Nadaraya-Watson Signature Estimator

Overview

Implementation of Nadaraya-Watson estimators using path signatures for non-parametric regression and classification on time series and path data.

Installation

git clone https://github.com/anonymous-review-submission/nw-signature.git
cd nw-signature
pip install -r requirements.txt

Quick Start

Classification

from nwsig import NWSignatureClassifier
import numpy as np

# Your time series data: shape (n_samples, n_timesteps, n_features)
X_train = np.random.randn(100, 50, 3)
y_train = np.random.randint(0, 2, 100)

# Extract initial conditions
X0_train = X_train[:, 0, :]
X0_test = X_test[:, 0, :]

# Fit and predict
classifier = NWSignatureClassifier(signature_level=2, cv_folds=5)
classifier.fit(X_train, X0_train, y_train)
y_pred = classifier.predict(X_test, X0_test)

Regression

from nwsig import NWSignatureRegressor

regressor = NWSignatureRegressor(signature_level=2, cv_folds=5)
regressor.fit(X_train, X0_train, y_train)
y_pred = regressor.predict(X_test, X0_test)

Examples

The examples/ directory contains four Jupyter notebooks:

1. 01_classification_examples.ipynb - Classification on 20+ benchmark datasets
2. 02_regression_examples.ipynb - Regression with baseline comparisons
3. 03_learning_sde_solution.ipynb - Learning SDE solution maps
4. 04_path_dependent_options.ipynb - Path-dependent option pricing

Run the examples:

cd examples
jupyter notebook

Key Parameters

• signature_level (int): Signature truncation level (default: 2)
• bandwidth_grid (list): Grid of bandwidth values for cross-validation
• cv_folds (int): Number of CV folds (default: 5)
• robust (bool): Use robust signature transformations (default: False)
• metric_choice (str): Distance metric - 'signature_metric', 'supremum_metric', 'l1', 'l2', 'pvar'

Input Format

X: shape (n_samples, n_timesteps, n_features)  # Path data
X0: shape (n_samples, n_features)               # Initial conditions (X[:, 0, :])
y: shape (n_samples,)                           # Target values

Dependencies

• numpy, scipy, scikit-learn
• torch (for GPU acceleration)
• iisignature (signature computation)
• numba (JIT compilation)
• aeon (for example datasets)

See requirements.txt for full list.

License

MIT License - see LICENSE file.