7,162 research outputs found
Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations
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. This paper presents two parallel GP regression methods that exploit low-rank covariance matrix approximations for distributing the computational load among parallel machines to achieve time efficiency and scalability. We theoretically guarantee the predictive performance of our proposed parallel GPs to be equivalent to that of some centralized approximate GP regression methods: The computation of their centralized counterparts can be distributed among parallel machines, hence achieving greater time efficiency and scalability. We analytically compare the properties of our parallel GPs such as time, space, and communication complexity. Empirical evaluation on two real-world datasets in a cluster of 20 computing nodes shows that our parallel GPs are significantly more time-efficient and scalable than their centralized counterparts and exact/full GP while achieving predictive performances comparable to full GP
Forecasting of commercial sales with large scale Gaussian Processes
This paper argues that there has not been enough discussion in the field of
applications of Gaussian Process for the fast moving consumer goods industry.
Yet, this technique can be important as it e.g., can provide automatic feature
relevance determination and the posterior mean can unlock insights on the data.
Significant challenges are the large size and high dimensionality of commercial
data at a point of sale. The study reviews approaches in the Gaussian Processes
modeling for large data sets, evaluates their performance on commercial sales
and shows value of this type of models as a decision-making tool for
management.Comment: 1o pages, 5 figure
High-Dimensional Bayesian Geostatistics
With the growing capabilities of Geographic Information Systems (GIS) and
user-friendly software, statisticians today routinely encounter geographically
referenced data containing observations from a large number of spatial
locations and time points. Over the last decade, hierarchical spatiotemporal
process models have become widely deployed statistical tools for researchers to
better understand the complex nature of spatial and temporal variability.
However, fitting hierarchical spatiotemporal models often involves expensive
matrix computations with complexity increasing in cubic order for the number of
spatial locations and temporal points. This renders such models unfeasible for
large data sets. This article offers a focused review of two methods for
constructing well-defined highly scalable spatiotemporal stochastic processes.
Both these processes can be used as "priors" for spatiotemporal random fields.
The first approach constructs a low-rank process operating on a
lower-dimensional subspace. The second approach constructs a Nearest-Neighbor
Gaussian Process (NNGP) that ensures sparse precision matrices for its finite
realizations. Both processes can be exploited as a scalable prior embedded
within a rich hierarchical modeling framework to deliver full Bayesian
inference. These approaches can be described as model-based solutions for big
spatiotemporal datasets. The models ensure that the algorithmic complexity has
floating point operations (flops), where the number of spatial
locations (per iteration). We compare these methods and provide some insight
into their methodological underpinnings
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