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Enhanced portrayal of neural and behavioral reaction properties utilizing point-process state-space structure. Anna Alexandra Dreyer. Harvard-MIT Division of Wellbeing Sciences and Innovation Discourse and Listening to Bioscience and Innovation Program Neurostatistics Research Lab, MIT

Enhanced portrayal of neural and behavioral reaction properties utilizing point-prepare state-space system Anna Alexandra Dreyer Harvard-MIT Division of Health Sciences and Technology Speech and Hearing Bioscience and Technology Program Neurostatistics Research Laboratory, MIT PI: Emery Brown, M.D., Ph.D. September 27, 2007

Action possibilities as paired occasions Action possibilities (spikes) are parallel occasions Cells utilizing timing and recurrence of activity possibilities to speak with neighboring cells Most cell discharge activity possibilities suddenly without incitement Models ought to start with spikes to most precisely depict the reaction Figure from research center of Mark Ungless

Point Process Framework: Definition of Conditional Intensity Function Given a recording interim of [0,T) , the tallying procedure N(t) speaks to the quantity of spikes that have happened on the interim [0,t). A model can be totally portrayed by the restrictive power work (CIF) that characterizes the momentary terminating rate at each point in time as: where H(t) speaks to the autoregressive history until time t . Cocoa et al., 2003; Daley and Vere-Jones, 2003; Brown, 2005

Joint Probability of Spiking (Likelihood work) Discretize time on length [0,T) into B interims. As turns out to be progressively little (t b | Ψ , H k ), where Ψ are parameters and H b is the autoregressive history up to container b , approaches the likelihood of seeing one occasion in the binwidth of . On the off chance that we select an adequately little binwidth , , with the end goal that the likelihood of seeing more than one occasion in this binwidth approaches 0, the joint likelihood can be composed as the result of Bernoulli free occasions (Truccolo, et al., 2005): where o( J ) speaks to the likelihood of seeing at least two occasions on the interim (t b - 1,t b ] . Truccolo et al., 2005

A case of utilizing PP models to break down sound-related information: Experimental Paradigm Recordings of activity possibilities to 19 boost levels for different redundancies of the jolt Need to create encoding model to portray reactions to every boost level and additionally the clamor in the framework Inference: locate the most reduced jolt level for which the reaction is more than framework commotion Given new reactions from a similar cell, need to disentangle the boost from which reaction began Data from Lim and Anderson (2006)

Modeling case of cortical reaction crosswise over jolt levels Response qualities incorporate Autoregressive parts Temporal and rate-subordinate components To have satisfactory integrity of-fit and prescient power, must catch these components from crude information Current strategy Typical autoregressive segments Does NOT catch

Point prepare state space system Instantaneous Firing Intensity Model: The terminating force in each Δ = 1ms receptacle, b , is displayed as an element of the past spiking history, H l,k,b Δ and of the impact of the jolt Observation Equation State condition Conditional terminating force Stimulus impact Past spiking history impact where ε l+1,r is a Gaussian arbitrary vector Computational strategies created with G Czanner, U Eden, E Brown

Encoding and Decoding Methodology Estimation/Encoding/Inference The Expectation-Maximization calculation utilized Monte Carlo procedures to gauge certainty limits for jolt impact Goodness-of-fit KS and autocorrelation of rescaled times Decoding and reaction property derivation

Expectation-Maximization calculation Used in figuring greatest probability (ML) parameters in measurable models with concealed factors or missing information. The calculation comprises of two stages desire (E) step where the desire of the entire probability is evaluated amplification (M) step when the most extreme probability of the desire is taken. As the calculation advances, the underlying assessments of the parameters are enhanced by taking cycles until the gauge meets on the most extreme probability estimator. Dempster et al., 1977; McLachlan and Krishnan, 1997; Pawitan, 2001

SS-GLM model of boost impact Level ward jolt impact catches numerous marvels found in information Increase of spiking with level Spread of excitation in time Removes the impact of autoregressive history which is framework (not jolt subordinate) property Stimulus Effect (spikes/s) Level Number Time since boost onset (ms)

Threshold induction in view of all trials and all levels Define limit as the principal boost level for which we can be sensibly (>0.95) sure that the reaction at that level is not quite the same as the clamor and keeps on contrasting for higher boost levels For this case, we characterize edge as level 8 Compare to normal technique of rate-level capacity (level 11) Dreyer et al., 2007; Czanner et al., 2007

