• Corpus ID: 226956076

An exact kernel framework for spatio-temporal dynamics

@article{Szehr2020AnEK,
  title={An exact kernel framework for spatio-temporal dynamics},
  author={Oleg Szehr and Dario Azzimonti and Laura Azzimonti},
  journal={arXiv: Statistics Theory},
  year={2020}
}
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves time-dependent kernels. Such kernels occur commonly in the expansion of solutions of partial differential equations. The representer theorem is applied to find among all solutions of a dynamic equation the one that minimizes the error with given spatio-temporal samples… 

References

SHOWING 1-10 OF 27 REFERENCES
A general science-based framework for dynamical spatio-temporal models
Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time.
Kernel density estimation via diffusion
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a
Kernel Mean Estimation and Stein Effect
TLDR
Focusing on a subset of this class of estimators, this work proposes efficient shrinkage estimators for the kernel mean that can be improved due to a well-known phenomenon in statistics called Stein's phenomenon.
When is there a representer theorem? Vector versus matrix regularizers
TLDR
This paper provides a necessary and sufficient condition characterizing this class of matrix regularizers and it is proved the necessity of the above condition, in the case of differentiable regularizers.
A Hilbert Space Embedding for Distributions
We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert
An introduction to stochastic processes with applications to biology
Review of Probability Theory and an Introduction to Stochastic Processes Introduction Brief Review of Probability Theory Generating Functions Central Limit Theorem Introduction to Stochastic
Tobler's First Law and Spatial Analysis
‘‘ I invoke the first law of geography: everything is related to everything else, but near things are more related than distant things’’ (Tobler 1970). How could a sentence justifying heuristic
Direct meshless kernel techniques for time-dependent equations
We provide a class of positive definite kernels that allow to solve certain evolution equations of parabolic type for scattered initial data by kernel-based interpolation or approximation, avoiding
Kernel techniques: From machine learning to meshless methods
TLDR
This contribution explains why and how kernels are applied in these disciplines and uncovers the links between them, in so far as they are related to kernel techniques.
Some results on Tchebycheffian spline functions
Abstract This report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on
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