Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-12T09:07:35.138Z Has data issue: false hasContentIssue false

Probabilistic approaches to uncover rat hippocampal population codes

from Part I - State space methods for neural data

Published online by Cambridge University Press:  05 October 2015

Z. Chen
Affiliation:
New York University
F. Kloosterman
Affiliation:
IMEC
M. A. Wilson
Affiliation:
Massachusetts Institute of Technology
Zhe Chen
Affiliation:
New York University
Get access

Summary

Background

In the neocortex, information is represented by patterns of spike activity occurring over populations of neurons. A fundamental task in neuroscience is to understand how the information is encoded and transmitted in neural population activity. In comparison with the single unit activity, population activity is more information rich and robust in representation.With the advancement of multielectrode array and imaging technologies, neuroscientists have been able to record a large population of neurons at a fine temporal and spatial resolution. In the past few decades, probabilistic modeling and Bayesian methods have become increasingly popular in the analysis of neural codes (Ma et al. 2006; Yu et al. 2007, 2009; Kemere et al. 2008; Gerwinn et al. 2009; Pillow et al. 2011).

State space analyses (Chen et al. 2010, 2013) provides a powerful framework for modeling temporal neuronal dynamics and behavior. The state space model (SSM) consists of two basic equations. The state equation characterizes the dynamics of latent state variable, which is either known or modeled by prior knowledge. The observation equation captures the likelihood of the observations conditional on the latent state and other observed variables. Chapters 1 and 2 of this volume provide a detailed account of the mathematical framework.

In this chapter, we present two examples of state space analysis of rat hippocampal population codes. The first example is aimed to decode unsorted neuronal spikes, and the second example is aimed to uncover hippocampal population codes using a hidden Markov model (HMM). The common idea is to use probabilistic modeling and Bayesian inference to discover spatiotemporal structures of hippocampal ensemble spike activity.

