Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n^3) to O(n^2). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n^3) to O(n^2). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.

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Python is the de-facto language for software development in artificial intelligence (AI). Commonly used libraries, such as PyTorch and TensorFlow, rely on parallelization built into their BLAS backends to achieve speedup on CPUs. However, only applying parallelization in a low-level backend can lead to performance and scaling degradation. In this work, we present a novel way of binding task-based C++ code built on the asynchronous runtime model HPX to a high-level Python API using pybind11. We develop a parallel Gaussian process (GP) li- brary as an application. The resulting Python library GPRat combines the ease of use of commonly available GP libraries with the performance and scalability of asynchronous runtime systems. We evaluate the per- formance on a mass-spring-damper system, a standard benchmark from control theory, for varying numbers of regressors (features). The results show almost no binding overhead when binding the asynchronous HPX code using pybind11. Compared to GPyTorch and GPflow, GPRat shows superior scaling on up to 64 cores on an AMD EPYC 7742 CPU for train- ing. Furthermore, our library achieves a prediction speedup of 7.63 over GPyTorch and 25.25 over GPflow. If we increase the number of features from eight to 128, we observe speedups of 29.62 and 21.19, respectively. These results showcase the potential of using asynchronous tasks within Python-based AI applications.

Ever wonder how you can create non-parametric supervised learning models with unlimited expressive power? Look no further than Gaussian Process Regression (GPR), an algorithm that learns to make predictions almost entirely from the data itself (with a little help from hyperparameters). Combining this algorithm with recent advances in computing, such as automatic differentiation, allows for applying GPRs to solve a variety of supervised machine learning problems in near-real-time. In this article, we'll discuss: This is the second article in my GPR series. For a rigorous, Ab initio introduction to Gaussian Process Regression, please check out my previous article here. Before we dive into how we can implement and use GPR, let's quickly review the mechanics and theory behind this supervised machine learning algorithm.

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n^3) to O(n^2). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.