Kernel-based probability measures for data analysis

Time: 2019-10-21 17:43:39

● The kernel-based probability measures provide a numerical tool to construct the estimators for interpolations and collocations.

● The main idea of the new kernel-based algorithms is to solve a deterministic problem by a stochastic approach.

● All algorithms and theorems are the deterministic representations including the conditions and the conclusions.

● The theory of stochastic analysis are used in the proofs of the algorithms and theorems such as the Bayesian estimation, the Skorokhod's representation theorem, the Portmanteau theorem, the structure theorem of Gaussian measures, and etc.

References：

1. Qi Ye. Kernel-based probability measures for generalized interpolations: A deterministic or stochastic problem? Journal of Mathematical Analysis and Applications, 477(1), 420-436, 2019. DOI: 10.1016/j.jmaa.2019.04.039

2. Qi Ye. Kernel-based probability measures for interpolations. Applied and Computational Harmonic Analysis, 47(1), 226-234, 2019. DOI: 10.1016/j.acha.2018.07.002