Decode unsorted neuronal spikes from the rat hippocampus

Overview

Despite rapid progresses in the field of neural decoding, several challenges still remain: First, it is not clear how the spiking activity of individual neurons can reliably represent information. This is often reflected by complex neuronal tuning curves, which are poorly described by simple parametric models. Second, most population decoding methods are based on sorted single units, which will inevitably suffer from various spike-sorting errors, especially in the presence of few wires or probes (Wehr et al. 1999; Harris et al. 2000; Wood et al. 2004; Won et al. 2007).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barbieri, R., Frank, L. M., Nguyen, D. P., Quirk, M. C., Solo, V., Wilson, M. A. & Brown, E. N. (2004). Dynamic analyses of information encoding in neural ensembles. Neural Computation 16(2), 277–307.Google Scholar
Beal, M. J., Ghahramani, Z. & Rasmussen, C. E. (2002). The infinite hidden Markov model. In Advances in Neural Information Processing Systems 14, Cambridge, MA: MIT Press, pp. 577–585.
Beal, M. J. & Ghahramani, Z. (2006). Variational Bayesian learning of directed graphical models. Bayesian Analysis 1, 793–832.Google Scholar
Brown, E. N., Frank, L. M., Tang, D., Quirk, M. C. & Wilson, M. A. (1998). 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.Google Scholar
Carr, M. F., Jadhav, S. P. & Frank, L. M. (2011). Hippocampal replay in the awake state: a potential physiological substrate of memory consolidation and retrieval. Nature Neuroscience 14, 147–153.Google Scholar
Chen, Z. (2013). An overview of Bayesian methods for neural spike train analysis. Computational Intelligence and Neuroscience 2013, doi:10.1155/2013/251905.Google Scholar
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, Amsterdam: Elsevier, pp. 175–218.
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.Google Scholar
Chen, Z., Kloosterman, F., Brown, E. N. & Wilson, M. A. (2012b). Uncovering spatial topology represented by rat hippocampal population neuronal codes. Journal of Computational Neuroscience 33(2), 227–255.Google Scholar
Chen, Z., Kloosterman, F., Layton, S. & Wilson, M. A. (2012a). Transductive neural decoding for unsorted neuronal spikes of rat hippocampus. In Proceedings of IEEE Conference on Engineering in Medicine and Biology, pp. 1310–1313.Google Scholar
Curto, C. & Itskov, V. (2008). Cell groups reveal structure of stimulus space. PLoS Computational Biology 4(10), e1000205.Google Scholar
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, IGI Global, pp. 293–320.Google Scholar
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.Google Scholar
Doucet, A., de Freitas, N. & Gordon, N. (2001). Sequential Monte Carlo Methods in Practice, Berlin: Springer-Verlag.
Filippone, M. & Sanguinetti, G. (2011). Approximate inference of the bandwidth in multivariate kernel density estimation. Computational Statistics and Data Analysis 55, 3104–3122.Google Scholar
Fraser, G. W., Chase, S. M., Whitford, A. & Schwartz, A. B. (2009). Control of a brain-computer interface without spike sorting. Journal of Neural Engineering 6(5), 055004.Google Scholar
Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D. B. (2004). Bayesian Data Analysis, 2nd edn, London: Chapman & Hall/CRC Press.
Gerwinn, S., Macke, J. & Bethge, M. (2009). Bayesian population decoding of spiking neurons. Frontiers in Computational Neuroscience 3, 14.Google Scholar
Gray, A. G. & Moore, A. W. (2001). N-body problems in statistical learning. In T. K., Leen, T.G., Dietterich & V., Tresp, eds, Advances in Neural Information Processing Systems 13, Cambridge, MA: MIT Press, pp. 521–527.
Gray, A. G. & Moore, A. W. (2003). Nonparametric density estimation: toward computational tractability. In Proceedings of the Third SIAM International Conference on Data Mining, pp. 203–211.Google Scholar
Greengard, L. & Strain, J. (1991). The fast Gauss transform. SIAM Journal on Scientific and Statistical Computing 12(1), 79–94.
Harris, K. D., Henze, D. A., Csicsvari, J., Hirase, H. & Buzsáki, G. (2000). Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. Journal of Neurophysiology 84(1), 401–414.Google Scholar
Ji, D. & Wilson, M. A. (2007). Coordinated memory replay in the visual cortex and hippocampus during sleep. Nature Neuroscience 10, 100–107.Google Scholar
Johnson, M. J. & Willsky, A. S. (2013). Bayesian nonparametric hidden semi-Markov models. Journal of Machine Learning Research 14, 673–701.Google Scholar
Kemere, C., Santhanam, G., Yu, B. M., Afshar, A., Ryu, S. I., Meng, T. H. & Shenoy, K. V. (2008). Detecting neural-state transition using hidden Markov models for motor cortical prostheses. Journal of Neurophysiology 100, 2441–2452.Google Scholar
Kloosterman, F., Layton, S., Chen, Z. & Wilson, M. A. (2014). Bayesian decoding of unsorted spikes in the rat hippocampus. Journal of Neurophysiology 111(1), 217–227.Google Scholar
