论文标题
通过非参数力矩方法，在州空间模型中无监督的观察功能学习
Unsupervised learning of observation functions in state-space models by nonparametric moment methods
论文作者
论文摘要
我们研究了非线性状态空间模型中对不可糊化的观察功能的无监督学习。假设观察过程的大量数据以及状态过程的分布，我们引入了一种非参数通用力矩方法，以通过约束回归来估计观察函数。主要的挑战来自观察函数的不可逆转性以及国家与观察之间缺乏数据对。我们解决了二次损失功能可识别性的基本问题，并表明可识别性的功能空间是闭合状态过程的RKHS。数值结果表明，前两个矩和时间相关以及上限和下限可以识别从分段多项式到平滑函数的功能，从而导致收敛估计器。还讨论了该方法的局限性，例如由于对称性和平稳性而引起的非识别性。
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.
