Probability distributions for analog-to-target distances
- URL: http://arxiv.org/abs/2101.10640v1
- Date: Tue, 26 Jan 2021 09:10:12 GMT
- Title: Probability distributions for analog-to-target distances
- Authors: Paul Platzer, Pascal Yiou (ESTIMR), Philippe Naveau (ESTIMR),
Jean-Fran\c{c}ois Filipot, Maxime Thiebaut, Pierre Tandeo (IMT Atlantique -
SC)
- Abstract summary: We show that dimensionality plays a role on the size of the catalog needed to find good analogs.
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.
- Score: 0.12314765641075436
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
Related papers
- Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
This thesis is a series of independent contributions to statistics unified by a model-free perspective.
The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning.
The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
arXiv Detail & Related papers (2025-02-11T19:24:09Z) - Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation.
In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model.
We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
arXiv Detail & Related papers (2024-04-11T09:23:36Z) - ARN: Analogical Reasoning on Narratives [13.707344123755126]
We develop a framework that operationalizes dominant theories of analogy, using narrative elements to create surface and system mappings.
We show that while all LLMs can largely recognize near analogies, even the largest ones struggle with far analogies in a zero-shot setting.
arXiv Detail & Related papers (2023-10-02T08:58:29Z) - On the Non-Associativity of Analog Computations [0.0]
In this work, we observe that the ordering of input operands of an analog operation also has an impact on the output result.
We conduct a simple test by creating a model of a real analog processor which captures such ordering effects.
The results prove the existence of ordering effects as well as their high impact, as neglecting ordering results in substantial accuracy drops.
arXiv Detail & Related papers (2023-09-25T17:04:09Z) - Importance sampling for stochastic quantum simulations [68.8204255655161]
We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients.
We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage.
Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
arXiv Detail & Related papers (2022-12-12T15:06:32Z) - Counting Like Human: Anthropoid Crowd Counting on Modeling the
Similarity of Objects [92.80955339180119]
mainstream crowd counting methods regress density map and integrate it to obtain counting results.
Inspired by this, we propose a rational and anthropoid crowd counting framework.
arXiv Detail & Related papers (2022-12-02T07:00:53Z) - Numerically Stable Sparse Gaussian Processes via Minimum Separation
using Cover Trees [57.67528738886731]
We study the numerical stability of scalable sparse approximations based on inducing points.
For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
arXiv Detail & Related papers (2022-10-14T15:20:17Z) - Nonparametric likelihood-free inference with Jensen-Shannon divergence
for simulator-based models with categorical output [1.4298334143083322]
Likelihood-free inference for simulator-based statistical models has attracted a surge of interest, both in the machine learning and statistics communities.
Here we derive a set of theoretical results to enable estimation, hypothesis testing and construction of confidence intervals for model parameters using computation properties of the Jensen-Shannon- divergence.
Such approximation offers a rapid alternative to more-intensive approaches and can be attractive for diverse applications of simulator-based models.
arXiv Detail & Related papers (2022-05-22T18:00:13Z) - Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
We take a two-step approach by first modeling the probability distribution and then sampling from that model.
We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
arXiv Detail & Related papers (2021-10-20T12:25:22Z) - Probabilistic Inference of Simulation Parameters via Parallel
Differentiable Simulation [34.30381620584878]
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system.
We address the latter problem of estimating parameters through a Bayesian inference approach.
We leverage GPU code generation and differentiable simulation to evaluate the likelihood and its gradient for many particles in parallel.
arXiv Detail & Related papers (2021-09-18T03:05:44Z) - Using local dynamics to explain analog forecasting of chaotic systems [0.0]
This study investigates the properties of different analog forecasting strategies by taking local approximations of the system's dynamics.
We find that analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.
The proposed methodology allows to estimate analog forecasting errors, and to compare different analog methods.
arXiv Detail & Related papers (2020-07-22T08:43:11Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.