Related papers: pylspack: Parallel algorithms and data structures …
Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…
Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
In recent years, mesh subdivision---the process of forging smooth free-form surfaces from coarse polygonal meshes---has become an indispensable production instrument. Although subdivision performance is crucial during simulation, animation…
Neuromorphic computing, characterized by its event-driven computation and massive parallelism, is particularly effective for handling data-intensive tasks in low-power environments, such as computing the minimum spanning tree (MST) for…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and…
Skyline queries are one of the most widely adopted tools for Multi-Criteria Analysis, with applications covering diverse domains, including, e.g., Database Systems, Data Mining, and Decision Making. Skylines indeed offer a useful overview…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…
Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms.…
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…