings into reproducing kernel Hilbert space (RKHS). An inhomogeneous Bernoulli process is designed to combine with a kernel logistic regression that operates on the binless kernel to generate an output spike train as a point process. Weights of the proposed model are estimated by maximizing the log likelihood of output spike trains in RKHS, which allows a global-optimal solution. To reduce computational complexity, we design a streaming-based clustering algorithm to extract typical and important spike train features. The cluster centers and their weights enable the visualization of the important input spike train patterns that motivate or inhibit output neuron firing. We test the proposed model on both synthetic data and real spike train data recorded from the dorsal premotor cortex and the primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaling Kolmogorov-Smirnov tests. Our model outperforms the existing methods with higher stability regardless of weight initialization and demonstrates higher eficiency in analyzing neural patterns from spike timing with less historical input (50%). Meanwhile, the typical spike train patterns selected according to weights are validated to encode output spike from the spike train of single-input neuron and the interaction of two input neurons.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2018) 30 (12): 3189–3226.
Published: 01 December 2018
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Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.