“early_warnings” package

This is the antiCPy.early_warnings package. It contains two resilience or early warning metrics:

  1. the drift_slope with basically three fit objects:

    1. the LangevinEstimation class that provides possibilities to parameterize the drift and diffusion function in terms of polynomials. The parameters of these functions can be estimated via Markov Chain Monte Carlo (MCMC) sampling or maximum posterior (MAP) estimation and the drift slope can be calculated in a rolling window approach in order to detect changes in the resilience and noise level of a system.

    2. the BinningLangevinEstimation class that is designed to perform a bin-wise MAP LangevinEstimation inspired by [Kleinhans2012] . In general, the MAP approach is of course much faster than the MCMC approach. In cases of high amount of data per window or a single estimation over a huge dataset the binning approach is computationally more efficient.

    3. the NonMarkovEstimation class that introduces a second unobserved Ornstein-Uhlenbeck (OU) process that couples with a constant coefficient into the observed dynamics. The short-term propagator is adjusted following [Willers2021] . Furthermore, a time scale separation of adjustable degree can be assumed a priori.

    Important

    A fourth RocketFastResilienceEstimation is introduced. As superclass it works as a kind of wrapper of the former. Basically, it adds the fast_resilience_scan(...) and fast_MAP_resilience_scan(...) functionalities to the former Fit classes. They involve a strong parallelization of the fitting procedures on multiple rolling windows at the same time. This improves the computational costs significantly and is the most up-to-date procedure.

  2. the dominant_eigenvalue which provides modules to

    1. optimize the method parameters in param_opt,

    2. perform the dominant eigenvalue estimation in analysis,

    3. visualize the parameter optimization and the results in graphics,

    4. get started with the package by a tutorial.

Hint

The dominant_eigenvalue package is procedural up to now. Therefore, its modules contain a collection of functions. In consequence, the import has to be done via

# correct import
import antiCPy.early_warnings.dominant_eigenvalue as dev
...
dev.analysis.AR_EV_calc(...)
...
# not working import
from antiCPy.early_warnings.dominant_eigenvalue import *

In case you want to have easy access to a subset of functionalities of antiCPy including the dominant_eigenvalue package you can use the following work arounds:

import antiCPy.early_warnings as ews
...
ews.AR_EV_calc(...)
...
ews.LangevinEstimation(...)
...
# or
import antiCPy as apy
...
        ...
apy.AR_EV_calc(...)
...
apy.LangevinEstimation(...)
...
apy.CPSegmentFit(...)
...

The original implementation [Grziwotz2023] uses sequential maps (S-maps) to estimate the Jacobian’s coefficients involved in the procedure. We replaced the S-map approach by a simple autoregression scheme of order \(p\) (AR(\(p\))).

Contents:

Bibliography

[Kleinhans2012]

David Kleinhans. ”Estimation of drift and diffusion functions from time series data: A maximum likelihood framework”. In: Phys. Rev. E 85(2), pp. 026705-026715 (Feb 2012). American Physical Society, 10.1103/PhysRevE.85.026705, https://link.aps.org/doi/10.1103/PhysRevE.85.026705.

[Willers2021]

Clemens Willers and Oliver Kamps. ”Non-parametric estimation of a Langevin model driven by correlated noise”. In: Eur. Phys. J. B 94, 149 (2021). https://doi.org/10.1140/epjb/s10051-021-00149-0.

[Grziwotz2023]

Florian Grziwotz et al. ”Anticipating the occurrence and type of critical transitions”. In: Sci. Adv. 9, eabq4558(2023). DOI:10.1126/sciadv.abq4558