Binless Kernel Machine: Modeling Spike Train Transformation for Cognitive Neural Prostheses

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.

[1]  V. Marmarelis.  Identification of nonlinear biological systems using laguerre expansions of kernels , 1993, Annals of Biomedical Engineering.

[2]  José Carlos Príncipe,et al.  A comparison of binless spike train measures , 2010, Neural Computing and Applications.

[3]  L. Paninski,et al.  Inferring input nonlinearities in neural encoding models , 2008, Network.

[4]  Xiang Zhang,et al.  Clustering Neural Patterns in Kernel Reinforcement Learning Assists Fast Brain Control in Brain-Machine Interfaces , 2019, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[5]  Zhaohui Wu,et al.  Intelligence-Augmented Rat Cyborgs in Maze Solving , 2016, PloS one.

[6]  Fang Wang,et al.  Local-learning-based neuron selection for grasping gesture prediction in motor brain machine interfaces. , 2013, Journal of neural engineering.

[7]  Zhaohui Wu,et al.  Cyborg Intelligence: Recent Progress and Future Directions , 2016, IEEE Intelligent Systems.

[8]  José Carlos Príncipe,et al.  Reinforcement learning via kernel temporal difference , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[9]  Kai Xu,et al.  Quantized Attention-Gated Kernel Reinforcement Learning for Brain–Machine Interface Decoding , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Robert E. Hampson,et al.  Manuscript Information Manuscript Files on Parsing the Neural Code in the Prefrontal Cortex of Primates Using Principal Dynamic Modes on Parsing the Neural Code in the Prefrontal Cortex of Primates Using Principal Dynamic Modes , 2022 .

[11]  Kan Li,et al.  Transfer Learning in Adaptive Filters: The Nearest Instance Centroid-Estimation Kernel Least-Mean-Square Algorithm , 2017, IEEE Transactions on Signal Processing.

[12]  Gang Pan,et al.  Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model , 2018, Neural Computation.

[13]  Theodore W Berger,et al.  A cortical neural prosthesis for restoring and enhancing memory , 2011, Journal of neural engineering.

[14]  Uri T Eden,et al.  A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. , 2005, Journal of neurophysiology.

[15]  Badong Chen,et al.  Quantized Kernel Least Mean Square Algorithm , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[16]  José Carlos Príncipe,et al.  Kernel Methods on Spike Train Space for Neuroscience: A Tutorial , 2013, IEEE Signal Processing Magazine.

[17]  Dipankar Das,et al.  Enhanced SenticNet with Affective Labels for Concept-Based Opinion Mining , 2013, IEEE Intelligent Systems.

[18]  Theodore W. Berger,et al.  Identification of functional synaptic plasticity from spiking activities using nonlinear dynamical modeling , 2015, Journal of Neuroscience Methods.

[19]  Vasilis Z. Marmarelis,et al.  Nonlinear Dynamic Modeling of Physiological Systems , 2004 .

[20]  KrkovVra.  Kolmogorov's theorem is relevant , 1991 .

[21]  L. Paninski.  Maximum likelihood estimation of cascade point-process neural encoding models , 2004, Network.

[22]  Robert E. Hampson,et al.  Nonlinear Dynamic Modeling of Spike Train Transformations for Hippocampal-Cortical Prostheses , 2007, IEEE Transactions on Biomedical Engineering.

[23]  Sheila Nirenberg,et al.  Decoding neuronal spike trains: How important are correlations? , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Fang Wang,et al.  Neural Control of a Tracking Task via Attention-Gated Reinforcement Learning for Brain-Machine Interfaces , 2015, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[25]  Sudipto Guha,et al.  Clustering Data Streams , 2000, FOCS.

[26]  Xiang Zhang,et al.  Clustering Based Kernel Reinforcement Learning for Neural Adaptation in Brain-Machine Interfaces , 2018, 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[27]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[28]  Ji Zhu,et al.  Kernel Logistic Regression and the Import Vector Machine , 2001, NIPS.

[29]  T.W. Berger,et al.  Restoring lost cognitive function , 2005, IEEE Engineering in Medicine and Biology Magazine.

[30]  Hao Yu,et al.  Improved Computation for Levenberg–Marquardt Training , 2010, IEEE Transactions on Neural Networks.

[31]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[32]  Gang Pan,et al.  Predicting Spike Trains from PMd to M1 Using Discrete Time Rescaling Targeted GLM , 2018, IEEE Transactions on Cognitive and Developmental Systems.

[33]  Anthony Widjaja,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2003, IEEE Transactions on Neural Networks.

[34]  Jerald D. Kralik,et al.  Chronic, multisite, multielectrode recordings in macaque monkeys , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Vra Krkov.  Kolmogorov's Theorem Is Relevant , 1991, Neural Computation.

[36]  Nir Ailon,et al.  Streaming k-means approximation , 2009, NIPS.

[37]  Robert E. Hampson,et al.  Mechanism-Based and Input-Output Modeling of the Key Neuronal Connections and Signal Transformations in the CA3-CA1 Regions of the Hippocampus , 2018, Neural Computation.

[38]  José Carlos Príncipe,et al.  A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing , 2009, Neural Computation.

[39]  D. McCandless.  Neuroanatomy: an atlas of structures, sections and systems , 1994, Metabolic Brain Disease.

[40]  Hae-Sang Park,et al.  A simple and fast algorithm for K-medoids clustering , 2009, Expert Syst. Appl..

[41]  José Carlos Príncipe,et al.  Sequential Monte Carlo Point-Process Estimation of Kinematics from Neural Spiking Activity for Brain-Machine Interfaces , 2009, Neural Computation.

[42]  Emery N. Brown,et al.  The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis , 2002, Neural Computation.

[43]  John P. Cunningham,et al.  An L1-regularized logistic model for detecting short-term neuronal interactions , 2011, Journal of Computational Neuroscience.

[44]  Robert E. Hampson,et al.  Sparse Large-Scale Nonlinear Dynamical Modeling of Human Hippocampus for Memory Prostheses , 2018, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[45]  Ian H. Stevenson,et al.  Bayesian Inference of Functional Connectivity and Network Structure From Spikes , 2009, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[46]  Robert L. Ruff.  Neuroanatomy An Atlas of Structures, Sections, and Systems, 4th Ed. , 1995 .

[47]  Yuwei Cui,et al.  Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs , 2013, PLoS Comput. Biol..

[48]  Vasilis Z. Marmarelis,et al.  Nonlinear Dynamic Modeling of Physiological Systems: Marmarelis/Nonlinear , 2004 .

[49]  T.,et al.  Training Feedforward Networks with the Marquardt Algorithm , 2004 .

[50]  Rosa H. M. Chan,et al.  A Nonlinear Model for Hippocampal Cognitive Prosthesis: Memory Facilitation by Hippocampal Ensemble Stimulation , 2012, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[51]  Emery N. Brown,et al.  Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking , 2010, Neural Computation.