Abstract
Neural activity is noisy (“stochastic”) and dynamic at various spatiotemporal scales. We consider a general class of latent variable models for characterizing neuronal population dynamics or analyzing various sorts of neural data. The inference of latent variable models can lead to novel solutions for signal detection, neural decoding, denoising, dimensionality reduction, and data visualization. We review general modeling and inference strategies for latent variable models. Finally, we illustrate our methods with several neuroscience applications using population spike trains recorded from the animal’s hippocampus and neocortices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aghagolzadeh, M., & Truccolo, W. (2016). Inference and decoding of motor cortex low-dimensional dynamics via latent state-space models. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 24(2), 272–282.
Ames, K. C., Ryu, S. I., & Shenoy, K. V. (2014). Neural dynamics of reaching following incorrect or absent motor preparation. Neuron, 81(2), 438–451.
Beal, M., & Ghahramani, Z. (2006). Variational Bayesian learning of directed graphical models. Bayesian Analysis, 1(4), 793–832.
Buesing, L., Macke, J. H., & Sahani, M. (2012a). Learning stable, regularized latent models of neural population dynamics. Network: Computation in Neural Systems, 23, 24–47.
Buesing, L., Macke, J. H., & Sahani, M. (2012b). Spectral learning of linear dynamics from generalised-linear observations with application to neural population data. In Advances in neural information processing systems (Vol. 25, pp. 1682–1690). New York: Curran Associates.
Buonomano, D. V., & Laje, R. (2010). Population clocks: Motor timing with neural dynamics. Trends in Cognitive Science, 14, 520–527.
Bushnell, M. C., Ceko, M., & Low, L. A. (2013). Cognitive and emotional control of pain and its disruption in chronic pain. Nature Review Neuroscience, 14, 502–511.
Chen, Z. (2013). An overview of Bayesian methods for neural spike train analysis. Computational Intelligence and Neuroscience, 2013, 251905.
Chen, Z. (2015a). Estimating latent attentional states based on simultaneous binary and continuous behavioral measures. Computational Intelligence in Neuroscience, 2015, 493769.
Chen, Z. (Ed.). (2015b). Advanced state space methods in neural and clinical data. Cambridge: Cambridge University Press.
Chen, Z. (2017). Unfolding representations of trajectory coding in neuronal population spike activity. In Proceedings of Conference on Information Sciences and Systems (CISS’17).
Chen, Z., Barbieri, R., & Brown, E. N. (2010). State-space modeling of neural spike train and behavioral data. In K. Oweiss (Ed.), Statistical signal processing for neuroscience and neurotechnology (pp. 175–218). Amsterdam: Elsevier.
Chen, Z., Gomperts, S. N., Yamamoto, J., & Wilson, M. A. (2014). Neural representation of spatial topology in the rodent hippocampus. Neural Computation, 26(1), 1–39.
Chen, Z., Grosmark, A. D., Penagos, H., & Wilson, M. A. (2016a). Uncovering representations of sleep-associated hippocampal ensemble spike activity. Scientific Reports, 6, 32193.
Chen, Z., Hu, S., Zhang, Q., & Wang, J. (2017b). Quickest detection of abrupt changes in neuronal ensemble spiking activity using model-based and model-free approaches. In Proceedings of 8th International IEEE/EMBS Conference on Neural Engineering (NER).
Chen, G., King, J. A., Burgess, N., & O’Keefe, J. (2013). How vision and movement combine in the hippocampal place code. Proceedings of National Academy of Sciences USA, 110, 378–383.
Chen, Z., Kloosterman, F., Brown, E. N., & Wilson, M. A. (2012). Uncovering spatial topology represented by rat hippocampal population neuronal codes. Journal of Computational Neuroscience, 33(2), 227–255.
Chen, Z., Linderman, S., & Wilson, M. A. (2016b). Bayesian nonparametric methods for discovering latent structures of rat hippocampal ensemble spikes. In Proceedings of IEEE Workshop on Machine Learning for Signal Processing (pp. 1–6).
Chen, Z., & Wilson, M. A. (2017). Deciphering neural codes of memory during sleep. Trends in Neurosciences, 40(5), 260–275.
Chen, Z., Zhang, Q., Tong, A. P. S., Manders, T. R., & Wang, J. (2017a). Deciphering neuronal population codes for acute thermal pain. Journal of Neural Engineering, 14(3), 036023.
Ching, W.-K., Huang, X., Ng, M. K., & Siu, T.-K. (2015). Markov chains: Models, algorithms and applications (2nd ed.). Berlin: Springer.
