Hidden Markov Models for the Stimulus-Response Relationships of Multistate Neural Systems
Hidden Markov Models for the Stimulus-Response Relationships of Multistate Neural Systems
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DOI：
10.1162/neco_a_00118
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发表时间：
2011-05-01
影响因子：
2.9
通讯作者：
Paninski, Liam
中科院分区：
文献类型：
--
作者：
Escola, Sean;Fontanini, Alfredo;Paninski, Liam
鉴于最近的实验结果表明，神经电路可能会演变通过多个发射状态，我们开发了一个框架，估计状态依赖的神经响应特性的尖峰序列数据。我们修改了传统的隐马尔可夫模型（HMM）的框架，将刺激驱动，非泊松点过程的观察。为了获得最大的灵活性，我们允许外部时变刺激和神经元自身的尖峰历史来驱动每个状态中的尖峰行为和状态之间的过渡行为。我们采用适当修改的期望最大化算法来估计模型参数。期望步长由标准的HISTORY前向-后向算法求解。最大化步骤减少到一组可分离的凹优化问题，如果该模型是轻微的限制。我们首先在模拟数据上测试我们的算法，并且能够完全恢复用于生成数据的参数，并准确地概括隐藏状态的序列。然后，我们将我们的算法应用于最近发布的数据集，其中观察到的神经元集合显示多状态行为，并表明包含尖峰历史信息显着提高了模型的拟合度。此外，我们表明，一个简单的底层马尔可夫链的状态空间的重新制定，使我们能够实现一个混合的半多状态，半直方图模型，可能更适合捕捉某些数据集的复杂性比一个简单的HMM或一个简单的peristimulus时间直方图模型。
Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-varying stimuli and the neurons' own spike histories to drive both the spiking behavior in each state and the transitioning behavior between states. We employ an appropriately modified expectation-maximization algorithm to estimate the model parameters. The expectation step is solved by the standard forward-backward algorithm for HMMs. The maximization step reduces to a set of separable concave optimization problems if the model is restricted slightly. We first test our algorithm on simulated data and are able to fully recover the parameters used to generate the data and accurately recapitulate the sequence of hidden states. We then apply our algorithm to a recently published data set in which the observed neuronal ensembles displayed multistate behavior and show that inclusion of spike history information significantly improves the fit of the model. Additionally, we show that a simple reformulation of the state space of the underlying Markov chain allows us to implement a hybrid half-multistate, half-histogram model that may be more appropriate for capturing the complexity of certain data sets than either a simple HMM or a simple peristimulus time histogram model alone.