Distributed Gaussian Processes (1502.02843v3)

Abstract: To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP approximations, the rBCM is conceptually simple and does not rely on inducing or variational parameters. The key idea is to recursively distribute computations to independent computational units and, subsequently, recombine them to form an overall result. Efficient closed-form inference allows for straightforward parallelisation and distributed computations with a small memory footprint. The rBCM is independent of the computational graph and can be used on heterogeneous computing infrastructures, ranging from laptops to clusters. With sufficient computing resources our distributed GP model can handle arbitrarily large data sets.

• The paper introduces rBCM, a distributed product-of-experts model that scales Gaussian Processes to datasets with up to 10^7 points.
• It avoids complex inducing or variational parameters by partitioning the data among GP experts on heterogeneous infrastructures.
• It refines predictions by calibrating expert weights, outperforming traditional BCM and gPoE models, especially in data-sparse regions.

An Examination of Distributed Gaussian Processes

The paper "Distributed Gaussian Processes" by Marc Peter Deisenroth and Jun Wei Ng introduces the Robust Bayesian Committee Machine (rBCM), a novel approach to scaling Gaussian Processes (GPs) efficiently to handle large datasets. This work addresses the primary challenge of traditional GPs, which scale poorly with both the number of data points and computational resources required, making them impractical for large-scale applications. The rBCM presents a structured, scalable solution that leverages distributed computations without the complications associated with inducing or variational parameters, as seen in state-of-the-art sparse GP approximations.

Gaussian Processes are a powerful tool for probabilistic nonlinear regression due to their non-parametric nature and flexible modeling capabilities. They have been widely used across various domains including optimization, robotics, and spatial-temporal modeling. However, their application is significantly limited by computational requirements that scale cubically with the data size $N$. The introduction of sparse approximations mitigated this bottleneck, enabling the handling of larger datasets through the use of inducing points or variational parameters. These techniques typically involve approximations that reduce computational complexity but come with drawbacks such as potential information loss or the need for additional optimization stages for the selection of inducing points.

The central contribution of this paper lies in the implementation of the rBCM, a distributed product-of-experts (PoE) model that recursively decomposes the computational workload into smaller, manageable units (or "experts"), which are then recombined to produce the final prediction. The distributed nature of rBCM allows it to function effectively on heterogeneous computing infrastructures, which range from laptops to high-performance clusters. Each component GP expert operates on a partition of the data, making the model versatile and remarkably scalable.

Key Results and Analysis

The authors report that rBCM can handle datasets of sizes as large as $10^7$, a vast improvement over traditional methods that struggle beyond $N = 10^4$. In their experiments on large non-stationary datasets, including airline delays and the Kin40K robotics dataset, rBCM demonstrated competitive performance growth against other distributed GP models like the generalized product of experts (gPoE) and Bayesian Committee Machines (BCM). The rBCM delivers predictive means and variances analytically, obviating the need for Metropolis-Hastings or variational inference, which are commonly used in mixture models for GPs.

One of the paper's salient points is the contrast between rBCM and earlier models like BCM and gPoE. While BCM suffers from the potential weakness of individual experts and propensity to poorly adjusted predictions when exiting the scope of the observed data, gPoE tends to be overly conservative, often overly broadening predictive variances. rBCM harmonizes these issues by introducing calibrated expert importances (weights), enhancing the model's robustness, and ensuring a fallback to the GP prior in regions with sparse data.

Implications for Future Research and Practice

The implications of this research are multifold. Theoretically, it opens avenues for exploring more generalized distributed learning frameworks in probabilistic modeling, synthesizing multiple expert opinions efficiently under a Bayesian framework. Practically, rBCM's design for distributed computations makes it highly applicable in real-world scenarios where distributed or parallel processing is advantageous, such as in sensor networks or large-scale environmental modeling.

Moving forward, potential areas of research could include refining the partition strategies of data amongst GP experts to optimize performance further, or adapting the rBCM in contexts of deep learning architectures where hybrid methods could exploit the strengths of both paradigms. Additionally, a deeper exploration into non-stationary kernels within rBCM could broaden its applicability to dynamically evolving datasets.

In conclusion, the paper presents a thoughtfully crafted methodology to resolve inherent scaling issues with Gaussian Processes. The rBCM's methodological innovations and experimental validations offer a foundation for both academic progression and practical deployment in large-scale machine learning applications.