IEEE Trans Cybern. 2020 Mar;50(3):1347-1354. doi: 10.1109/TCYB.2018.2871144. Epub 2018 Oct 3.
Hidden Markov models (HMMs) underpin the solution to many problems in computational neuroscience. However, it is still unclear how to implement inference of HMMs with a network of neurons in the brain. The existing methods suffer from the problem of being nonspiking and inaccurate. Here, we build a precise equivalence between the inference equation of HMMs with time-invariant hidden variables and the dynamics of spiking winner-take-all (WTA) neural networks. We show that the membrane potential of each spiking neuron in the WTA circuit encodes the logarithm of the posterior probability of the hidden variable in each state, and the firing rate of each neuron is proportional to the posterior probability of the HMMs. We prove that the time course of the neural firing rate can implement posterior inference of HMMs. Theoretical analysis and experimental results show that the proposed WTA circuit can get accurate inference results of HMMs.
隐马尔可夫模型（HMMs）是计算神经科学中许多问题的解决方案的基础。然而，目前尚不清楚如何在大脑中的神经元网络中实现 HMM 的推断。现有的方法存在非尖峰和不准确的问题。在这里，我们建立了隐马尔可夫模型（HMMs）与具有时不变隐藏变量的推断方程和尖峰胜者通吃（WTA）神经网络动力学之间的精确等价关系。我们表明，WTA 电路中每个尖峰神经元的膜电位编码每个状态中隐藏变量的后验概率的对数，并且每个神经元的放电率与 HMM 的后验概率成正比。我们证明了神经元放电率的时间过程可以实现 HMM 的后验推断。理论分析和实验结果表明，所提出的 WTA 电路可以得到 HMM 的准确推断结果。
