Probability distributions for analog-to-target distances
Some properties of chaotic dynamical systems can be probed through features of recurrences, also called analogs. In practice, analogs are nearest neighbours of the state of a system, taken from a large database called the catalog. Analogs have been used in many atmospheric applications including forecasts, downscaling, predictability estimation, and attribution of extreme events. The distances of the analogs to the target state condition the performances of analog applications. These distances can be viewed as random variables, and their probability distributions can be related to the catalog size and properties of the system at stake. A few studies have focused on the first moments of return time statistics for the best analog, fixing an objective of maximum distance from this analog to the target state. However, for practical use and to reduce estimation variance, applications usually require not just one, but many analogs. In this paper, we evaluate from a theoretical standpoint and with numerical experiments the probability distributions of the $K$-best analog-to-target distances. We show that dimensionality plays a role on the size of the catalog needed to find good analogs, and also on the relative means and variances of the $K$-best analogs. Our results are based on recently developed tools from dynamical systems theory. These findings are illustrated with numerical simulations of a well-known chaotic dynamical system and on 10m-wind reanalysis data in north-west France. A practical application of our derivations for the purpose of objective-based dimension reduction is shown using the same reanalysis data.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Wasserstein Exponential Kernels
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recen…
Schoenberg-Rao distances: Entropy-based and geometry-aware statistical Hilbert distances
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learn…
BIG-bench Machine LearningDensity EstimationA Gaussian Process Regression Model for Distribution Inputs
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, …
BIG-bench Machine LearningGaussian ProcessesmodelregressionThe Observable Wasserstein Distance
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractabilit…
Computational EfficiencyControlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have …