论文标题
Monte Carlo扭曲粒子过滤器
Monte Carlo twisting for particle filters
论文作者
论文摘要
我们考虑为扭曲的Feynman-KAC模型设计有效的粒子过滤器的问题。使用扭曲模型的粒子过滤器可以提供统计量的低误差近似值，并且可以迭代地学习此类扭曲功能。这些算法的实际实现使得（i）从扭曲过渡动力学中进行样本以及（ii）计算扭曲的电势函数变得复杂。我们使用（i）的拒绝采样和（ii）使用随机权重粒子滤波器扩展了适用模型的类别。我们表征了粒子滤波器内的平均接受率，以控制计算成本并分析渐近方差。经验结果表明，我们方法中归一化恒定估计值的平方平方误差小于内存等效粒子滤波器，而不是计算等效过滤器。当可能的采样效率更高时，我们在随机波动率模型上证明了这两种比较。
We consider the problem of designing efficient particle filters for twisted Feynman--Kac models. Particle filters using twisted models can deliver low error approximations of statistical quantities and such twisting functions can be learnt iteratively. Practical implementations of these algorithms are complicated by the need to (i) sample from the twisted transition dynamics, and (ii) calculate the twisted potential functions. We expand the class of applicable models using rejection sampling for (i) and unbiased approximations for (ii) using a random weight particle filter. We characterise the average acceptance rates within the particle filter in order to control the computational cost, and analyse the asymptotic variance. Empirical results show the mean squared error of the normalising constant estimate in our method is smaller than a memory-equivalent particle filter but not a computation-equivalent filter. Both comparisons are improved when more efficient sampling is possible which we demonstrate on a stochastic volatility model.
