Deep FPF: Gain function approximation in high-dimensional setting
Deep FPF: Gain function approximation in high-dimensional setting
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Deep FPF：高维设置中的增益函数近似
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
P. Mehta
中科院分区：
文献类型：
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作者：
S. Y. Olmez;A. Taghvaei;P. Mehta
提出了一种逼近反馈粒子滤波(FPF)增益函数的新方法。精确的增益函数是包含概率加权拉普拉斯的泊松方程的解。数值问题是利用从概率分布中抽取的有限个粒子来逼近精确的增益函数，受最近深度学习方法的成功启发，我们将增益函数表示为神经网络输出的梯度。在此基础上，考虑泊松方程的某种变分形式，提出了学习神经网络权值的优化问题。为此，提出了一种随机梯度算法。该方法具有两个显著的性质/优点：(1)随机优化算法只允许并行处理一批样本(粒子)，并保证随粒子数量的变化具有良好的标度特性；(2)神经网络的显著表示能力意味着该算法在解决高维问题方面具有潜在的适用性和实用性。我们用数值方法建立了这两个性质，并与现有的方法进行了广泛的比较。
In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem is to approximate the exact gain function using only finitely many particles sampled from the probability distribution.Inspired by the recent success of the deep learning methods, we represent the gain function as a gradient of the output of a neural network. Thereupon considering a certain variational formulation of the Poisson equation, an optimization problem is posed for learning the weights of the neural network. A stochastic gradient algorithm is described for this purpose.The proposed approach has two significant properties/advantages: (i) The stochastic optimization algorithm allows one to process, in parallel, only a batch of samples (particles) ensuring good scaling properties with the number of particles; (ii) The remarkable representation power of neural networks means that the algorithm is potentially applicable and useful to solve high-dimensional problems. We numerically establish these two properties and provide extensive comparison to the existing approaches.
反馈粒子滤波器中基于扩散图的增益函数逼近算法
DOI：
10.1137/19m124513x
发表时间：
2020
期刊：
SIAM/ASA Journal on Uncertainty Quantification
影响因子：
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作者：
Taghvaei, Amirhossein;Mehta, Prashant G.;Meyn, Sean P.
通讯作者：
Meyn, Sean P.