Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood

TL;DR

This paper introduces a novel approach for Gaussian process regression that enables learning from summarized data, such as features and statistics, addressing confidentiality and cost issues in spatial data analysis.

Contribution

It proposes the concept of sample quasi-likelihood and analyzes approximation errors, allowing effective inference from summarized data in Gaussian process models.

Findings

Approximation errors depend on data granularity and covariance length scale.

The method effectively models non-Gaussian likelihoods with summarized data.

Experimental results confirm practical applicability in spatial modeling.

Abstract

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit from this development. Difficulties still arise when we can only access summarized data consisting of representative features, summary statistics, and data point counts. Such situations frequently occur primarily due to concerns about confidentiality and management costs associated with spatial data. This study tackles learning and inference using only summarized data within the framework of Gaussian process regression. To address this challenge, we analyze the approximation errors in the marginal likelihood and posterior distribution that arise from utilizing representative features. We also introduce the concept of sample quasi-likelihood, which facilitates learning and inference using only summarized data. Non-Gaussian likelihoods satisfying certain assumptions can be captured by specifying a variance function that characterizes a sample quasi-likelihood function. Theoretical and experimental results demonstrate that the approximation performance is influenced by the granularity of summarized data relative to the length scale of covariance functions. Experiments on a real-world dataset highlight the practicality of our method for spatial modeling.