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A common goodness-of-fit framework for neural population models using marked point process time-rescaling. (English) Zbl 1402.92120

Summary: A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.

MSC:

92C20 Neural biology
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Arai, K.; Kass, RE, Inferring oscillatory modulation in neural spike trains, PLoS Computational Biology, 13, e1005,596, (2017)
[2] Ba, D.; Temereanca, S.; Brown, EN, Algorithms for the analysis of ensemble neural spiking activity using simultaneous-event multivariate point-process models, Frontiers in Computational Neuroscience, 8, 6, (2014)
[3] Baddeley, A.; Turner, R.; etal., Spatstat: an r package for analyzing spatial point patterns, Journal of Statistical Software, 12, 1-42, (2005)
[4] Berrendero, JR; Cuevas, A.; Vjosázquez-grande, F., Testing multivariate uniformity: The distance-to-boundary method, Canadian Journal of Statistics, 34, 693-707, (2006) · Zbl 1115.62046
[5] Berrendero, JR; Cuevas, A.; Pateiro-López, B., A multivariate uniformity test for the case of unknown support, Statistics and Computing, 22, 259-271, (2012) · Zbl 1322.62142
[6] Brockwell, AE; Rojas, AL; Kass, R., Recursive bayesian decoding of motor cortical signals by particle filtering, Journal of Neurophysiology, 91, 1899-1907, (2004)
[7] Brown, EN; Frank, LM; Tang, D.; Quirk, MC; Wilson, MA, A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells, Journal of Neuroscience, 18, 7411-7425, (1998)
[8] Brown, EN; Barbieri, R.; Ventura, V.; Kass, RE; Frank, LM, The time-rescaling theorem and its application to neural spike train data analysis, Neural Computation, 14, 325-346, (2002) · Zbl 0989.62060
[9] Brown, EN; Kass, RE; Mitra, PP, Multiple neural spike train data analysis: state-of-the-art and future challenges, Nature Neuroscience, 7, 456-461, (2004)
[10] Brown, TC; Nair, MG, A simple proof of the multivariate random time change theorem for point processes, Journal of Applied Probability, 25, 210-214, (1988) · Zbl 0648.60057
[11] Chen, Z.; Putrino, DF; Ghosh, S.; Barbieri, R.; Brown, EN, Statistical inference for assessing functional connectivity of neuronal ensembles with sparse spiking data, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 19, 121-135, (2011)
[12] Daley, D.J., & Vere-Jones, D. (2003). An introduction to the theory of point processes. New York: Springer. · Zbl 1026.60061
[13] Deng, X.; Eskandar, EN; Eden, UT, A point process approach to identifying and tracking transitions in neural spiking dynamics in the subthalamic nucleus of parkinson’s patients, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23, 046,102, (2013)
[14] Deng, X.; Liu, DF; Kay, K.; Frank, LM; Eden, UT, Clusterless decoding of position from multiunit activity using a marked point process filter, Neural Computation, 27, 1438-1460, (2015)
[15] Eden, UT; Frank, LM; Barbieri, R.; Solo, V.; Brown, EN, Dynamic analysis of neural encoding by point process adaptive filtering, Neural Computation, 16, 971-998, (2004) · Zbl 1054.92008
[16] Eden, U.T., Frank, L.M., Tao, L. (2018). Characterizing complex, multi-scale neural phenomena using state-space models. In Dynamic neuroscience (pp. 29-52). Springer.
[17] Gelfand, AE; Smith, AF, Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398-409, (1990) · Zbl 0702.62020
[18] Geman, S.; Geman, D., Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Transac- tions on Pattern Analysis and Machine Intelligence, 6, 721-741, (1984) · Zbl 0573.62030
[19] Georgopoulos, AP; Schwartz, AB; Kettner, RE, Neuronal population coding of movement direction, Science, 233, 1416-1419, (1986)
[20] Gerhard, F.; Haslinger, R.; Pipa, G., Applying the multivariate time-rescaling theorem to neural population models, Neural Computation, 23, 1452-1483, (2011) · Zbl 1217.92027
[21] Huang, Y.; Brandon, MP; Griffin, AL; Hasselmo, ME; Eden, UT, Decoding movement trajectories through a t-maze using point process filters applied to place field data from rat hippocampal region ca1, Neural Computation, 21, 3305-3334, (2009) · Zbl 1181.92009
[22] Jain, A.K., Xu, X., Ho, T.K., Xiao, F. (2002). Uniformity testing using minimal spanning tree. In Proceedings of the 16th international conference on pattern recognition, 2002 (Vol. 4, pp. 281-284). IEEE.
