GPBoost: Tree-Boosting, Gaussian Processes, and Mixed-Effects Models
Table of Contents
- Introduction
- Modeling background
- News
- Open issues - contribute
- References
- License
Introduction
GPBoost is a software library for tree-boosting, Gaussian processes, and mixed-effects models (aka latent Gaussian variable models). It allows for combining tree-boosting with Gaussian process and random effects models ( = GPBoost algorithm) as wells as for independently applying Gaussian processes, (generalized) linear mixed effects models (LMMs and GLMMs), and tree-boosting. 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:
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
Open issues - contribute
- See the open issues on GitHub with an enhancement label
Note for contributors: every contribution must pass the unit tests and the additional checks (CRAN compatibility, compiler warnings, ASan / UBSan sanitizer checks) described in the Testing section of the R package README.
Methodological ToDos
- 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
- Support other distances besides the Euclidean distance (e.g., great circle distance) for Gaussian processes
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).
- Kündig Pascal and Sigrist Fabio. "Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models". Journal of the American Statistical Association (2024, in press)
- 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.
