geoews

Information-geometric early warning signals for critical transitions

Detect tipping points earlier using the geometry of statistical manifolds — KL divergence rates, Fisher–Rao distances, and geodesic acceleration on sliding-window Gaussian models.

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Why geoews?

Classical early warning signals (rising variance, lag-1 autocorrelation, Kendall trend tests) detect critical slowing down - but they measure individual summary statistics of a time series window. geoews takes a fundamentally different approach: it tracks how the entire probability distribution of the data evolves over time, using the natural geometry of statistical manifolds.

Feature	Classical EWS (ewstools, etc.)	geoews
What is tracked	Single statistics (variance, ACF)	Full distribution geometry
Theoretical scaling	Variance ~ |r|^-1/2 near bifurcation	KL rate ~ |r|^-2 (provably faster divergence)
Geometric acceleration	-	Geodesic acceleration on the Fisher-Rao manifold
Multi-moment sensitivity	Separate indicators for each moment	Intrinsically captures mean, variance, and higher-order shifts simultaneously
Classical benchmarks	yes	yes (built-in for direct comparison)

The theoretical advantage is not just asymptotic: on empirical data (paleoclimate, ecology, clinical medicine), the information-geometric indicators provide earlier and more robust warnings. See our upcoming paper for proofs and validation.

Installation

From PyPI (recommended):

pip install geoews

Upgrade to latest:

pip install geoews --upgrade

Development install (from source):

git clone https://github.com/vonixxxxx/geoews.git
cd geoews
pip install -e ".[dev]"
pytest  # run test suite

Requires Python >= 3.10. Dependencies: numpy, scipy, matplotlib, pandas.

Quick start

High-level API: ManifoldEWS

The ManifoldEWS class provides a scikit-learn-style interface - fit sliding-window Gaussians, compute all geometric indicators, and run baseline-threshold detection in three lines:

import numpy as np
from geoews import ManifoldEWS

# Simulate a time series approaching a bifurcation
rng = np.random.default_rng(42)
n = 1000
r = np.linspace(1.0, 0.01, n)  # control parameter approaching zero
x = np.cumsum(rng.normal(scale=np.sqrt(1 / (2 * r))))  # OU process with diverging variance

# Fit and detect
result = ManifoldEWS(window=50, cumul_window=30).fit(x).detect()

# Access results
print(result.kl_rate)               # KL divergence rate between consecutive windows
print(result.geodesic_acceleration)  # acceleration on the Fisher-Rao manifold
print(result.alert_index)            # index where threshold is first exceeded

Lower-level API (full control)

For custom pipelines or when you need direct access to the underlying computations:

import numpy as np
from geoews.windows import estimate_gaussian_params
from geoews.indicators import kl_rate, fisher_rao_distance, geodesic_acceleration

# Your time series data
x = np.loadtxt("my_data.csv")

# Step 1: Fit sliding-window Gaussians
times, mus, sigmas = estimate_gaussian_params(x, window_size=50, step=1)

# Step 2: Compute geometric indicators
kl = kl_rate(mus, sigmas)                                   # KL divergence rate
fr = fisher_rao_distance(mus, sigmas)                        # Fisher-Rao step distances
acc = geodesic_acceleration(mus, sigmas, cumul_window=30)    # geodesic acceleration

# Step 3: Compare with classical EWS
from geoews import variance_ews, acf_ews
times_v, var_series = variance_ews(x, window=50, step=1)
times_a, acf_series = acf_ews(x, window=50, step=1)

Built-in classical benchmarks

geoews includes classical EWS for direct head-to-head comparisons:

from geoews import variance_ews, acf_ews

times_v, var = variance_ews(x, window=50, step=1)
times_a, acf = acf_ews(x, window=50, step=1)

Examples

The examples/ directory contains Jupyter notebooks demonstrating geoews on real-world data:

• Peter Lake - detecting regime shifts in a whole-lake manipulation experiment (ecology)
• PhysioNet Sepsis - early prediction of sepsis onset from clinical vital signs (medicine)

Scientific background

geoews implements the theoretical framework developed in:

Information-geometric early warning signals for critical transitions Alexander Sokol (2026). In preparation.

Core idea. Given a time series, geoews fits a Gaussian distribution N(mu_t, sigma_t^2) to each sliding window. The sequence of fitted distributions traces a curve on the 2D Gaussian statistical manifold, equipped with the Fisher information metric. As the system approaches a bifurcation:

1. KL divergence rate between consecutive windows diverges as |r|^-2, provably faster than the classical variance scaling of |r|^-1/2.
2. Fisher-Rao distance (the geodesic distance on the statistical manifold) captures simultaneous changes in both mean and variance in a single, geometrically natural scalar.
3. Geodesic acceleration detects changes in the rate of change - a second-order signal that can flag an approaching tipping point even before first-order indicators rise appreciably.

Regularization: all covariance estimates use a diagonal ridge of epsilon = 10^-6 (geoews.windows.COVARIANCE_REGULARIZATION) for numerical stability.

API reference

Core classes

Class / Function	Module	Description
ManifoldEWS	geoews	High-level fit -> detect pipeline
EWSResult	geoews	Structured result container

Geometric indicators

Function	Module	Description
kl_rate / kl_divergence_rate	geoews.indicators	KL divergence rate D(p_t
fisher_rao_distance	geoews.indicators	Geodesic distance on the Gaussian manifold
geodesic_acceleration	geoews.indicators	Second derivative of the manifold trajectory

Classical EWS

Function	Module	Description
variance_ews	geoews	Rolling variance
acf_ews	geoews	Lag-1 autocorrelation

Windowing

Function / Constant	Module	Description
estimate_gaussian_params	geoews.windows	Sliding-window Gaussian MLE
COVARIANCE_REGULARIZATION	geoews.windows	Ridge constant (default 1e-6)

Data loaders

Function	Module	Description
load_peter_lake	geoews.data	Load Peter Lake dataset (requires local file)
load_ngrip	geoews.data	Load NGRIP ice core dataset (requires local file)

Comparison with ewstools

geoews is designed to complement, not replace, ewstools. The two packages address different layers of the EWS stack:

• ewstools provides a comprehensive classical EWS toolbox with detrending, spectral EWS, deep learning classifiers, and visualization - a mature, JOSS-published package.
• geoews introduces a new class of indicators based on information geometry, with a theoretical basis for earlier detection. It includes classical benchmarks so you can compare directly.

A typical workflow might use both: run ewstools for classical analysis and deep learning classifiers, then run geoews for geometric indicators that may detect the transition earlier.

Citation

If you use geoews in your research, please cite:

@software{sokol2026geoews,
  author    = {Sokol, Alexander},
  title     = {geoews: Information-geometric early warning signals},
  year      = {2026},
  url       = {https://github.com/vonixxxxx/geoews},
  version   = {0.2.0},
  license   = {MIT}
}

See CITATION.cff for machine-readable metadata. When citing the underlying theory, please also cite the accompanying paper (reference to be added upon publication).

Roadmap

• ReadTheDocs documentation with full API reference and tutorials
• Publication-quality example notebooks with ewstools side-by-side comparisons
• Multivariate extension (matrix Fisher-Rao geometry)
• Spectral EWS on the manifold (power spectrum curvature)
• Zenodo DOI and archival release
• arXiv preprint link
• JOSS submission

Contributing

Contributions are welcome. Please open an issue to discuss proposed changes before submitting a pull request.

git clone https://github.com/vonixxxxx/geoews.git
cd geoews
pip install -e ".[dev]"
pytest                # run tests

License

MIT - see LICENSE.