Recent research has shown the potential utility of deep Gaussian processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current published body of work is placed in a common framework and, through recursion, several classes of deep Gaussian processes are deﬁned. The resulting samples generated from a deep Gaussian process have a Markovian structure with respect to the depth parameter, and the eﬀective depth of the resulting process is interpreted in terms of the ergodicity, or nonergodicity, of the resulting Markov chain. For the classes of deep Gaussian processes introduced,more »
SMART LINEAR ALGEBRAIC OPERATIONS FOR EFFICIENT GAUSSIAN MARKOV IMPROVEMENT ALGORITHM
This paper studies computational improvement of the Gaussian Markov improvement algorithm (GMIA)
whose underlying response surface model is a Gaussian Markov random field (GMRF). GMIA’s computational
bottleneck lies in the sampling decision, which requires factorizing and inverting a sparse, but large
precision matrix of the GMRF at every iteration. We propose smart GMIA (sGMIA) that performs expensive
linear algebraic operations intermittently, while recursively updating the vectors and matrices necessary to
make sampling decisions for several iterations in between. The latter iterations are much cheaper than the
former at the beginning, but their costs increase as the recursion continues and ultimately surpass the cost
of the former. sGMIA adaptively decides how long to continue the recursion by minimizing the average
periteration cost. We perform a floatingpoint operation analysis to demonstrate the computational benefit
of sGMIA. Experiment results show that sGMIA enjoys computational efficiency while achieving the same
search effectiveness as GMIA.
 Editors:
 Bae, KH; Feng, B; Kim, S; LazarovaMolnar, S; Zheng, Z; Roeder, T; Thiesing, R
 Award ID(s):
 1854562
 Publication Date:
 NSFPAR ID:
 10233326
 Journal Name:
 Proceedings of the Winter Simulation Conference
 Page Range or eLocationID:
 28872898
 ISSN:
 15584305
 Sponsoring Org:
 National Science Foundation
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