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We develop a Bayesian point process modeling generalization of convolutive nonnegative matrix factorization, which was recently used by Peter et al and Mackevicius et al to model neural sequences

Point process models for sequence detection in high-dimensional neural spike trains

NIPS 2020, (2020)

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摘要

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising recent work utilized a convolutive nonnegative matrix factorization model to tackle this challenge. Ho...更多
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简介
  • Identifying interpretable patterns in multi-electrode recordings is a longstanding and increasingly pressing challenge in neuroscience.
  • Neural sequences are an important example of high-dimensional structure: if N neurons fire sequentially with no overlap, the resulting dynamics are N -dimensional and cannot be efficiently summarized by PCA or other linear dimensionality reduction methods [4].
  • Such sequences underlie current theories of working memory [1, 25], motor production [2], and memory replay [10].
  • Sequence type probabilities The conditional distribution of the sequence type probability vector π is, p(π | {(rk, τk, Ak)}Kk=∗1, ξ) ∝ Dir(π | γ1R) Cat(rk | π) (83)
重点内容
  • Identifying interpretable patterns in multi-electrode recordings is a longstanding and increasingly pressing challenge in neuroscience
  • We develop a Bayesian point process modeling generalization of convolutive nonnegative matrix factorization, which was recently used by Peter et al [8] and Mackevicius et al [4] to model neural sequences
  • Our Contributions We propose a point process model for neural sequences (PP-Seq) which extends and generalizes convolutive nonnegative matrix factorization (convNMF) to continuous time and uses a fully probabilistic Bayesian framework
  • We treat held-out spikes as missing data and sample them as part of the Markov chain Monte Carlo (MCMC) algorithm. (Their conditional distribution is given by the PP-Seq generative model.) This approach involving a speckled holdout pattern and multiple imputation of missing data may be viewed as a continuous time extension of the methods proposed by Mackevicius et al [27] for convNMF
  • We proposed a point process model (PP-Seq) inspired by convolutive NMF [4, 8, 9] to identify neural sequences
  • PP-Seq is formulated in a probabilistic framework that better quantifies uncertainty and handles low firing rate regimes (see fig
方法
  • The authors evaluate model performance by computing the log-likelihood assigned to held-out data.
  • (Their conditional distribution is given by the PP-Seq generative model.) This approach involving a speckled holdout pattern and multiple imputation of missing data may be viewed as a continuous time extension of the methods proposed by Mackevicius et al [27] for convNMF.
  • The likelihood of the train and test sets improves over the course of MCMC sampling, and can be used as a metric for model comparison—in agreement with the ground truth, test performance plateaus for models containing greater than R = 2 sequence types
结果
  • The authors further improve performance by interspersing “split-merge” Metropolis-Hastings updates [51, 52] between Gibbs sweeps.
  • The authors can improve performance substantially by parallelizing the computation [53]
结论
  • The authors proposed a point process model (PP-Seq) inspired by convolutive NMF [4, 8, 9] to identify neural sequences.
  • 25 s introduction of time warping, as well as other possibilities like truncated sequences and “clusterless” observations [57], which could be explored in future work
  • Despite these benefits, fitting PP-Seq involves a tackling a challenging trans-dimensional inference problem inherent to Neyman-Scott point processes.
  • These innovations are sufficient to fit PP-Seq on datasets containing hundreds of thousands of spikes in just a few minutes on a modern laptop
基金
  • A.H.W. received funding support from the National Institutes of Health BRAIN initiative (1F32MH122998-01), and the Wu Tsai Stanford Neurosciences Institute Interdisciplinary Scholar Program
  • S.W.L. was supported by grants from the Simons Collaboration on the Global Brain (SCGB 697092) and the NIH BRAIN Initiative (U19NS113201 and R01NS113119)
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作者
Anthony Degleris
Anthony Degleris
Yixin Wang
Yixin Wang
Scott Linderman
Scott Linderman
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