Robust Variational Gaussian Process Regression for Count Data with the Trimmed Marginal Likelihood

Implementation of the Trimmed Marginal Likelihood GP for regression of count data as proposed in Robust Variational Gaussian Process Regression for Count Data with the Trimmed Marginal Likelihood.

Requirements

• Python >= 3.12
• PyTorch >= 2.0.1
• GPyTorch >= 1.13

Preparation

1. Create experiment environment using e.g. conda as follows

conda create -n GPs python=3.12
conda activate GPs
pip3 install gpytorch matplotlib

2. Create nessecary folders for saving pre-processed data and results

mkdir all_results && mkdir all_results_hyper_params && mkdir all_summary_data && mkdir all_plots && mkdir openDatasets_prepared

3. (OPTIONAL - Only necessary for experiments with real data)

mkdir openDatasets_raw

Place the real data in openDatasets_raw and run prepare_real_count_data.py

4. Create synthetic data and/or add outliers to real data

python prepare_splits_add_outliers_count_data.py

Run Experiments and Evaluate Results

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1. Run Experiments

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Run proposed method $\nu$-GP with Negative Binomial (NB) likelihoodon synthetic data with 5% outliers (without inducing points):

python runExperiments.py --likelihood=NB --method=trimmedLB --noise_type=lowest --true_outlier_ratio=0.05 

Same as above but using 200 inducing points:

python runExperiments.py --likelihood=NB --method=trimmedLB --noise_type=lowest --true_outlier_ratio=0.05 --reduced_rank=200 --learn_inducing_points=True 

Run ordinary count GP with Negative Binomial likelihood:

python runExperiments.py --likelihood=NB --method=variationalApprox --noise_type=lowest --true_outlier_ratio=0.05

Run OLRE (observation-level random effect) model with Poisson likelihood:

python runExperiments.py --likelihood=Poisson --method=OLRE --noise_type=lowest --true_outlier_ratio=0.05

Run $w$-GP model with NB likelihood:

python runExperiments.py --likelihood=NB --method=wGP --noise_type=lowest --true_outlier_ratio=0.05

Run GP with Poisson Likelihood trained by optimizing the $\gamma$-divergence ($\gamma$-div):

python runExperiments.py --likelihood=RobustPoisson --method=variationalApprox --noise_type=lowest --true_outlier_ratio=0.05

Run GP with NB Likelihood and post-hoc trimming (Post-Hoc) where $\nu$ is set to 0.2:

python runExperiments.py --likelihood=NB --method=variationalApproxPostHocTrimming --pre_specified_nu=0.2 --noise_type=lowest --true_outlier_ratio=0.05

For more details see argument description in runExperiments.py All results for analysis are saved into folder "all_results/".

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3. Show summary of all results

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Determine outlier ratio (using Algorithm 2 and 3) and create summary data by running:

python create_summary_data.py --noise_type=lowest --true_outlier_ratio=0.05

Shows summary of negative log-likelihood (nll) results (requires results of all methods on all datasets):

python show_summary.py

Shows scaled continuous ranked probability scores (SCRPS) (requires results of all methods on all datasets):

python show_summary.py --scrps 

Shows outlier estimates (requires results of all methods on all datasets):

python show_outlier_estimates.py

Plots the difference of a model's predictive cumulative distribution function (CDF) and the empirical CDF (requires results of all methods on all datasets):

python create_plots.py

Citation

If you are using part of the code in your work please cite the following paper:

Andrade, Daniel. "Robust Variational Gaussian Process Regression for Count Data with the Trimmed Marginal Likelihood." Statistics and Computing 36, 139 (2026): https://doi.org/10.1007/s11222-026-10895-9