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gaussian_process

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gaussian process examples

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# Gaussian Process

## Dependency

- [python](https://www.python.org/)
  - version 3.10 or higher is recommended.

- [rye](https://rye.astral.sh/)
  - seting up python environment easily and safely.
  - only `numpy`, `matplotlib`, `notebook` are needed to run all scripts in this repository.

## Setup
```sh
git clone https://github.com/MizuhoAOKI/gaussian_process.git
cd gaussian_process
rye sync
```

## Usage

### Gaussian Process Regression

```sh
cd gaussian_process
rye run jupyter notebook notebooks/gp_regression_1d.ipynb
```

```sh
cd gaussian_process
rye run jupyter notebook notebooks/gp_regression_2d.ipynb
```
<img src="./media/gpr_2d_prediction.png" width="500px" alt="gaussian process regression (2 dim)">

### Bayesian Optimization

```sh
cd gaussian_process
rye run jupyter notebook notebooks/bayesian_optimization_1d.ipynb
```

https://github.com/MizuhoAOKI/gaussian_process/assets/63337525/36b2d534-8d9f-4a5e-b26d-dc41e0032590

```sh
cd gaussian_process
rye run jupyter notebook notebooks/bayesian_optimization_2d.ipynb
```

https://github.com/user-attachments/assets/6e01d71f-f5d6-4ca8-90a3-6792bac1da56

```sh
cd gaussian_process
rye run jupyter notebook notebooks/bayesian_optimization_path_tracking.ipynb
```

https://github.com/user-attachments/assets/6d2cbb48-3d44-46c5-ba76-3fc29aa1ca1d

## References

Great textbooks to learn Gaussian Process:

- [持橋大地, 大羽成征 (2019). ガウス過程と機械学習. 講談社（MLP機械学習プロフェッショナルシリーズ）](https://www.kodansha.co.jp/book/products/0000147677)
- [Rasmussen, C. E., & Williams, C. K. I. (2006). *Gaussian Processes for Machine Learning*. MIT Press](https://gaussianprocess.org/gpml/)
- [Bishop, C. M. (2006). *Pattern Recognition and Machine Learning*. Springer (PDF via Microsoft Research)](https://www.microsoft.com/en-us/research/wp-content/uploads/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf)

gaussian_process

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