Chung, J., Kastner, K., Dinh, L., Goel, K., Courville, A., & Bengio, Y. (2016). A Recurrent Latent Variable Model for Sequential Data. Technical report. https://arxiv.org/pdf/1506.02216.pdf
Churchland, M. M., Cunningham, J. P., Kaufman, M. T., Foster, J. D., Nuyujukian, P., Ryu, S. I., et al. (2012). Neural population dynamics during reaching. Nature, 487, 51–56.
Cunningham, J. P., & Yu, B. M. (2014). Dimensionality reduction for large-scale neural recordings. Nature Neuroscience, 17(11), 1500–1509.
Curto, C., & Itskov, V. (2008). Cell groups reveal structure of stimulus space. PLoS Computational Biology, 4(10), e1000205.
Dabaghian, Y., Cohn, A. G., & Frank, L. M. (2011). Topological coding in the hippocampus. In Computational modeling and simulation of intellect: Current state and future prospectives (pp. 293–320). Hershey: IGI Global.
Dabaghian, Y., Memoli, F., Frank, L. M., & Carlsson, G. (2012). A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS Computational Biology, 8(8), e1002581.
Dahl, G., Yu, D., Deng, L., & Acero, A. (2012). Context-dependent, pre-trained deep neural networks for large vocabulary speech recognition. IEEE Transactions on Audio, Speech & Language Processing, 20(1), 30–42.
Davidson, T. J., Kloostserman, F., & Wilson, M. A. (2009). Hippocampal replay of extended experience. Neuron, 63, 497–507.
Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39(1), 1–38.
Eden, U. T., Frank, L. M., Barbieri, R., Solo, V., & Brown, E. N. (2004). Dynamic analysis of neural encoding by point process adaptive filtering. Neural Computation, 16(5), 971–998.
Feeney, D. F., Meyer, F. G., Noone, N., & Enoka, R. M. (2017). A latent low-dimensional common input drives a pool of motor neurons: A probabilistic latent state-space model. Journal of Neurophysiology, 117, 1690–1701.
Fine, S., Singer, Y., & Tishby, N. (1998). The hierarchical hidden Markov model: Analysis and applications. Machine Learning, 32, 41–62.
Fuchs, P. N., Peng, Y. B., Boyette-Davis, J. A., & Uhelski, M. L. (2014). The anterior cingulate cortex and pain processing. Frontiers in Integrative Neuroscience, 8, 35.
Gao, Y., Archer, E., Paninski, L., & Cunningham, J. P. (2016). Linear dynamical neural population models through nonlinear embeddings. In Advances in Neural Information Processing Systems. New York: Curran Associates.
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC Press.
Gershman, S., & Blei, D. M. (2012). A tutorial on Bayesian nonparametric models. Journal of Mathematical Psychology, 56, 1–12.
Ghahramani, Z., & Jordan, M. I. (1997). Factorial hidden Markov models. Machine Learning, 29(2), 245–273.
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. Cambridge, MA: MIT Press.
Grosmark, A. D., & Buzsaki, G. (2016). Diversity in neural firing dynamics supports both rigid and learned hippocampal sequences. Science, 351, 1440–1443.
Guédon, Y. (2003). Estimating hidden semi-Markov chains from discrete sequences. Journal of Computational and Graphical Statistics, 12, 604–639.
Haggerty, D. C., & Ji, D. (2015a). Activities of visual cortical and hippocampal neurons co-fluctuate in freely-moving rats during spatial behavior. eLife, 4, e08902.
Haggerty, D. C., & Ji, D. (2015b). Coordinated sequence replays between the visual cortex and hippocampus. In M. Matsuno (Ed.), Analysis and modeling of coordinated multi-neuronal activity (pp. 183–206). New York: Springer.
Hu, S., Zhang, Q., Wang, J., & Chen, Z. (2017). A real-time rodent neural interface for deciphering acute pain signals from neuronal ensemble spike activity. In Proceedings of the 51st Asilomar Conference on Signals, Systems and Computers.
Hu, S., Zhang, Q., Wang, J., & Chen, Z. (2018). Real-time particle filtering and smoothing algorithms for detecting abrupt changes in neural ensemble spike activity. Journal of Neurophysiology, in press.
Ji, D., & Wilson, M. A. (2007). Coordinated memory replay in the visual cortex and hippocampus during sleep. Nature Neuroscience, 10, 100–107.
Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37, 183–233.
Jordan, M. I., & Sejnowski, T. J. (Eds.). (2001). Graphical models: Foundations of neural computation. Cambridge, MA: MIT Press.
