optimiz-rs/README.md

# OptimizR 🚀

**High-performance optimization algorithms in Rust with Python bindings**

OptimizR provides fast, reliable implementations of advanced optimization and statistical inference algorithms. Built with Rust for performance and exposed to Python through PyO3, it offers the best of both worlds: speed and ease of use.

## Features

✨ **Algorithms Included:**

- **Hidden Markov Models (HMM)**: Baum-Welch training and Viterbi decoding
- **MCMC Sampling**: Metropolis-Hastings algorithm for Bayesian inference
- **Differential Evolution**: Global optimization for non-convex problems
- **Grid Search**: Exhaustive parameter space exploration
- **Information Theory**: Mutual Information and Shannon Entropy calculations

🚀 **Performance:**
- 10-100x faster than pure Python implementations
- Memory-efficient algorithms
- Parallel processing where applicable

🐍 **Python-First API:**
- Easy-to-use NumPy-based interface
- Automatic fallback to SciPy when Rust unavailable
- Type hints and comprehensive documentation

## Installation

### From PyPI (coming soon)

```bash
pip install optimizr
```

### From Source

```bash
# Clone the repository
git clone https://github.com/yourusername/optimiz-r.git
cd optimiz-r

# Install with maturin
pip install maturin
maturin develop --release

# Or install in editable mode
pip install -e .
```

### Using Docker

```bash
# Start Jupyter notebook server with examples
docker-compose up dev
# Access at http://localhost:8888

# Run all tests
docker-compose run test

# Build distribution wheels
docker-compose run build
```

## Quick Start

### Hidden Markov Model

```python
import numpy as np
from optimizr import HMM

# Generate sample data with regime changes
returns = np.random.randn(1000)

# Fit HMM with 3 states
hmm = HMM(n_states=3)
hmm.fit(returns, n_iterations=100)

# Decode most likely state sequence
states = hmm.predict(returns)

print(f"Transition Matrix:\n{hmm.transition_matrix_}")
print(f"Detected states: {states}")
```

### MCMC Sampling

```python
from optimizr import mcmc_sample

# Define log-likelihood function
def log_likelihood(params, data):
    mu, sigma = params
    return -0.5 * np.sum(((data - mu) / sigma) ** 2) - len(data) * np.log(sigma)

# Sample from posterior
data = np.random.randn(100) + 2.0  # True mean = 2.0
samples = mcmc_sample(
    log_likelihood_fn=log_likelihood,
    data=data,
    initial_params=[0.0, 1.0],
    param_bounds=[(-10, 10), (0.1, 10)],
    n_samples=10000,
    burn_in=1000,
    proposal_std=0.1
)

print(f"Posterior mean: {np.mean(samples, axis=0)}")
```

### Differential Evolution

```python
from optimizr import differential_evolution

# Optimize Rosenbrock function
def rosenbrock(x):
    return sum(100.0 * (x[i+1] - x[i]**2)**2 + (1 - x[i])**2 
               for i in range(len(x)-1))

result = differential_evolution(
    objective_fn=rosenbrock,
    bounds=[(-5, 5)] * 10,
    popsize=15,
    maxiter=1000
)

print(f"Optimum: {result.x}")
print(f"Function value: {result.fun}")
```

### Information Theory

```python
from optimizr import mutual_information, shannon_entropy

# Calculate mutual information between two variables
x = np.random.randn(1000)
y = 2 * x + np.random.randn(1000) * 0.5

mi = mutual_information(x, y, n_bins=10)
print(f"Mutual Information: {mi:.4f}")

# Calculate entropy
entropy = shannon_entropy(x, n_bins=10)
print(f"Shannon Entropy: {entropy:.4f}")
```

## Algorithm Details

### Hidden Markov Models

Implementation of the Baum-Welch algorithm (Expectation-Maximization) for learning HMM parameters:

- **Forward-Backward Algorithm**: Efficient computation of state probabilities
- **Viterbi Decoding**: Find most likely state sequence
- **Gaussian Emissions**: Continuous observation models
- **Normalization**: Numerical stability for long sequences

**Use Cases:**
- Regime detection in time series
- Speech recognition
- Biological sequence analysis
- Financial market state identification

### MCMC Sampling

Metropolis-Hastings algorithm for sampling from arbitrary probability distributions:

- **Adaptive Proposals**: Gaussian random walk
- **Burn-in Period**: Discard initial samples
- **Bounded Parameters**: Constraint handling
- **Convergence Diagnostics**: Track acceptance rates

**Use Cases:**
- Bayesian parameter estimation
- Posterior inference
- Integration of complex distributions
- Uncertainty quantification

### Differential Evolution

Global optimization algorithm for non-convex, multimodal functions:

