Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant to AD techniques because widely used particle filter algorithms yield an estimated likelihood function that is discontinuous as a function of the model parameters. We show how to embed two existing AD particle filter methods in a theoretical framework that provides an extension to a new class of algorithms. This new class permits a bias/variance tradeoff and hence a mean squared error substantially lower than the existing algorithms. We develop likelihood maximization algorithms suited to the Monte Carlo properties of the AD gradient estimate. Our algorithms require only a differentiable simulator for the latent dynamic system; by contrast, most previous approaches to AD likelihood maximization for particle filters require access to the system's transition probabilities. Numerical results indicate that a hybrid algorithm that uses AD to refine a coarse solution from an iterated filtering algorithm show substantial improvement on current state-of-the-art methods for a challenging scientific benchmark problem.

翻译：自动微分（AD）推动了机器学习领域的最新进展，包括深度神经网络和哈密顿马尔可夫链蒙特卡洛方法。部分可观测非线性随机动力系统已被证明对AD技术具有抵抗性，因为广泛使用的粒子滤波算法产生的似然函数估计值在模型参数上是非连续的。我们展示了如何将两种现有的AD粒子滤波方法嵌入到一个理论框架中，该框架可扩展至一类新算法。这类新算法允许进行偏差/方差权衡，从而获得比现有算法显著更低的均方误差。我们开发了适用于AD梯度估计蒙特卡洛特性的似然最大化算法。我们的算法仅需潜在动态系统的可微分模拟器；相比之下，先前大多数针对粒子滤波的AD似然最大化方法需要获取系统的转移概率。数值结果表明，采用AD对迭代滤波算法得到的粗解进行优化的混合算法，在一个具有挑战性的科学基准问题上相比当前最先进方法展现出显著改进。