Methods for Generating Random Orthogonal Matrices

By Alan Genz. 2000

45 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability, Numerical Methods & Scientific Computing

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Citations in the corpus

Variational Inference with Normalizing Flows (2015, background): “The resulting Q-matrix will be a random orthogonal matrix (Genz, 1998).”
Unifying Orthogonal Monte Carlo Methods (2019, methodology): “Several methods are known for solving this problem exactly (Genz, 1998; Mezzadri, 2007”
Robustifying Generalized Linear Mixed Models Using a New Class of Mixtures of Multivariate Polya Trees (2009, methodology): “Finally, the orthogonal matrix can be updated using a random-walk Metropolis based on the methods described in Stewart (1980) and Genz (1996). The basic computational method is based on the result that random orthogonal matrices with Haar distribution can be generated by computing the QR factorizati”
Orthogonal Estimation of Wasserstein Distances (2019, unknown): “A variety of methods for approximately sampling from UnifOrt( S d − 1 ; N ) at a cost of O ( d 2 log d ) exist (see for example (Genz, 1999; Choromanski et al., 2017; Andoni et al., 2015)), reducing the cost to approximately that of sampling independent projection directions (i.e.”
Rao–Blackwellization for Bayesian Variable Selection and Model Averaging in Linear and Binary Regression: A Novel Data Augmentation Approach (2011, methodology): “Generating random orthogonal matrices, however, will increase computational complexity of the algorithm; standard algorithms for generating orthogonal matrices are of order O(p(3)) although Genz (1998) describes methods using butterfly matrices that are of order O(log(p)p(2)).”