Kuo, C. C., & Yen, C. T. (2005). Comparison of anterior cingulate and primary somatosensory neuronal responses to noxious laser-heat stimuli in conscious, behaving rats. Journal of Neurophysiology, 94, 1825–1836.
Kurihara, K., & Welling, M. (2009). Bayesian k-means as ‘maximization-expectation’ algorithm. Neural Computation, 21, 1145–1172.
Latimer, K. L., Yates, J. L., Meister, M. L. R., Huk, A. C., & Pillow, J. W. (2015). Single-trial spike trains in parietal cortex reveal discrete steps during decision-making. Science, 349, 184–187.
Lawhern, V., Wu, W., Hatsopoulos, N. G., & Paninski, L. (2010). Population decoding of motor cortical activity using a generalized linear model with hidden states. Journal of Neuroscience Methods, 189, 267–280.
LeCun, Y., Bengio, Y., & Hinton, G. E. (2015). Deep learning. Nature, 521, 436–444.
Lee, L.-M. (2011). High-order hidden Markov model and application to continuous mandarin digit recognition. Journal of Information Science and Engineering, 27(13), 1919–1930.
Linderman, S., Johnson, M. J., Wilson, M. A., & Chen, Z. (2016). A Bayesian nonparametric approach for uncovering rat hippocampal population codes during spatial navigation. Journal of Neuroscience Methods, 263, 36–47.
Liu, S., Grosmark, A. D., & Chen, Z. (2018). Methods for assessment of memory reactivation. Neural Computation, to appear.
Macke, J. H., Buesing, L., Cunningham, J. P., Yu, B. M., Shenoy, K. V., & Sahani, M. (2012). Empirical models of spiking in neural populations. In Advances in neural information processing systems (Vol. 24). New York: Curran Associates.
Michaels, J. A., Dann, B., & Scherberger, H. (2016). Neural population dynamics during reaching are better explained by a dynamical system than representational tuning. PLoS Computational Biology, 12(11), e1005175.
Müller, P., Quintana, F. A., Jara, A., & Hanson, T. (2015). Bayesian nonparametric data analysis. Cham: Springer.
O’Keefe, J., & Dostrovsky, J. (1971). The hippocampus as a spatial map: preliminary evidence from unit activity in the freely-moving rat. Brain Research, 34(1), 171–175.
O’Keefe, J., & Nadel, L. (1978). The hippocampus as a cognitive map. London: Oxford University Press.
Omigbodun, A., Doyle, W. K., Devinsky, O., & Gilja, V. (2016). Hidden-Markov factor analysis as a spatiotemporal model for electrocorticography. In Proceedings of IEEE Engineering in Medicine and Biology Conference (pp. 1632–1635).
Pachitariu, M., Petreska, B., & Sahani, M. (2013). Recurrent linear models of simultaneously-recorded neural populations. In L. Bottou, C. J. C. Burges, M. Welling, Z. Ghahramani & K. Q. Weinberger (Eds.), Advances in neural information processing systems (Vol. 26). New York: Curran Associates.
Pawitan, Y. (2001). In all likelihood: Statistical modeling and inference using likelihood. Oxford: Clarendon Press.
Penny, W., Ghahramani, Z., & Friston, K. (2005). Bilinear dynamical systems. Philosophical Transactions of Royal Society of London B: Biological Sciences, 360, 983–993.
Rivkind, A., & Barak, O. (2017). Local dynamics in trained recurrent neural networks. Physics Review Letter, 118, 258101.
Robert, C. P. (2007). The Bayesian choice: From decision-theoretic foundations to computational implementation (2nd ed.). Berlin: Springer.
Santhanam, G., Yu, B. M., Gija, V., Ryu, S. I., Afshar, A., Sahani, M., et al. (2009). Factor-analysis methods for higher-performance neural prostheses. Journal of Neurophysiology, 102(2), 1315–1330.
Saul, L. K., & Jordan, M. I. (1999). Mixed memory Markov models: Decomposing complex stochastic processes as mixtures of simpler ones. Machine Learning, 37, 75–86.
Saul, L. K., & Rahim, M. G. (2000). Markov processes on curves. Machine Learning, 41, 345–363.
Smith, A. C., & Brown, E. N. (2003). Estimating a state-space model from point process observations. Neural Computation, 15(5), 965–991.
Stevenson, I. H. (2016). Flexible models for spike count data with both over- and under-dispersion. Journal of Computational Neuroscience, 41, 29–43.
Székely, G. J., & Rizzo, M. L. (2009). Brownian distance covariance. Annals of Applied Statistics, 3/4, 1233–1303.
