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Data Sketching and Stacking: A Confluence of Two Strategies for Predictive Inference in Gaussian Process Regressions with High-Dimensional Features
No full textThis 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 noisy low dimensional manifold. Bayesian estimation of the regression relationship using Markov Chain Monte Carlo and subsequent predictive inference is computationally prohibitive and may lead to inferential inaccuracies since accurate variable selection is essentially impossible in such high-dimensional GP regressions. As an alternative, this article proposes a strategy to sketch the high-dimensional feature vector with a carefully constructed sketching matrix, before fitting a GP with the scalar outcome and the sketched feature vector to draw predictive inference. The analysis is performed in parallel with many different sketching matrices and smoothing parameters in different processors, and the predictive inferences are combined using \emph{Bayesian predictive stacking}. Since posterior predictive distribution in each processor is analytically tractable, the algorithm allows bypassing the robustness issues due to convergence and mixing of MCMC chains, leading to fast implementation with very large number of features. The approach outperforms competitors in drawing point prediction with predictive uncertainties of outdoor air pollution from satellite images.National Science Foundatio
Black Fire authors
No full textPWAM, 1960-1922, Black Fire Authors, Selected Author Pages out of Total Pages, as a percentage, zoom.Referenced in Chapter 4 of the book "Digital Literary Redlining: African American Anthologies, Digital Humanities, and the Canon .
Energy Efficiency/Renewable Energy Impact in the Texas Emissions Reduction Plan (TERP), Volume II ��� Technical Appendix, Annual Report to the Texas Commission on Environmental Quality January 2022 ��� December 2022
No full textThe Energy Systems Laboratory (ESL) at the Texas A&M Engineering Experiment Station of the Texas A&M University System is pleased to provide its annual report, ���Energy
Efficiency/Renewable Energy Impact in the Texas Emissions Reduction Plan (TERP),��� as required under Texas Health and Safety Code 386.205, 386.252, 388.006, 389.003 (e), and under Texas Utilities Code Sec. 39.9051 (g) (h), and Sec. 39.9052 (c) (d)
Exact QR factorizations of rectangular matrices
No full textQR factorization is a key tool in mathematics, computer science, operations research, and engineering. This paper presents the roundoff-error-free (REF) QR factorization framework comprising integer-preserving versions of the standard and the thin QR factorizations and associated algorithms to compute them. Specifically, the standard REF QR factorization factors a given matrix as , where has pairwise orthogonal columns, is a diagonal matrix, and is an upper trapezoidal matrix; notably, the entries of and are integral, while the entries of are reciprocals of integers. In the thin REF QR factorization, also has pairwise orthogonal columns, and is also an upper triangular matrix. In contrast to traditional (i.e., floating-point) QR factorizations, every operation used to compute these factors is integral; thus, REF QR is guaranteed to be an exact orthogonal decomposition. Importantly, the bit-length of every entry in the REF QR factorizations (and within the algorithms to compute them) is bounded polynomially. Notable applications of our REF QR factorizations include finding exact least squares or exact basic solutions (i.e., a rational n-dimensional vector ) to any given full column rank or rank deficient linear system , respectively. In addition, our exact factorizations can be used as a subroutine within exact and/or high-precision quadratic programming. Altogether, REF QR provides a framework to obtain exact orthogonal factorizations of any rational matrix (as any rational/decimal matrix can be easily transformed into an integral matrix).The United States Naval Academy partially supported the first author with a Junior NARC grant, and the National Science Foundation partially supported the second author under Grant No OAC-1835499
