Unsupervised learning of observation functions in state space models by nonparametric moment methods

IF 1.7 Q2 MATHEMATICS, APPLIED
Qingci An, Yannis Kevrekidis, Fei Lu, Mauro Maggioni
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引用次数: 1

Abstract

We investigate the unsupervised learning of non-invertible observation functions in nonlinear state space models. Assuming abundant data of the observation process along with the distribution of the state process, we introduce a nonparametric generalized moment method to estimate the observation function via constrained regression. The major challenge comes from the non-invertibility of the observation function and the lack of data pairs between the state and observation. We address the fundamental issue of identifiability from quadratic loss functionals and show that the function space of identifiability is the closure of a RKHS that is intrinsic to the state process. Numerical results show that the first two moments and temporal correlations, along with upper and lower bounds, can identify functions ranging from piecewise polynomials to smooth functions, leading to convergent estimators. The limitations of this method, such as non-identifiability due to symmetry and stationarity, are also discussed.
非参数矩法在状态空间模型中观测函数的无监督学习
研究了非线性状态空间模型中不可逆观测函数的无监督学习问题。假设观测过程数据丰富,且状态过程分布均匀,采用非参数广义矩法对观测函数进行约束回归估计。主要的挑战来自于观测函数的不可逆性以及状态和观测之间缺乏数据对。我们从二次损失函数中解决了可辨识性的基本问题,并证明了可辨识性的函数空间是状态过程固有的RKHS的闭包。数值结果表明,前两个矩和时间相关以及上界和下界可以识别从分段多项式到光滑函数的函数,从而得到收敛估计量。本文还讨论了该方法的局限性,如对称性和平稳性所导致的不可识别性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
3.30
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0.00%
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