CHG

CHG Algorithm Package

CHG (Covariance-based Hilbert Geometry) Algorithm is a sophisticated implementation of Gaussian Process regression with enhanced multi-head attention mechanisms for improved covariance computation and uncertainty quantification.

Features

• Multi-head Attention: Advanced attention mechanism for better feature representation
• Enhanced Covariance: Sophisticated covariance computation using neural network components
• Uncertainty Quantification: Built-in uncertainty estimation for predictions
• Optimization Support: Gradient-based parameter optimization
• Robust Implementation: Handles numerical instabilities gracefully

Installation

From Source

git clone <repository-url>
cd chg_package
pip install -e .

Development Installation

pip install -e ".[dev]"

Quick Start

Basic Usage

from chg_algorithm import CHG
import numpy as np

# Initialize model
model = CHG(input_dim=3, hidden_dim=24, num_heads=4)

# Generate sample data
X_train = np.random.randn(100, 3)
y_train = np.sum(X_train**2, axis=1) + 0.1 * np.random.randn(100)
X_test = np.random.randn(20, 3)

# Make predictions
pred_mean, pred_var = model.fit_predict(X_train, y_train, X_test)

print(f"Predictions: {pred_mean}")
print(f"Uncertainties: {np.sqrt(pred_var)}")

Running Demo

from chg_algorithm import run_chg_experiment

# Run complete demonstration
model, predictions, variances = run_chg_experiment()

Using Optimizer

from chg_algorithm import CHG, CHGOptimizer

# Initialize model and optimizer
model = CHG(input_dim=3, hidden_dim=24, num_heads=4)
optimizer = CHGOptimizer(model, learning_rate=0.001)

# Optimize model parameters
for epoch in range(10):
    optimizer.step(X_train, y_train)
    lml = model.log_marginal_likelihood(X_train, y_train)
    print(f"Epoch {epoch}: Log Marginal Likelihood = {lml:.4f}")

API Reference

CHG Class

Main model class implementing the CHG algorithm.

Parameters:

• input_dim (int): Dimensionality of input features
• hidden_dim (int): Hidden dimension for feature transformation
• num_heads (int): Number of attention heads

Key Methods:

• fit_predict(X_train, y_train, X_test, noise_var=1e-6): Fit model and predict
• log_marginal_likelihood(X, y, noise_var=1e-6): Compute log marginal likelihood
• get_covariance_matrix(X): Get covariance matrix for inputs

CHGOptimizer Class

Optimizer for CHG model parameters.

Parameters:

• model (CHG): CHG model instance to optimize
• learning_rate (float): Learning rate for parameter updates

Key Methods:

• step(X, y, noise_var=1e-6): Perform one optimization step
• compute_gradients(X, y, noise_var=1e-6): Compute parameter gradients

Algorithm Details

The CHG algorithm combines several advanced techniques:

1. Multi-head Attention: Uses multiple attention heads to capture different aspects of feature relationships
2. Enhanced Covariance: Computes covariance using feedforward networks and layer normalization
3. Gaussian Process Framework: Built on solid GP foundations for uncertainty quantification
4. Numerical Stability: Includes fallback methods for numerical edge cases

Requirements

• Python >= 3.7
• NumPy >= 1.19.0
• typing-extensions >= 3.7.4

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

1. Fork the repository
2. Create your feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add some amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

Citation

If you use this software in your research, please cite:

@software{chg_algorithm,
  title={CHG Algorithm: Covariance-based Hilbert Geometry for Gaussian Processes},
  author={CHG Algorithm Team},
  year={2024},
  url={https://github.com/your-username/chg-algorithm}
}

Contact

For questions and support, please contact:[email protected]

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