rhmm - Rust Hidden Markov Models

A Rust library for Hidden Markov Models (HMM), inspired by Python's hmmlearn. This library provides efficient implementations of various HMM models and algorithms using ndarray for numerical computations.

🚀 Features

• Multiple HMM Model Types

  • Gaussian HMM: Models continuous data with Gaussian emission distributions
  • Beta HMM: Models data in the range [0, 1] (e.g., conversion rates, proportions)
  • Multinomial HMM(Not implemented yet, coming soon): Models discrete categorical data
  • Gaussian Mixture Model HMM (GMM-HMM) (Not implemented yet, coming soon): Models complex continuous distributions

• Standard HMM Algorithms

  • Forward Algorithm: Compute observation probabilities
  • Backward Algorithm: Compute backward probabilities
  • Viterbi Algorithm: Find the most likely state sequence
  • Baum-Welch Algorithm: Train model parameters using EM

• Efficient Implementation

  • Built on ndarray for fast numerical operations
  • Support for multiple covariance types (diagonal, spherical, full, tied)
  • Robust numerical stability with log-space computations

📦 Installation

Add this to your Cargo.toml:

[dependencies]
rhmm = "0.0.1"

Or install from source:

git clone https://github.com/yourusername/rhmm.git
cd rhmm
cargo build --release

🔧 Dependencies

• ndarray - N-dimensional arrays
• ndarray-linalg - Linear algebra operations
• rand - Random number generation
• rand_distr - Probability distributions
• thiserror - Error handling
• serde - Serialization support

📖 Quick Start

Gaussian HMM Example

use ndarray::array;
use rhmm::models::GaussianHMM;
use rhmm::base::HiddenMarkovModel;

fn main() {
    // Create training data
    let observations = array![
        [0.5, 1.0],
        [0.6, 1.1],
        [5.0, 6.0],
        [5.1, 6.2],
    ];

    // Create and train model with 2 hidden states
    let mut model = GaussianHMM::new(2);
    model.fit(&observations, None).unwrap();

    // Predict hidden states
    let states = model.predict(&observations).unwrap();
    println!("Predicted states: {:?}", states);

    // Calculate log-likelihood
    let log_prob = model.score(&observations).unwrap();
    println!("Log probability: {:.4}", log_prob);

    // Generate synthetic data
    let (sampled_obs, sampled_states) = model.sample(10).unwrap();
    println!("Generated {} samples", sampled_obs.nrows());
}

Beta HMM Example (Conversion Rate Analysis)

use ndarray::array;
use rhmm::models::BetaHMM;
use rhmm::base::HiddenMarkovModel;

fn main() {
    // Conversion rates (values between 0 and 1)
    let observations = array![
        [0.12, 0.15],  // Low conversion
        [0.10, 0.13],  // Low conversion
        [0.75, 0.82],  // High conversion
        [0.78, 0.85],  // High conversion
    ];

    // Create and train model
    let mut model = BetaHMM::new(2);
    model.fit(&observations, None).unwrap();

    // Predict states
    let states = model.predict(&observations).unwrap();
    println!("States: {:?}", states);

    // Get learned parameters
    if let (Some(alphas), Some(betas)) = (model.alphas(), model.betas()) {
        println!("Alpha parameters: {:?}", alphas);
        println!("Beta parameters: {:?}", betas);
    }
}

🎯 Use Cases

Gaussian HMM

• Speech Recognition: Model acoustic features
• Financial Markets: Detect market regimes (bull/bear)
• Sensor Data: Analyze time-series sensor readings
• Bioinformatics: Gene sequence analysis

Beta HMM

• E-commerce: Conversion rate analysis
• Marketing: Click-through rate modeling
• Finance: Market share dynamics
• Quality Control: Success rate tracking

Multinomial HMM

• Natural Language Processing: Part-of-speech tagging
• Bioinformatics: DNA sequence modeling
• User Behavior: Clickstream analysis
• Weather Modeling: Discrete weather states

📚 API Overview

Core Trait: HiddenMarkovModel

All HMM models implement this trait:

pub trait HiddenMarkovModel {
    /// Get the number of hidden states
    fn n_states(&self) -> usize;

    /// Get the number of features/dimensions
    fn n_features(&self) -> usize;

    /// Fit the model to observed data
    fn fit(&mut self, observations: &Array2<f64>, lengths: Option<&[usize]>) -> Result<()>;

    /// Predict the most likely state sequence (Viterbi)
    fn predict(&self, observations: &Array2<f64>) -> Result<Array1<usize>>;

    /// Compute the log probability of observations
    fn score(&self, observations: &Array2<f64>) -> Result<f64>;

    /// Sample from the model
    fn sample(&self, n_samples: usize) -> Result<(Array2<f64>, Array1<usize>)>;

    /// Decode the most likely state sequence
    fn decode(&self, observations: &Array2<f64>) -> Result<(f64, Array1<usize>)>;
}

Model Types

GaussianHMM

let model = GaussianHMM::new(n_states);
let model = GaussianHMM::with_covariance_type(n_states, CovarianceType::Diagonal);

BetaHMM

let model = BetaHMM::new(n_states);

MultinomialHMM

let model = MultinomialHMM::new(n_states, n_features);

GaussianMixtureHMM

let model = GaussianMixtureHMM::new(n_states, n_mix);

🔬 Examples

Run the included examples:

# Beta HMM example (conversion rate analysis)
cargo run --example beta_hmm_example

# Polars integration example
cargo run --example polars_example

🧪 Testing

Run the test suite:

# Run all tests
cargo test

# Run with output
cargo test -- --nocapture

# Run specific test
cargo test integration_tests

📊 Performance

The library is optimized for performance:

• Uses ndarray for efficient numerical operations
• Log-space computations for numerical stability
• Vectorized operations where possible
• Minimal allocations in hot paths

🛠️ Advanced Usage

Multiple Sequences

Train on multiple sequences of different lengths:

let observations = array![/* concatenated sequences */];
let lengths = vec![10, 15, 20]; // Length of each sequence
model.fit(&observations, Some(&lengths)).unwrap();

Custom Initialization

let mut model = GaussianHMM::new(3);
// Set custom initial parameters before fitting
// model.set_start_prob(...);
// model.set_transition_matrix(...);
model.fit(&observations, None).unwrap();

Covariance Types

use rhmm::base::CovarianceType;

// Diagonal covariance (default)
let model = GaussianHMM::with_covariance_type(3, CovarianceType::Diagonal);

// Spherical covariance (single variance)
let model = GaussianHMM::with_covariance_type(3, CovarianceType::Spherical);

// Full covariance matrix
let model = GaussianHMM::with_covariance_type(3, CovarianceType::Full);

🤝 Contributing

Contributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.

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

📝 License

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

🙏 Acknowledgments

• Inspired by hmmlearn (Python)
• Built with ndarray

📧 Contact

• Author: YanXu Fu
• Email: unico-serein@hotmail.com
• GitHub: @unico-serein

🗺️ Roadmap

• Add more emission distributions (Poisson, Exponential)
• Implement parallel training for multiple sequences
• Add model serialization/deserialization
• Improve documentation with more examples
• Add benchmarks
• Support for GPU acceleration

Star ⭐ this repository if you find it helpful!