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Keywords: definite
Journal Article
Analytic natural gradient updates for Cholesky factor in Gaussian variational approximation Get access
Journal of the Royal Statistical Society Series B: Statistical Methodology, qkaf001, https://doi.org/10.1093/jrsssb/qkaf001
Published: 29 January 2025
... positive definiteness. To tackle this issue, we derive analytic natural gradient updates of the Cholesky factor of the covariance or precision matrix and consider sparsity constraints representing different posterior correlation structures. Stochastic normalized natural gradient ascent with momentum...
Journal Article
Positive definite functions on a regular domain Get access
IMA Journal of Numerical Analysis, drae074, https://doi.org/10.1093/imanum/drae074
Published: 05 November 2024
...Martin Buhmann; Yuan Xu In other words, from the above becomes . Definition 1.1. A continuous function is called a positive definite function (PDF) on if for every and set of distinct points , the matrix is non-negative definite, and it is called...
Journal Article
Universal Prediction Band via Semi-Definite Programming
Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 84, Issue 4, September 2022, Pages 1558–1580, https://doi.org/10.1111/rssb.12542
Published: 19 August 2022
... a new method with provable uncertainty quantification via semi-definite programming. This paper provides an alternative approach to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The proposed method learns a data...
Journal Article
Projection-free nonconvex stochastic optimization on Riemannian manifolds Get access
IMA Journal of Numerical Analysis, Volume 42, Issue 4, October 2022, Pages 3241–3271, https://doi.org/10.1093/imanum/drab066
Published: 28 September 2021
... that are comparable to the best-known rates for their Euclidean counterparts. Finally, we discuss applications to two classic tasks: the computation of the Karcher mean of positive definite matrices and Wasserstein barycenters for multivariate normal distributions. For both tasks, stochastic Fw methods yield...
Journal Article
The Semantics of Comparatives: A Difference-Based Approach Get access
Journal of Semantics, Volume 38, Issue 2, May 2021, Pages 249–303, https://doi.org/10.1093/jos/ffab003
Published: 18 May 2021
... arithmetic interval subtraction degree questions definite descriptions downward-entailing operators additivity anaphoricity Humans measure objects along some dimension or scale and make comparisons among measurements. As illustrated in (1), we can compare how tall a giraffe is to a certain tree; we...
Journal Article
Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure Get access
IMA Journal of Numerical Analysis, Volume 42, Issue 2, April 2022, Pages 1500–1525, https://doi.org/10.1093/imanum/drab012
Published: 03 May 2021
... is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( https://dbpia.nl.go.kr/journals/pages/open_access/funder_policies/chorus/standard_publication_model ) Abstract The paper introduces a new characterization of strict positive definiteness...
Journal Article
Geostatistical Modeling of Positive-Definite Matrices: An Application to Diffusion Tensor Imaging
in
Biometrics
Biometrics, Volume 78, Issue 2, June 2022, Pages 548–559, https://doi.org/10.1111/biom.13445
Published: 11 February 2021
... and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive-definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing...
Journal Article
Modeling Sparse Longitudinal Data on Riemannian Manifolds
in
Biometrics
Biometrics, Volume 77, Issue 4, December 2021, Pages 1328–1341, https://doi.org/10.1111/biom.13385
Published: 09 October 2020
... and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine-invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely...
Journal Article
Nonsmooth algorithms for minimizing the largest eigenvalue with applications to inner numerical radius Get access
IMA Journal of Numerical Analysis, Volume 40, Issue 4, October 2020, Pages 2342–2376, https://doi.org/10.1093/imanum/drz041
Published: 13 November 2019
... are applied to, and the deduced results are illustrated on the computation of the inner numerical radius, the modulus of the point on the boundary of the field of values closest to the origin, which carries significance for instance for the numerical solution of a symmetric definite generalized eigenvalue...
Journal Article
Successful treatment of giant abdominal haemophilic pseudotumours causing hydronephrosis Get access
Postgraduate Medical Journal, Volume 95, Issue 1130, December 2019, Pages 673–674, https://doi.org/10.1136/postgradmedj-2019-136753
Published: 09 October 2019
...-publication-reuse-rights ) haemophilia haemophilic pseudotumour abdomen definite diagnosis surgical treatment perioperative management complication Peking Union Medical College Graduate Student Innovation Fund No. 2018-1002-02-08 National Natural Science Foundation of China 10.13039...
