Efficient Bayesian Inference for a Gaussian Process Density Model
This work provides an incremental improvement in Bayesian inference methods for Gaussian process density models, potentially benefiting researchers and practitioners in machine learning and statistics.
The authors tackled the problem of nonparametric density estimation by developing a Gaussian process model with latent variable augmentation, enabling efficient Bayesian inference via Gibbs sampling and variational methods. They demonstrated the performance of their algorithms on datasets with up to several thousand data points, showing comparisons with other density estimators.
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent Pólya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and comparisons with other density estimators are demonstrated on artificial and real datasets with up to several thousand data points.