Related papers: pylspack: Parallel algorithms and data structures …
Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
This work studies one of the parallel decision tree learning algorithms, pdsCART, designed for scalable and efficient data analysis. The method incorporates three core capabilities. First, it supports real-time learning from data streams,…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…
In recent years, large-scale models have demonstrated state-of-the-art performance across various domains. However, training such models requires various techniques to address the problem of limited computing power and memory on devices…
We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting…
This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…
We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Sketches are probabilistic data structures that can provide approximate results within mathematically proven error bounds while using orders of magnitude less memory than traditional approaches. They are tailored for streaming data analysis…
The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…