Learning In Spike Trains: Estimating Within-Session Changes In Firing Rate Using Weighted Interpolation

The electrophysiological study of learning is hampered by modern procedures for estimating firing rates: Such procedures usually require large datasets, and also require that included trials be functionally identical. Unless a method can track the real-time dynamics of how firing rates evolve, learning can only be examined in the past tense. We propose a quantitative procedure, called ARRIS, that can uncover trial-by-trial firing dynamics. ARRIS provides reliable estimates of firing rates based on small samples using the reversible-jump Markov chain Monte Carlo algorithm. Using weighted interpolation, ARRIS can also provide estimates that evolve over time. As a result, both real-time estimates of changing activity, and of task-dependent tuning, can be obtained during the initial stages of learning.

[1]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[2]  Nikolaus Kriegeskorte,et al.  Frontiers in Systems Neuroscience Systems Neuroscience , 2022 .

[3]  G. Wahba Smoothing noisy data with spline functions , 1975 .

[4]  E. Vaadia,et al.  Preparatory activity in motor cortex reflects learning of local visuomotor skills , 2003, Nature Neuroscience.

[5]  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.

[6]  Robert E. Kass,et al.  A Spike-Train Probability Model , 2001, Neural Computation.

[7]  Nicolai Schipper Jespersen,et al.  An Introduction to Markov Chain Monte Carlo , 2010 .

[8]  Benjamin Lindner,et al.  Superposition of many independent spike trains is generally not a Poisson process. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  R. Kass,et al.  Bayesian curve-fitting with free-knot splines , 2001 .

[10]  Shigeru Shinomoto,et al.  Kernel bandwidth optimization in spike rate estimation , 2009, Journal of Computational Neuroscience.

[11]  James G. Scott,et al.  Fully Bayesian inference for neural models with negative-binomial spiking , 2012, NIPS.

[12]  Adhemar Bultheel,et al.  Generalized cross validation for wavelet thresholding , 1997, Signal Process..

[13]  Jorge Navarro,et al.  Kernel density estimation using weighted data , 1998 .

[14]  Nicolas Brunel,et al.  Dynamics of a recurrent network of spiking neurons before and following learning , 1997 .

[15]  Eero P. Simoncelli,et al.  Dimensionality reduction in neural models: an information-theoretic generalization of spike-triggered average and covariance analysis. , 2006, Journal of vision.

[16]  Tatsuo K Sato,et al.  Correlated Coding of Motivation and Outcome of Decision by Dopamine Neurons , 2003, The Journal of Neuroscience.

[17]  Robert E Kass,et al.  Statistical issues in the analysis of neuronal data. , 2005, Journal of neurophysiology.

[18]  Jeffrey D. Schall,et al.  Relationship of presaccadic activity in frontal eye field and supplementary eye field to saccade initiation in macaque: Poisson spike train analysis , 2004, Experimental Brain Research.

[19]  R. Kass,et al.  Statistical smoothing of neuronal data. , 2003, Network.

[20]  W. Cleveland Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[21]  R. E. Wheeler Statistical distributions , 1983, APLQ.

[22]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. I. The single spike train. , 1967, Biophysical journal.

[23]  Robert A. Jacobs,et al.  Nonlinear integration of texture and shading cues on a slant discrimination task , 2010 .

[24]  E. Olivier,et al.  Pupil size variations correlate with physical effort perception , 2014, Front. Behav. Neurosci..

[25]  M. Evans Statistical Distributions , 2000 .

[26]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[27]  K. D. Punta,et al.  An ultra-sparse code underlies the generation of neural sequences in a songbird , 2002 .

[28]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[29]  I. Fried,et al.  Internally Generated Reactivation of Single Neurons in Human Hippocampus During Free Recall , 2008, Science.

[30]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[31]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[32]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[33]  A. Nieder,et al.  Dopamine Regulates Two Classes of Primate Prefrontal Neurons That Represent Sensory Signals , 2013, The Journal of Neuroscience.

[34]  Maarten Jansen,et al.  Generalized Cross Validation in variable selection with and without shrinkage , 2015 .

[35]  Ming-Hui Chen,et al.  Monte Carlo Estimation of Bayesian Credible and HPD Intervals , 1999 .

[36]  Greg Jensen,et al.  Transfer of a Serial Representation between Two Distinct Tasks by Rhesus Macaques , 2013, PloS one.

[37]  E. Eskandar,et al.  Reward and reinforcement activity in the nucleus accumbens during learning , 2014, Front. Behav. Neurosci..

[38]  Sara E. Morrison,et al.  Different Time Courses for Learning-Related Changes in Amygdala and Orbitofrontal Cortex , 2011, Neuron.

[39]  Robert E Kass,et al.  An Implementation of Bayesian Adaptive Regression Splines (BARS) in C with S and R Wrappers. , 2008, Journal of statistical software.

[40]  Peter Harremoës,et al.  Binomial and Poisson distributions as maximum entropy distributions , 2001, IEEE Trans. Inf. Theory.

[41]  Tobias Teichert,et al.  Performance Monitoring in Monkey Frontal Eye Field , 2014, The Journal of Neuroscience.

[42]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[43]  Andreas Kiermeier,et al.  Visualizing and Assessing Acceptance Sampling Plans: The R Package AcceptanceSampling , 2008 .

[44]  Richard Hans Robert Hahnloser,et al.  An ultra-sparse code underliesthe generation of neural sequences in a songbird , 2002, Nature.

[45]  P. Green,et al.  Reversible jump MCMC , 2009 .

[46]  Julie Josse,et al.  Selecting the number of components in principal component analysis using cross-validation approximations , 2012, Comput. Stat. Data Anal..