加速迭代滤波

摘要：

在部分观测马尔可夫过程模型（POMP）的基于模拟的推断中，蒙特卡罗滤波的副产品是对数似然函数的近似。最近，迭代滤波[14，13]最初已经被引入，并且已经表明对数似然的梯度也可以近似。因此，可以应用不同的随机最优化算法来估计底层模型的参数。由于加速梯度是优化文献中的一种有效方法，我们证明了我们可以以相同的方式加速迭代滤波，并在放松无偏梯度近似的限制条件的同时继承了高收敛速度。我们表明，这种新的算法可以适用于凸和非凸的日志似然函数。此外，这种方法在玩具示例和传染病建模的挑战性科学问题中大大优于大多数其他先前的方法。

英文摘要：

In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been introduced and it has been shown that the gradient of the log likelihood can also be approximated. Consequently, different stochastic optimization algorithm can be applied to estimate the parameters of the underlying models. As accelerated gradient is an efficient approach in the optimization literature, we show that we can accelerate iterated filtering in the same manner and inherit that high convergence rate while relaxing the restricted conditions of unbiased gradient approximation. We show that this novel algorithm can be applied to both convex and non-convex log likelihood functions. In addition, this approach has substantially outperformed most of other previous approaches in a toy example and in a challenging scientific problem of modeling infectious diseases.

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