Model selection workflow

This page demonstrates how the sklearn-style meta-estimators in xyz can be used to search embedding settings and interaction delays before running a final TE analysis.

Why this workflow exists

TRENTOOL-style TE analysis is not only about the low-level estimator. It also depends on:

• choosing a sensible embedding dimension,

• choosing an embedding spacing,

• and choosing a plausible interaction delay.

The xyz search classes make these choices explicit and reproducible in a Pythonic, scikit-learn-like form.

Example: embedding and delay search

import numpy as np
from xyz import (
    GaussianTransferEntropy,
    InteractionDelaySearchCV,
    RagwitzEmbeddingSearchCV,
)

rng = np.random.default_rng(123)
n = 700
driver = rng.normal(size=n)
target = np.zeros(n)
for t in range(2, n):
    target[t] = 0.45 * target[t - 1] + 0.20 * target[t - 2] + 0.35 * driver[t - 2] + 0.1 * rng.normal()

data = np.column_stack([target, driver])

base = GaussianTransferEntropy(driver_indices=[1], target_indices=[0], lags=1)

embedding = RagwitzEmbeddingSearchCV(
    base,
    target_index=0,
    dimensions=(1, 2, 3),
    taus=(1, 2, 3),
).fit(data)

delay = InteractionDelaySearchCV(
    base.set_params(**embedding.best_params_),
    delays=(1, 2, 3, 4, 5),
).fit(data)

print(embedding.best_params_, embedding.best_score_)
print(delay.best_delay_, delay.best_score_)

Interactive example

The two figures below show:

1. a heatmap of the Ragwitz-style embedding search surface,

2. a delay profile after fixing the best embedding.

Interpretation

• A smooth embedding surface is usually easier to trust than a highly erratic one.

• Delay reconstruction is most convincing when the TE profile has a clear and interpretable maximum.

• In real data, do not rely on model selection alone; combine it with significance testing and domain knowledge.