Gaussian process based nonlinear latent structure discovery in multivariate spike train data
Gaussian process based nonlinear latent structure discovery in multivariate spike train data
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发表时间：
2017
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通讯作者：
Anqi Wu;Nicholas A. Roy;Stephen L. Keeley;Jonathan W. Pillow
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作者：
Anqi Wu;Nicholas A. Roy;Stephen L. Keeley;Jonathan W. Pillow
最近的大量工作集中在从多神经元棘波训练数据中提取低维潜在结构的方法。大多数这样的方法要么使用线性潜在动力学，要么使用来自潜在空间的线性映射来记录尖峰率。在这里，我们提出了一个双重非线性潜变量模型，它可以识别明显高维的棘波序列数据背后的低维结构。我们介绍了泊松-高斯过程潜变量模型(P-GPLVM)，它由泊松尖峰观测和两个潜在的高斯过程组成--一个控制一个时间潜变量，另一个控制一组非线性调谐曲线。使用非线性调谐曲线能够发现低维潜在结构，即使当棘波反应表现出高线性维度(例如，如在海马区细胞编码中发现的)时也是如此。为了从数据中学习模型，我们引入了解耦拉普拉斯近似，这是一种快速的近似推理方法，允许我们有效地优化潜在路径，同时对调谐曲线进行边际化。结果表明，该方法在收敛速度和精度上均优于以往的基于拉普拉斯近似的推理方法。我们将该模型应用于从海马区细胞记录的棘波训练，结果表明，该模型在潜在结构发现方面优于以往的各种方法，包括基于变分自动编码器(VAE)的方法，该方法使用深度神经网络来参数化从潜在空间到棘波频率的非线性映射。
A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes-one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes). To learn the model from data, we introduce the decoupled Laplace approximation, a fast approximate inference method that allows us to efficiently optimize the latent path while marginalizing over tuning curves. We show that this method outperforms previous Laplace-approximation-based inference methods in both the speed of convergence and accuracy. We apply the model to spike trains recorded from hippocampal place cells and show that it compares favorably to a variety of previous methods for latent structure discovery, including variational auto-encoder (VAE) based methods that parametrize the nonlinear mapping from latent space to spike rates with a deep neural network.