Training Image Free High-Order Stochastic Simulation Based on Aggregated Kernel Statistics
| Autor: | Michel Gamache, Lingqing Yao, Roussos Dimitrakopoulos |
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| Rok vydání: | 2021 |
| Předmět: |
Computer science
0207 environmental engineering Sample (statistics) 02 engineering and technology 010502 geochemistry & geophysics 01 natural sciences Article Mathematics (miscellaneous) Stochastic simulation Statistical inference Kernel space 020701 environmental engineering Spatial analysis 0105 earth and related environmental sciences Spatial statistics business.industry Pattern recognition Conditional probability distribution High-order sequential simulation Statistical learning Moment (mathematics) Kernel (statistics) General Earth and Planetary Sciences Probability distribution Artificial intelligence business |
| Zdroj: | Mathematical Geosciences |
| ISSN: | 1874-8953 1874-8961 |
| DOI: | 10.1007/s11004-021-09923-3 |
| Popis: | A training image free, high-order sequential simulation method is proposed herein, which is based on the efficient inference of high-order spatial statistics from the available sample data. A statistical learning framework in kernel space is adopted to develop the proposed simulation method. Specifically, a new concept of aggregated kernel statistics is proposed to enable sparse data learning. The conditioning data in the proposed high-order sequential simulation method appear as data events corresponding to the attribute values associated with the so-called spatial templates of various geometric configurations. The replicates of the data events act as the training data in the learning framework for inference of the conditional probability distribution and generation of simulated values. These replicates are mapped into spatial Legendre moment kernel spaces, and the kernel statistics are computed thereafter, encapsulating the high-order spatial statistics from the available data. To utilize the incomplete information from the replicates, which partially match the spatial template of a given data event, the aggregated kernel statistics combine the ensemble of the elements in different kernel subspaces for statistical inference, embedding the high-order spatial statistics of the replicates associated with various spatial templates into the same kernel subspace. The aggregated kernel statistics are incorporated into a learning algorithm to obtain the target probability distribution in the underlying random field, while preserving in the simulations the high-order spatial statistics from the available data. The proposed method is tested using a synthetic dataset, showing the reproduction of the high-order spatial statistics of the sample data. The comparison with the corresponding high-order simulation method using TIs emphasizes the generalization capacity of the proposed method for sparse data learning. |
| Databáze: | OpenAIRE |
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