23,953 research outputs found
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
We introduce a new structured kernel interpolation (SKI) framework, which
generalises and unifies inducing point methods for scalable Gaussian processes
(GPs). SKI methods produce kernel approximations for fast computations through
kernel interpolation. The SKI framework clarifies how the quality of an
inducing point approach depends on the number of inducing (aka interpolation)
points, interpolation strategy, and GP covariance kernel. SKI also provides a
mechanism to create new scalable kernel methods, through choosing different
kernel interpolation strategies. Using SKI, with local cubic kernel
interpolation, we introduce KISS-GP, which is 1) more scalable than inducing
point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for
substantial additional gains in scalability, without requiring any grid data,
and 3) can be used for fast and expressive kernel learning. KISS-GP costs O(n)
time and storage for GP inference. We evaluate KISS-GP for kernel matrix
approximation, kernel learning, and natural sound modelling.Comment: 19 pages, 4 figure
Measuring Blood Glucose Concentrations in Photometric Glucometers Requiring Very Small Sample Volumes
Glucometers present an important self-monitoring tool for diabetes patients
and therefore must exhibit high accu- racy as well as good usability features.
Based on an invasive, photometric measurement principle that drastically
reduces the volume of the blood sample needed from the patient, we present a
framework that is capable of dealing with small blood samples, while
maintaining the required accuracy. The framework consists of two major parts:
1) image segmentation; and 2) convergence detection. Step 1) is based on
iterative mode-seeking methods to estimate the intensity value of the region of
interest. We present several variations of these methods and give theoretical
proofs of their convergence. Our approach is able to deal with changes in the
number and position of clusters without any prior knowledge. Furthermore, we
propose a method based on sparse approximation to decrease the computational
load, while maintaining accuracy. Step 2) is achieved by employing temporal
tracking and prediction, herewith decreasing the measurement time, and, thus,
improving usability. Our framework is validated on several real data sets with
different characteristics. We show that we are able to estimate the underlying
glucose concentration from much smaller blood samples than is currently
state-of-the- art with sufficient accuracy according to the most recent ISO
standards and reduce measurement time significantly compared to
state-of-the-art methods
Understanding and Comparing Scalable Gaussian Process Regression for Big Data
As a non-parametric Bayesian model which produces informative predictive
distribution, Gaussian process (GP) has been widely used in various fields,
like regression, classification and optimization. The cubic complexity of
standard GP however leads to poor scalability, which poses challenges in the
era of big data. Hence, various scalable GPs have been developed in the
literature in order to improve the scalability while retaining desirable
prediction accuracy. This paper devotes to investigating the methodological
characteristics and performance of representative global and local scalable GPs
including sparse approximations and local aggregations from four main
perspectives: scalability, capability, controllability and robustness. The
numerical experiments on two toy examples and five real-world datasets with up
to 250K points offer the following findings. In terms of scalability, most of
the scalable GPs own a time complexity that is linear to the training size. In
terms of capability, the sparse approximations capture the long-term spatial
correlations, the local aggregations capture the local patterns but suffer from
over-fitting in some scenarios. In terms of controllability, we could improve
the performance of sparse approximations by simply increasing the inducing
size. But this is not the case for local aggregations. In terms of robustness,
local aggregations are robust to various initializations of hyperparameters due
to the local attention mechanism. Finally, we highlight that the proper hybrid
of global and local scalable GPs may be a promising way to improve both the
model capability and scalability for big data.Comment: 25 pages, 15 figures, preprint submitted to KB
Scalable Sparse Cox's Regression for Large-Scale Survival Data via Broken Adaptive Ridge
This paper develops a new scalable sparse Cox regression tool for sparse
high-dimensional massive sample size (sHDMSS) survival data. The method is a
local -penalized Cox regression via repeatedly performing reweighted
-penalized Cox regression. We show that the resulting estimator enjoys the
best of - and -penalized Cox regressions while overcoming their
limitations. Specifically, the estimator is selection consistent, oracle for
parameter estimation, and possesses a grouping property for highly correlated
covariates. Simulation results suggest that when the sample size is large, the
proposed method with pre-specified tuning parameters has a comparable or better
performance than some popular penalized regression methods. More importantly,
because the method naturally enables adaptation of efficient algorithms for
massive -penalized optimization and does not require costly data driven
tuning parameter selection, it has a significant computational advantage for
sHDMSS data, offering an average of 5-fold speedup over its closest competitor
in empirical studies
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