论文标题
从总体观察中学习隐藏的马尔可夫模型
Learning Hidden Markov Models from Aggregate Observations
论文作者
论文摘要
在本文中，我们提出了一种算法，用于估算从骨料观测值的时间均匀隐藏的马尔可夫模型的参数。当只有每个时间步骤的个体数量的人口数量计数时，就会出现这个问题，人们试图从中学习个人隐藏的马尔可夫模型。我们的算法建立在期望最大化和最近提出的总体推理算法（sindhorn信仰传播）的基础上。与现有的方法（例如期望最大化的方法）和非线性信念传播相比，我们的算法表现出融合的保证。此外，当记录与单个个体相对应的观察值时，我们的学习框架自然会减少到标准的鲍姆 - 沃尔奇学习算法。我们进一步扩展了学习算法以通过连续观察来处理HMM。我们的算法的功效在各种数据集上得到了证明。
In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time step are available, from which one seeks to learn the individual hidden Markov model. Our algorithm is built upon expectation-maximization and the recently proposed aggregate inference algorithm, the Sinkhorn belief propagation. As compared with existing methods such as expectation-maximization with non-linear belief propagation, our algorithm exhibits convergence guarantees. Moreover, our learning framework naturally reduces to the standard Baum-Welch learning algorithm when observations corresponding to a single individual are recorded. We further extend our learning algorithm to handle HMMs with continuous observations. The efficacy of our algorithm is demonstrated on a variety of datasets.