[23] Johnson, N., & Kotz, S. (1970). Distributions in statistics-continuous univariate distributions, 2nd edn. New York: Wiley. · Zbl 0213.21101
[24] Kass, RE; Ventura, V., A spike-train probability model, Neural Computation, 13, 1713-1720, (2001) · Zbl 0985.92017
[25] Kass, RE; Ventura, V.; Brown, EN, Statistical issues in the analysis of neuronal data, Journal of Neurophysiology, 94, 8-25, (2005)
[26] Kass, R.E., Eden, U.T., Brown, E.N. (2014). Analysis of neural data, Vol. 491. Springer. · Zbl 1404.62002
[27] Kloosterman, F.; Layton, SP; Chen, Z.; Wilson, MA, Bayesian decoding using unsorted spikes in the rat hippocampus, Journal of Neurophysiology, 111, 217-227, (2014)
[28] Macke, J.H., Buesing, L., Cunningham, J.P., Byron, M.Y., Shenoy, K.V., Sahani, M. (2011). Empirical models of spiking in neural populations. In Advances in neural information processing systems (pp. 1350-1358).
[29] Merzbach, E.; Nualart, D., A characterization of the spatial poisson process and changing time, Annals of Probability, 14, 1380-1390, (1986) · Zbl 0615.60047
[30] Meyer, P.A. (1971). Demonstration simplifiee d’un theoreme de knight. In Séminaire de probabilités v université de strasbourg (pp. 191-195). Springer.
[31] Ogata, Y., Statistical models for earthquake occurrences and residual analysis for point processes, Journal of the American Statistical Association, 83, 9-27, (1988)
[32] Paninski, L.; Pillow, J.; Lewi, J., Statistical models for neural encoding, decoding, and optimal stimulus design, Progress in Brain Research, 165, 493-507, (2007)
[33] Paninski, L., Brown, E.N., Iyengar, S., Kass, R.E. (2009). Statistical models of spike trains (pp. 278-303). Stochastic Methods in Neuroscience.
[34] Papangelou, F., Integrability of expected increments of point processes and a related random change of scale, Transactions of the American Mathematical Society, 165, 483-506, (1972) · Zbl 0236.60036
[35] Petrie, A.; Willemain, TR, An empirical study of tests for uniformity in multidimensional data, Computational Statistics & Data Analysis, 64, 253-268, (2013) · Zbl 1468.62159
[36] Pillow, JW; Shlens, J.; Paninski, L.; Sher, A.; Litke, AM; Chichilnisky, E.; Simoncelli, EP, Spatio-temporal correlations and visual signalling in a complete neuronal population, Nature, 454, 995-999, (2008)
[37] Port, S.C. (1994). Theoretical probability for applications, Vol. 206. Wiley-Interscience. · Zbl 0860.60001
[38] Prerau, MJ; Eden, UT, A general likelihood framework for characterizing the time course of neural activity, Neural Computation, 23, 2537-2566, (2011) · Zbl 1231.92024
[39] Ripley, BD, Modelling spatial patterns, Journal of the Royal Statistical Society. Series B (Methodological), 39, 172-212, (1977)
[40] Ross, S.M. (1996). Stochastic processes 1996. New York: Wiley.
[41] Shanechi, MM; Hu, RC; Powers, M.; Wornell, GW; Brown, EN; Williams, ZM, Neural population partitioning and a concurrent brain-machine interface for sequential motor function, Nature Neuroscience, 15, 1715-1722, (2012)
[42] Smith, AC; Brown, EN, Estimating a state-space model from point process observations, Neural Computation, 15, 965-991, (2003) · Zbl 1085.68651
[43] Sodkomkham, D.; Ciliberti, D.; Wilson, MA; Ki, Fukui; Moriyama, K.; Numao, M.; Kloosterman, F., Kernel density compression for real-time bayesian encoding/decoding of unsorted hippocampal spikes, Knowledge-Based Systems, 94, 1-12, (2016)
[44] Srinivasan, L.; Eden, UT; Willsky, AS; Brown, EN, A state-space analysis for reconstruction of goal-directed movements using neural signals, Neural Computation, 18, 2465-2494, (2006) · Zbl 1106.92017
[45] Truccolo, W.; Eden, UT; Fellows, MR; Donoghue, JP; Brown, EN, A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects, Journal of Neurophysiology, 93, 1074-1089, (2005)
[46] Vere-Jones, D.; Schoenberg, FP, Rescaling marked point processes, Australian & New Zealand Journal of Statistics, 46, 133-143, (2004) · Zbl 1078.60039
[47] Wu, S.; Si, A.; Nakahara, H., Population coding and decoding in a neural field: a computational study, Neural Computation, 14, 999-1026, (2002) · Zbl 0994.92011
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