With Machine Learning, Regression is Progress

January 3, 2023

There are many industries that seek to leverage the effects that successful model scaling can bring. In agriculture, for example, several different factors, such as the quality of the soil, the use of pesticides, or a sudden change in the climate need to be considered for their effect on crops. Deploying a Gaussian Process Regression (GPR) model is a good method for modeling geospatial problems (or processes), and processes where the inputs can be modeled as gaussian distributions. This lends itself to the generation of a variety of predictions for weather forecasts, crop yield, shelf life, etc. Real estate pricing can benefit from this model as well as each process carries its own set of risks that lend themselves to regression models. You can compare present real estate pricing and historical statistics with various parameters, allowing the GPR to perform a wider scope of analytics. This is the possibility to mitigate the risk that GPR models can provide. 

Bayesian ML was developed as a paradigm for constructing statistical models with the goal to estimate a posterior distribution on the outcome, given a set of observations (the training data) and a prior distribution. When training an ML model with the Bayesian paradigm we try to estimate the posterior distribution that maximizes the likelihood of the observations. Gaussian Process Regression (GPR) is an ML regression model that uses nonparametric Bayesian inference for regression. GPR can be thought of as a flexible model that can be applied to many different types of data. However, an important question has been “how can we scale Gaussian process models in production?” We need to address scaling the estimation from these models in production to generate better predictions based on our set parameters. In this blog, we’ll explore GPR, recent discoveries regarding scalability, and implementation use cases for GPR in production.

The Regression Model Moving Bayesian Inference Forward

While GPR models have their benefits, the standard algorithm has a computational complexity that is cubic in N (the dimensionality of the feature space). This quickly makes the algorithm impractical for even moderate-size problems. This has led to efforts devoted to improving the scalability of GPR models while retaining favorable prediction quality for big data, particularly with global approximations which approximate the kernel matrix through global distillation resulting in a sparse kernel matrix and representation between training points. Local approximations follow the divide-and-conquer methodology to focus on the subsets of training data. 

Global approximations, especially sparse approximations, have generally reduced the standard cubic complexity. Sparse approximations however are still impractical from a computational POV, particularly in scenarios requiring real-time predictions such as environmental sensing and monitoring. Alternatively, we can implement the sparse approximations using advanced computing infrastructure, e.g., GPUs and distributed clusters/processors, to speed up the computation. The model using GPU and distributed clusters implements parallel and fast linear algebra algorithms with modern distributed memory and multi-core/multi-GPU hardware.

Image courtesy of “When Gaussian Process Meets Big Data

Ideally, parallelization can achieve an increase in speed close to the number of machines in comparison to the centralized counterparts. Impressively, the first GPRs were implemented in a distributed computing platform using up to one billion training points and trained the model successfully within two hours. The local approximations generally have the same complexity as the global approximations if the training size for each expert is equal to the inducing size. The divide-and-conquer method of utilizing local approximations is only capable of capturing local patterns and is not able to describe global ones. To enhance the representational capability of scalable GPRs, hybrid approximations are a straightforward thread by combining global and local approximations in tandem.

Regression Model Deployment 

GPR has a long history, but its non-parametric flexibility and high interpretability remain their main attractions despite the challenges of scaling in the big data age. Along with its variety of uses, ranging from the agricultural industry to real estate pricing you can see why it is a popular Bayesian inference regression model. However, an alternative to investments in more infrastructure, like purchasing GPUs, is updating your model deployment. 

With Wallaroo’s Rust language distributed computing engine, you can quickly Iterate and scale your advanced GPR models so your enterprise can enjoy enhanced productivity and efficiency. Talk to an expert about the easiest way to deploy, run and observe your ML models in production and at scale or try Wallaroo CE yourself and optimize your MLOps with the simplicity, speed, and efficiency of Wallaroo.