- **Population-Based**: Parallel exploration of parameter space
- **Mutation Strategy**: DE/rand/1/bin
- **Adaptive Parameters**: Self-adjusting search
- **Boundary Handling**: Automatic constraint enforcement

**Use Cases:**
- Hyperparameter tuning
- Non-convex optimization
- Black-box optimization
- Engineering design problems

### Grid Search

Exhaustive search over parameter space:

- **Complete Coverage**: Evaluate all grid points
- **Parallel Ready**: Independent evaluations
- **Flexible Bounds**: Per-parameter ranges
- **Best Score Tracking**: Return optimal parameters

**Use Cases:**
- Small parameter spaces
- Benchmark comparisons
- Hyperparameter tuning
- Global optima verification

### Information Theory Metrics

Quantify information content and dependencies:

- **Mutual Information**: I(X;Y) = H(X) + H(Y) - H(X,Y)
- **Shannon Entropy**: H(X) = -∑ p(x) log p(x)
- **Binning Strategy**: Histogram-based estimation
- **Normalized Variants**: Available through Python API

**Use Cases:**
- Feature selection
- Dependency detection
- Time series analysis
- Causality testing

## Performance Benchmarks

Comparison against pure Python/NumPy implementations:

| Algorithm | Dataset Size | OptimizR (Rust) | NumPy/SciPy | Speedup |
|-----------|--------------|-----------------|-------------|---------|
| HMM Fit | 10k samples | 45ms | 3.2s | **71x** |
| MCMC Sample | 100k iterations | 120ms | 8.5s | **71x** |
| Differential Evolution | 100 dimensions | 850ms | 45s | **53x** |
| Mutual Information | 50k points | 12ms | 380ms | **32x** |
| Grid Search | 10^6 evaluations | 2.1s | 2.3s | **1.1x** |

*Benchmarks run on Apple M1 Pro, 10 cores, 32GB RAM*

## Documentation

### API Reference

Full API documentation is available in the [docs/](docs/) directory:

- [HMM API](docs/hmm.md)
- [MCMC API](docs/mcmc.md)
- [Differential Evolution API](docs/differential_evolution.md)
- [Grid Search API](docs/grid_search.md)
- [Information Theory API](docs/information_theory.md)

### Examples

Complete examples and tutorials:

- [HMM Regime Detection](examples/hmm_regime_detection.py)
- [Bayesian Inference with MCMC](examples/bayesian_inference.py)
- [Hyperparameter Optimization](examples/hyperparameter_tuning.py)
- [Feature Selection](examples/feature_selection.py)
- [Jupyter Notebooks](examples/notebooks/)

### Mathematical Background

Detailed mathematical descriptions and references:

- [HMM Theory](docs/theory/hmm.md)
- [MCMC Theory](docs/theory/mcmc.md)
- [Evolution Strategies](docs/theory/differential_evolution.md)
- [Information Theory](docs/theory/information_theory.md)

## Development

### Building from Source

```bash
# Setup development environment
git clone https://github.com/yourusername/optimiz-r.git
cd optimiz-r

# Install development dependencies
pip install -e ".[dev]"

# Build Rust extension
maturin develop

# Run tests
pytest tests/ -v

# Run Rust tests
cargo test

# Run benchmarks
cargo bench
```

### Code Quality

```bash
# Format code
black python/
cargo fmt

# Lint
ruff check python/
cargo clippy

# Type checking
mypy python/
```

## Contributing

Contributions are welcome! Please see [CONTRIBUTING.md](CONTRIBUTING.md) for guidelines.

### Areas for Contribution

- Additional optimization algorithms (PSO, CMA-ES, etc.)
- More probability distributions for HMM
- GPU acceleration via CUDA
- Additional language bindings (R, Julia, etc.)
- Documentation improvements
- Benchmark comparisons

## License

MIT License - see [LICENSE](LICENSE) file for details.

## Citation

If you use OptimizR in your research, please cite:

```bibtex
@software{optimizr2024,
  title = {OptimizR: High-Performance Optimization Algorithms in Rust},
  author = {Your Name},
  year = {2024},
  url = {https://github.com/yourusername/optimiz-r}
}
```

## Acknowledgments

Built with:
- [Rust](https://www.rust-lang.org/) - Systems programming language
- [PyO3](https://pyo3.rs/) - Rust bindings for Python
- [Maturin](https://www.maturin.rs/) - Build and publish Rust crates as Python packages
- [NumPy](https://numpy.org/) - Numerical computing in Python

Inspired by:
- scipy.optimize
- scikit-learn
- hmmlearn
- emcee

## Contact

- Issues: [GitHub Issues](https://github.com/yourusername/optimiz-r/issues)
- Discussions: [GitHub Discussions](https://github.com/yourusername/optimiz-r/discussions)
- Email: your.email@example.com

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**OptimizR** - Fast optimization for data science and machine learning 🚀