https://github.com/dmetivie/hiddenmarkovmodels.jl

A Julia package for simulation, inference and learning of Hidden Markov Models.

https://github.com/dmetivie/hiddenmarkovmodels.jl

Repository

A Julia package for simulation, inference and learning of Hidden Markov Models.

https://github.com/dmetivie/HiddenMarkovModels.jl/blob/main/

# HiddenMarkovModels.jl

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A Julia package for simulation, inference and learning of Hidden Markov Models.

## Getting started

This package can be installed using Julia's package manager:

```julia
pkg> add HiddenMarkovModels
```

Then, you can create your first model as follows:

```julia
using Distributions, HiddenMarkovModels
init = [0.6, 0.4]
trans = [0.7 0.3; 0.2 0.8]
dists = [Normal(-1.0), Normal(1.0)]
hmm = HMM(init, trans, dists)
```

Take a look at the [documentation](https://gdalle.github.io/HiddenMarkovModels.jl/stable/) to know what to do next!

## Some background

[Hidden Markov Models](https://en.wikipedia.org/wiki/Hidden_Markov_model) (HMMs) are a widely used modeling framework in signal processing, bioinformatics and plenty of other fields.
They explain an observation sequence $(Y_t)$ by assuming the existence of a latent Markovian state sequence $(X_t)$ whose current value determines the distribution of observations.
In some scenarios, the state and the observation sequence are also allowed to depend on a known control sequence $(U_t)$.
Each of the problems below has an efficient solution algorithm, available here:

| Problem    | Goal                                   | Algorithm        |
| ---------- | -------------------------------------- | ---------------- |
| Evaluation | Likelihood of the observation sequence | Forward          |
| Filtering  | Last state marginals                   | Forward          |
| Smoothing  | All state marginals                    | Forward-backward |
| Decoding   | Most likely state sequence             | Viterbi          |
| Learning   | Maximum likelihood parameter           | Baum-Welch       |

Take a look at this tutorial to know more about the math:

> [_A tutorial on hidden Markov models and selected applications in speech recognition_](https://ieeexplore.ieee.org/document/18626), Rabiner (1989)

## Main features

This package is **generic**.
Observations can be arbitrary Julia objects, not just scalars or arrays.
Number types are not restricted to floating point, which enables automatic differentiation.
Time-dependent or controlled HMMs are supported out of the box.

This package is **fast**.
All the inference functions have allocation-free versions, which leverage efficient linear algebra subroutines.
We will include extensive benchmarks against Julia and Python competitors.

This package is **reliable**.
It gives the same results as the previous reference package up to numerical accuracy.
The test suite incorporates quality checks as well as type stability and allocation analysis.

## Contributing

If you spot a bug or want to ask about a new feature, please [open an issue](https://github.com/gdalle/HiddenMarkovModels.jl/issues) on the GitHub repository.
Once the issue receives positive feedback, feel free to try and fix it with a pull request that follows the [BlueStyle](https://github.com/invenia/BlueStyle) guidelines.

## Acknowledgements

A big thank you to [Maxime Mouchet](https://www.maxmouchet.com/) and [Jacob Schreiber](https://jmschrei.github.io/), the respective lead devs of alternative packages [HMMBase.jl](https://github.com/maxmouchet/HMMBase.jl) and [pomegranate](https://github.com/jmschrei/pomegranate), for their help and advice.
Logo by [Clment Mantoux](https://cmantoux.github.io/) based on a portrait of [Andrey Markov](https://en.wikipedia.org/wiki/Andrey_Markov).

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