GPBoost: Combining Tree-Boosting with Gaussian Process and Mixed Effects Models

Introduction
Modeling background
News
Open issues - contribute
References
License

Introduction

GPBoost is a software library for combining tree-boosting with Gaussian process and grouped random effects models (aka mixed effects models or latent Gaussian models). It also allows for independently applying tree-boosting as well as Gaussian process and (generalized) linear mixed effects models (LMMs and GLMMs). The GPBoost library is predominantly written in C++, it has a C interface, and there exist both a Python package and an R package.

For more information, you may want to have a look at:

The Python package and R package including installation instructions
The companion articles Sigrist (2022, JMLR) and Sigrist (2023, TPAMI) for background on the methodology
Detailed Python examples and R examples
Main parameters: the most important parameters / settings for the GPBoost library
The following blog posts:
The CLI installation guide explaining how to install the command line interface (CLI) version
Comments on computational efficiency and large data
The documentation at https://gpboost.readthedocs.io

Modeling background

The GPBoost algorithm combines tree-boosting with latent Gaussian models such as Gaussian process (GP) and grouped random effects models. This allows to leverage advantages and remedy drawbacks of both tree-boosting and latent Gaussian models; see below for a list of strength and weaknesses of these two modeling approaches. The GPBoost algorithm can be seen as a generalization of both traditional (generalized) linear mixed effects and Gaussian process models and classical independent tree-boosting (which often has the highest prediction for tabular data).

Advantages of the GPBoost algorithm

Compared to (generalized) linear mixed effects and Gaussian process models, the GPBoost algorithm allows for

modeling the fixed effects function in a non-parametric and non-linear manner which can result in more realistic models which, consequently, have higher prediction accuracy

Compared to classical independent boosting, the GPBoost algorithm allows for

more efficient learning of predictor functions which, among other things, can translate into increased prediction accuracy
efficient modeling of high-cardinality categorical variables
modeling spatial or spatio-temporal data when, e.g., spatial predictions should vary continuously , or smoothly, over space

Modeling details

For Gaussian likelihoods (GPBoost algorithm), it is assumed that the response variable (aka label) y is the sum of a potentially non-linear mean function F(X) and random effects Zb:

y = F(X) + Zb + xi

where F(X) is a sum (="ensemble") of trees, xi is an independent error term, and X are predictor variables (aka covariates or features). The random effects Zb can currently consist of:

Gaussian processes (including random coefficient processes)
Grouped random effects (including nested, crossed, and random coefficient effects)
Combinations of the above

For non-Gaussian likelihoods (LaGaBoost algorithm), it is assumed that the response variable y follows a distribution p(y|m) and that a (potentially multivariate) parameter m of this distribution is related to a non-linear function F(X) and random effects Zb:

y ~ p(y|m)
m = G(F(X) + Zb)

where G() is a so-called link function. See here for a list of currently supported likelihoods p(y|m).

Estimating or training the above-mentioned models means learning both the covariance parameters (aka hyperparameters) of the random effects and the predictor function F(X). Both the GPBoost and the LaGaBoost algorithms iteratively learn the covariance parameters and add a tree to the ensemble of trees F(X) using a functional gradient and/or a Newton boosting step. See Sigrist (2022, JMLR) and Sigrist (2023, TPAMI) for more details.

Strength and weaknesses of tree-boosting and linear mixed effects and GP models

Classical independent tree-boosting

Strengths	Weaknesses
- State-of-the-art prediction accuracy	- Assumes conditional independence of samples
- Automatic modeling of non-linearities, discontinuities, and complex high-order interactions	- Produces discontinuous predictions for, e.g., spatial data
- Robust to outliers in and multicollinearity among predictor variables	- Can have difficulty with high-cardinality categorical variables
- Scale-invariant to monotone transformations of predictor variables
- Automatic handling of missing values in predictor variables

Linear mixed effects and Gaussian process (GPs) models (aka latent Gaussian models)

Strengths	Weaknesses
- Probabilistic predictions which allows for uncertainty quantification	- Zero or a linear prior mean (predictor, fixed effects) function
- Incorporation of reasonable prior knowledge. E.g. for spatial data: "close samples are more similar to each other than distant samples" and a function should vary continuously / smoothly over space
- Modeling of dependency which, among other things, can allow for more efficient learning of the fixed effects (predictor) function
- Grouped random effects can be used for modeling high-cardinality categorical variables

News

See the GitHub releases page
October 2022: Glad to announce that the two companion articles are published in the Journal of Machine Learning Research (JMLR) and IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI)
04/06/2020 : First release of GPBoost

Open issues - contribute

See the open issues on GitHub with an enhancement label

Software issues

Add Python tests (see corresponding R tests)
Setting up a CI environment
Support conversion of GPBoost models to ONNX model format

Methodological issues

Support multivariate models, e.g., using coregionalization
Support areal models for spatial data such as CAR and SAR models
Support multiclass classification, i.e., multinomial likelihoods
Implement more approaches such that computations scale well (memory and time) for Gaussian process models and mixed effects models with more than one grouping variable for non-Gaussian data
Support sample weights
Support other distances besides the Euclidean distance (e.g., great circle distance) for Gaussian processes

Computational issues

Add GPU support for Gaussian processes
Add CHOLMOD support

References

Sigrist Fabio. "Gaussian Process Boosting". Journal of Machine Learning Research (2022).
Sigrist Fabio. "Latent Gaussian Model Boosting". IEEE Transactions on Pattern Analysis and Machine Intelligence (2023).
Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong Ma, Qiwei Ye, Tie-Yan Liu. "LightGBM: A Highly Efficient Gradient Boosting Decision Tree". Advances in Neural Information Processing Systems 30 (2017).
Williams, Christopher KI, and Carl Edward Rasmussen. Gaussian processes for machine learning. MIT press, 2006.
Pinheiro, Jose, and Douglas Bates. Mixed-effects models in S and S-PLUS. Springer science & business media, 2006.

License

This project is licensed under the terms of the Apache License 2.0. See LICENSE for more information.

fabsig / GPBoost

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