# Multilabel Classification for Entry-Dependent Expert Selection in Distributed Gaussian Processes

## TL;DR

This paper introduces a new method for selecting experts in distributed Gaussian processes based on individual data characteristics, improving efficiency and adaptability.

## Contribution

A flexible expert-selection approach using multilabel classification that adapts to individual data points.

## Key findings

- The proposed method improves prediction quality and efficiency compared to fixed expert selection.
- The approach is scalable and works well on both synthetic and real-world datasets.
- The method is extendable to distributed learning and multi-agent models without Gaussian assumptions.

## Abstract

By distributing the training process, local approximation reduces the cost of the standard Gaussian process. An ensemble method aggregates predictions from local Gaussian experts, each trained on different data partitions, under the assumption of perfect diversity among them. While this assumption ensures tractable aggregation, it is frequently violated in practice. Although ensemble methods provide consistent results by modeling dependencies among experts, they incur a high computational cost, scaling cubically with the number of experts. Implementing an expert-selection strategy reduces the number of experts involved in the final aggregation step, thereby improving efficiency. However, selection approaches that assign a fixed set of experts to each data point cannot account for the unique properties of individual data points. This paper introduces a flexible expert-selection approach tailored to the characteristics of individual data points. To achieve this, we frame the selection task as a multi-label classification problem in which experts define the labels, and each data point is associated with specific experts. We discuss in detail the prediction quality, efficiency, and asymptotic properties of the proposed solution. We demonstrate the efficiency of the proposed method through extensive numerical experiments on synthetic and real-world datasets. This strategy is easily extendable to distributed learning scenarios and multi-agent models, regardless of Gaussian assumptions regarding the experts.