Teh, Y. W., Jordan, M. I., Beal, M. J., & Blei, D. M. (2006). Hierarchical Dirichlet processes. Journal of American Statistical Association, 101, 1566–1581.
Vierck, C. J., Whitsel, B. L., Favorov, O. V., Brown, A. W., & Tommerdahl, M. (2013). Role of primary somatosensory cortex in the coding of pains. Pain, 154, 334–344.
Vogelstein, J., Packer, A., Machado, T. A., Sippy, T., Babadi, B., Yuste, R., et al. (2010). Fast nonnegative deconvolution for spike train inference from population calcium imaging. Journal of Neurophysiology, 104, 3691–3704.
Vogelstein, J., Watson, B., Packer, A., Yuste, R., Jedynak, B., & Paninski, L. (2009). Spike inference from calcium imaging using sequential Monte Carlo methods. Biophysical Journal, 97(2), 636–655.
Wagner, T. D., Atlas, L. Y., Lindquist, M. A., Roy, M., Woo, C.-W., & Kross, E. (2013). An fMRI-based neurologic signature of physical pain. New England Journal of Medicine, 368, 1388–1397.
Whiteway, M. R., & Butts, D. A. (2017). Revealing unobserved factors underlying cortical activity with a rectified latent variable model applied to neural population recordings. Journal of Neurophysiology, 117, 919–936.
Wood, F., & Black, M. J. (2008). A nonparametric Bayesian alternative to spike sorting. Journal of Neuroscience Methods, 173(1), 1–12.
Wu, X., & Foster, D. (2014). Hippocampal replay captures the unique topological structure of a novel environment. Journal of Neuroscience, 34, 6459–6469.
Wu, W., Chen, Z., Gao, S., & Brown, E. N. (2011). A hierarchical Bayesian approach for learning sparse spatio-temporal decompositions of multichannel EEG. Neuroimage, 56(4), 1929–1945.
Wu, W., Kulkarni, J. E., Hatsopoulos, N. G., & Paninski, L. (2009). Neural decoding of hand motion using a linear state-space model with hidden states. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 17, 370–378.
Wu, W., Nagarajan, S., & Chen, Z. (2016). Bayesian machine learning: EEG/MEG signal processing measurements. IEEE Signal Processing Magazine, 33(1), 14–36.
Wu, W., & Srivastava, A. (2011). An information-geometric framework for statistical inferences in the neural spike train space. Journal of Computational Neuroscience, 31, 725–748.
Yu, B. M., Cunningham, J. P., Santhanam, G., Ryu, S. I., Shenoy, K. V., & Sahani, M. (2009). Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. Journal of Neurophysiology, 102(1), 614–635.
Yu, B. M., Kemere, C., Santhanam, G., Ryu, S. I., Meng, T. H., Sahani, M., et al. (2007). Mixture of trajectory models for neural decoding of goal-directed movements. Journal of Neurophysiology, 97, 3763–3780.
Yu, S.-Z. (2010). Hidden semi-Markov models. Artificial Intelligence, 174(2), 215–243.
Zhang, Y., Wang, N., Wang, J.-Y., Chang, J.-Y., Woodward, D. J., & Luo, F. (2011). Ensemble encoding of nociceptive stimulus intensity in the rat medial and lateral pain systems. Molecular Pain, 7, 64.
Zhao, Y., & Park, I. M. (2017). Variational latent Gaussian process for recovering single-trial dynamics from population spike trains. Neural Computation, 29, 1293–1316.
Zhou, F., De la Torre, F., & Hodgins, J. K. (2013). Hierarchical aligned cluster analysis for temporal clustering of human motion. IEEE Transactions Pattern Analysis and Machine Intelligence, 35(3), 582–596.
Acknowledgements
I would like to thank Emery N. Brown for the intellectual inspiration during my postdoctoral career and all coauthors who have contributed to previously published work. I also thank S.L. Hu and S.Z. Liu for assistance in preparing some figures. Reproduction of some copyrighted materials is granted from publishers. The work was partially supported by an NSF-CRCNS award IIS-1307645 from the US National Science Foundation and an NIH-CRCNS award R01-NS100065 from the NINDS.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Chen, Z. (2018). Latent Variable Modeling of Neural Population Dynamics. In: Chen, Z., Sarma, S.V. (eds) Dynamic Neuroscience. Springer, Cham. https://doi.org/10.1007/978-3-319-71976-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-71976-4_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71975-7
Online ISBN: 978-3-319-71976-4
eBook Packages: EngineeringEngineering (R0)