Censored Gaussian Processes

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This repository is the official implementation of the CGP, from Estimating latent demand of shared mobility through censored Gaussian Processes.

The full paper is available here: link1, link2

The implementation is based on GPy

Summary

This repository contains:

1. GPy/likelihoods/censored_gaussian.py: the proposed Censored-Gaussian distribution together with the respective moments for the EP inference procedure (Section 3.4 in the paper)
2. GPy/models/gp_censored_regression.py: the proposed CGP model

Using the Censored GP in your own GPy code for regression problems is very simple. For example, given (i) a censored dataset {x, y_censored}, (ii) a kernel function (kernel) and (iii) censorship labels (censoring), you just need to instatiate a GPCensoredRegression model (as you would normally do with GPy objects, e.g. GPRegression in the standard GP with homescedastic noise):

kernel = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.) # kernel function
censoring = ... # censorship labels (i.e. vector having c_i=1 if observation "i" is censored and c_i=0 otherwise)
likelihood = GPy.likelihoods.CensoredGaussian(censoring=censoring, variance=1.) # censored-Gaussian likelihood

# build model
gp = GPy.models.GPCensoredRegression(X=x, Y=y_censored, censoring=censoring, kernel=kernel, likelihood=likelihood) # CGP model

# optimize model
gp.optimize(optimizer="adam", max_iters=2500, messages=True)

Once the model is trained, you can obtain posterior samples and use it to make predictions:

f_samples = gp.posterior_samples_f(X=x, size=100) # get 100 posterior samples for the input x 

Training and Evaluation code

A working Jupyter Notebook is provided in CensoredGP_Intro.ipynb, replicating results for the synthetic dataset (more details in Section 4 of the paper).

The notebook contains:

1. Data Generation & Pre-processing
2. Training & Evaluation code for the synthetic dataset showcasing usage of the three models used in our experiments (i.e. NCGP, NCGP-A, CGP)

Summary of results

In our work, we show how the proposed model is able to achieve better performance in capturing the latent non-censored process on a variety of different tasks. Below is a summary of the presented results:

Acknowledgements

This code base builds on several other repositories. The biggest sources of inspiration are:

• https://github.com/SheffieldML/GPy
• https://github.com/BRML/climin

Thanks to the authors of these and the many other useful repositories!