Kristan, M., Leonardis, A. & Skocaj, D. (2011). Multivariate online kernel density estimation with Gaussian kernels. Pattern Recognition 44, 2630–2642.Google Scholar
Kudrimoti, H. S., Barnes, C. A. & McNaughton, B. L. (1999). Reactivation of hippocampal cell assemblies: effects of behavioral state, experience, and EEG dynamics. Journal of Neuroscience 19, 4090–4101.Google Scholar
Lee, A. K. & Wilson, M. A. (2002). Memory of sequential experience in the hippocampus during slow wave sleep. Neuron 36, 1183–1194.Google Scholar
Lee, D., Gray, A. G. & Moore, A.W. (2007). Dual-tree fast Gauss transforms. In Y., Weiss, B., Schölkopf & J. P., Platt, eds, Advances in Neural Information Processing Systems 18, Cambridge, MA: MIT Press, pp. 747–754.
Linderman, S., Johnson, M. J., Wilson, M. A. & Chen, Z. (2014). A nonparametric bayesian approach for uncovering rat hippocampal population codes during spatial navigation. Annals of Applied Statistics, arxiv.org/pdf/1411.7706v1.pdf.Google Scholar
Louie, K. & Wilson, M. A. (2001). Temporally structured REM sleep replay of awake hippocampal ensemble activity. Neuron 29, 145–156.Google Scholar
Ma, W. J., Beck, J. M., Latham, P. E. & Pouget, A. (2006). Bayesian inference with probabilistic population codes. Nature Neuroscience 9, 1432–1438.Google Scholar
McGrory, C. A. & Titterington, D. M. (2009). Variational Bayesian analysis for hidden Markov models. Australian & New Zealand Journal of Statistics 51(2), 227–244.Google Scholar
Morariu, V. I., Srinivasan, B. V., Raykar, V. C., Duraiswami, R. & Davis, L. S. (2009). Automatic online tuning for fast Gaussian summation. In D., Koller, D., Schuurmans, Y., Bengio & L., Bottou, eds, Advances in Neural Information Processing Systems, Cambridge, MA: MIT Press, pp. 1113–1120.
O'Keefe, J. & Nadel, L. (1978). The Hippocampus as a Cognitive Map, London: Oxford University Press.
Paisley, J. & Carin, L. (2009). Hidden Markov models with stick breaking priors. IEEE Transactions on Signal Processing 57(10), 3905–3917.Google Scholar
Pillow, J. W., Ahmadian, Y. & Paninski, L. (2011). Model-based decoding, information estimation, and change-point detection techniques for multineuron spike trains. Neural Computation 23(1), 1–45.Google Scholar
Silverman, B. (1986). Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.
Snyder, D. L. & Miller, M. I. (1991). Random Point Processes in Time and Space, Berlin: Springer-Verlag.
Streit, R. L. (2010). Poisson Point Processes: Imaging, Tracking, and Sensing, Berlin: Springer-Verlag.
Teh, Y. W., Jordan, M. I., Beal, M. J. & Blei, D.M. (2006). Hierarchical Dirichlet processes. Journal of American Statistical Association 101, 1566–1581.Google Scholar
Ventura, V. (2008). Spike train decoding without spike sorting. Neural Computation 20(4), 923–963.Google Scholar
Wand, M. P. & Jones, M. C. (1995). Kernel Smoothing, London: Chapman & Hall/CRC.
Wehr, M., Pezaris, J. & Sahani, M. (1999). Simultaneous paired intracellular and tetrode recordings for evaluating the performance of spike sorting algorithms. Neurocomputing 26, 1061–1068.Google Scholar
Wilson, M. A. & McNaughton, B. L. (1994). Reactivation of hippocampal ensemble memories during sleep. Science 265, 676–679.Google Scholar
Won, D. S., Tiesinga, P. H. E., Henriquez, C. S. & Wolf, P. D. (2007). An analytical comparison of the information in sorted and non-sorted cosine-tuned spike activity. Journal of Neural Engineering 4(3), 322–335.Google Scholar
Wood, F. & Black, M. J. (2008). A non-parametric Bayesian alternative to spike sorting. Journal of Neuroscience Methods 173, 1–12.Google Scholar
Wood, F., Black, M. J., Vargas-Irwin, C., Fellows, M. & Donoghue, J. P. (2004). On the variability of manual spike sorting. IEEE Transactions on Biomedical Engineering 51(6), 912–918.Google Scholar
Yang, C., Duraiswami, R. & Davis, L. (2005). Efficient kernel machines using the improved fast Gauss transform. In L. K., Saul, Y., Weiss & L., Bottou, eds, Advances in Neural Information Processing Systems 17, Cambridge, MA: MIT Press, pp. 1561–1568.
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.Google Scholar
Yu, B.M., Kemere, C., Santhanam, G., Ryu, S. I., Meng, T. H., Sahani, M. & Shenoy, K.V. (2007). Mixture of trajectory models for neural decoding of goal-directed movements. Journal of Neurophysiology 97, 3763–3780.Google Scholar
Zhang, K., Ginzburg, I., McNaughton, B. L. & Sejnowski, T. J. (1998). Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. Journal of Neurophysiology 79(2), 1017–1044.Google Scholar
Ziv, Y., Burns, L. D., Cocker, E. D., Hamel, E. O., Ghosh, K. K., Kitch, L. J., Gamal, A. E. & Schnitzer, M. J. (2013). Long-term dynamics of CA1 hippocampal place codes. Nature Neuroscience 16, 264–266.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×