# MuyGPyS (v0.9.0) Reference

MuyGPyS is toolkit for training approximate Gaussian Process (GP) models using the MuyGPs (Muyskens, Goumiri, Priest, Schneider) algorithm.

# Citation

If you use MuyGPyS in a research paper, please reference our article:

```
@article{muygps2021,
title={MuyGPs: Scalable Gaussian Process Hyperparameter Estimation Using Local Cross-Validation},
author={Muyskens, Amanda and Priest, Benjamin W. and Goumiri, Im{\`e}ne and Schneider, Michael},
journal={arXiv preprint arXiv:2104.14581},
year={2021}
}
```

# Variable Name Conventions

We make use of several canonical variable names that refer to tensor shape dimensions. Here is a partial list of the major names and their meanings.

train_count - the number of training observations.

test_count - the number of test or prediction observations.

batch_count - the number of elements to be predicted. Can coincide with train_count or test_count depending on usage. Sometimes also called data_count.

feature_count - the number of features in the observations. Omitted for univariate feature spaces.

response_count - the number of response variables. Omitted for univariate responses.

nn_count - the number of nearest neighbors upon which predictions are conditioned.

out_shape - a tuple referring to the shape associated with the output shape of the cross-covariance. For a univariate problem, in_shape = (nn_count,). For a multivariate problem, out_shape most likely refers to (nn_count, response_count).

in_shape - a tuple referring to the shape associated with how the covariance is conditioned on observations. For a univariate problem, in_shape == (nn_count,). For a multivariate problem, in_shape might refer to (nn_count, response_count), but could instead have a different second element if the observations do not come from the same space as the predictions.