Goodness-of-fit evaluation The KS plot fits near the 45 degree line demonstrating consistency of rescaled spike times The autocorrelation plot suggests that Gaussian rescaled spike times are moderately uncorrelated, inferring autonomy. Conversely, the KS plots for the fundamental rate-based models give an extremely poor fit to the information Johnson & Kotz, 1970; Brown et al, 2002; Box et al., 1994

Decoding in view of a solitary trial Decoding of new information in light of encoding parameters Given a spike prepare, appraise the probability that the spike prepare, n l* , originated from any boost, s l' , in our encoding model Calculate the probability for all jolts, s 1:L Take the in all probability level as the decoded jolt

Single-trial edge induction utilizing deciphering in view of ML more delicate around than ROC in light of number of spikes The region under ROC bend determines the likelihood that, when two reactions are drawn, one from a lower level and one from a more elevated amount, the calculation relegates a bigger incentive to the draw from a more elevated amount.

Decoding over various trials enhances execution

Neural Model Conclusions This philosophy has potential for portraying the conduct of any uproarious framework where division of flag from commotion is vital in anticipating reactions to future jolts

Bayesian systems – the other option to frequentist estimation Use Bayesian testing procedures to: Estimate behavioral reactions to sound-related boosts Apply strategy utilized for sound-related encoding models to learning examinations to find the neural components that encode for behavioral learning in the Basal Ganglia. In a joint effort with B. Pfingst, A. Smith, A. Graybiel, E. Chestnut

Bayesian examining philosophy Goal is to figure the back likelihood thickness of the parameters and the concealed state given the information Use Monte Carlo Markov Chain (MCMC) techniques to register the back likelihood by reenacting stationary Markov Chains. MCMC strategies give rough back likelihood thickness to parameters Can register trustworthy interims (closely resembling certainty interims for obscure parameter gauges) for parameter gauges Gilks et al., 1996; Congdon, 2003

References Box GEP, Jenkins GM, Reinsel GC. Time arrangement investigation, guaging and control . third ed. Englewood Cliffs, NJ: Prentice-Hall, 1994. Chestnut EN. Hypothesis of Point Processes for Neural Systems. In: Chow CC, Gutkin B, Hansel D, Meunier C, Dalibard J, eds. Techniques and Models in Neurophysics. Paris, Elsevier, 2005, Chapter 14: 691-726. Chestnut EN, Barbieri R, Eden UT, and Frank LM. Probability techniques for neural information investigation. In: Feng J, ed. Computational Neuroscience: A Comprehensive Approach. London: CRC, 2003, Chapter 9: 253-286. Cocoa EN, Barbieri R, Ventura V, Kass RE, Frank LM. Time-Rescaling hypothesis and its application to neural spike prepare information examination. Neural. Comput 2002: 14:325-346. Congdon P. Connected Bayesian Modeling . John Wiley and Sons Ltd., Chichester, United Kingdom, 2003. Daley D and Vere-Jones D. An Introduction to the Theory of Point Process . second ed., Springer-Verlag, New York, 2003. Czanner G, Dreyer AA , Eden UT, Wirth S, Lim HH, Suzuki W, Brown EN. Dynamic Models of Neural Spiking Activity. IEEE Conference on Decision and Control . 2007 Dec 12. Dempster A, Laird N, Rubin D. Greatest probability from fragmented information through the EM calculation. Diary of the Royal Statistical Society, Series B, 1977, 39(1): 1-38. Dreyer AA , Czanner G, Eden UT, Lim HH, Anderson DJ, Brown EN. Upgraded sound-related neural limit location utilizing a point procedure state-space demonstrate examination. Computational Systems Neuroscience Conference (COSYNE) . February, 2007 Gilks WR, Richardson S, Spiegelhalter DJ. Monte Carlo Markov chain practically speaking. New York: Chapman and Hall/CRC, 1996. Johnson A, Kotz S. Appropriations in Statistics: Continuous Univariate Distributions. New York: Wiley, 1970. Lim HH, Anderson DJ. Sound-related cortical reactions to electrical incitement of the second rate colliculus: Implications for a sound-related midbrain embed. J. Neurophysiol. 2006, 96(3): 975-88. McLachlan GJ and Krishnan T. The EM Algorithm and Extensions. John Wiley & Sons, 1997. Pawitan Y. Probably: Statistical Modeling and Inference Using Likelihood. New York: Oxford Univ. Press, 2001. Truccolo, W. Eden, U.T., Fellows, M.R., Donoghue, J.P. also, Brown, E.N. A point procedure structure for relating neural spiking movement to spiking history, neural group and extraneous covariate impacts. J. Neurophysiol . 2005, 93: 1074-1089.

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