Journal Article
Tumour-induced osteomalacia caused by a nodule of the palm Get access
Postgraduate Medical Journal, Volume 95, Issue 1129, November 2019, Page 624, https://doi.org/10.1136/postgradmedj-2019-136710
Published: 01 August 2019
... osteomalacia hypophosphatemia phosphaturic mesenchymal tumour palm definite diagnosis surgical treatment multidisciplinary treatment National Natural Science Foundation of China 10.13039/501100001809 Project No. 81871746 Peking Union Medical College Graduate Student Innovation Fund Project...
Journal Article
Analysis of a new class of rational RBF expansions
IMA Journal of Numerical Analysis, Volume 40, Issue 3, July 2020, Pages 1972–1993, https://doi.org/10.1093/imanum/drz015
Published: 10 April 2019
... definite kernels In this section we review the main theoretical aspects of kernel-based interpolation methods. For further details we refer the reader to the books Buhmann (2003) , Fasshauer (2007) , Fasshauer & McCourt (2015) and Wendland (2005) . The approximation problem we consider can...
Journal Article
The F-G Diagonalization Algorithm
Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 34, Issue 2, June 1985, Pages 177–183, https://doi.org/10.2307/2347375
Published: 05 December 2018
.../standard_publication_model ) Principal components Positive definite matrices Diagonalization References Flury , B. N. ( 1984 ) Common principal components in k groups . J. Amer. Statist. Ass. , 79 , 892 – 898 . Flury , B. and Gautschi , W. ( 1984 ) An algorithm for simultaneous...
Journal Article
The Distribution of a Positive Linear Combination of x2 Random Variables
Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 33, Issue 3, November 1984, Pages 332–339, https://doi.org/10.2307/2347721
Published: 05 December 2018
...:https://dbpia.nl.go.kr/journals/pages/open_access/funder_policies/chorus/standard_publication_model ) Chi-squared variables Linear combination Normal variables Positive definite quadratic form Series representation References Davies , R. B. ( 1980 ) Algorithm AS 155. The distribution of a linear...
Journal Article
The Distribution of Non-Negative Quadratic Forms in Normal Variables
Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 26, Issue 1, March 1977, Pages 92–98, https://doi.org/10.2307/2346884
Published: 05 December 2018
.../chorus/standard_publication_model ) Quadratic Form Distribution Non-negative Definite References Grad , A. and Solomon , H. ( 1955 ). Distribution of quadratic forms and some applications . Ann. Math. Statist ., 26 , 464 – 477 . Hill , I. D. ( 1973 ). Algorithm AS 66...
Journal Article
Parameter estimation in stock assessment modelling: caveats with gradient-based algorithms
ICES Journal of Marine Science, Volume 75, Issue 5, September-October 2018, Pages 1553–1559, https://doi.org/10.1093/icesjms/fsy044
Published: 18 April 2018
..., where the criteria for validation of results is limited to two expressions—“iteration has converged”, and “the Hessian is positive definite”. Fisheries scientists with background in mathematics/statistics may recognize that these expressions are necessary, but not sufficient conditions...
Journal Article
Demixing sines and spikes: Robust spectral super-resolution in the presence of outliers
Information and Inference: A Journal of the IMA, Volume 7, Issue 1, March 2018, Pages 105–168, https://doi.org/10.1093/imaiai/iax005
Published: 29 May 2017
.... The result holds under the assumption that the phases of the sinusoidal and sparse components are random and the line spectrum satisfies a minimum-separation condition. We show that the method can be implemented via semi-definite programming, and explain how to adapt it in the presence of dense perturbations...
Journal Article
The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation Get access
IMA Journal of Numerical Analysis, Volume 38, Issue 1, January 2018, Pages 495–517, https://doi.org/10.1093/imanum/drx015
Published: 10 April 2017
... assumptions. By a set of numerical tests, the Riemannian BB method with nonmonotone line search is shown to be competitive in several Riemannian optimization problems. When used to compute the matrix geometric mean, known as the Karcher mean of positive definite matrices, it notably outperforms existing first...
Journal Article
Modelling structured correlation matrices Get access
in
Biometrika
Biometrika, Volume 104, Issue 1, March 2017, Pages 237–242, https://doi.org/10.1093/biomet/asw061
Published: 13 January 2017
...Ruey S. Tsay; Mohsen Pourahmadi [email protected] 17 9 2015 © 2017 Biometrika Trust 2017 SUMMARY Ensuring positive definiteness of an estimated structured correlation matrix is challenging. We show that reparameterizing Cholesky factors of correlation matrices using hyperspherical...
Journal Article
Gauss quadrature for quasi-definite linear functionals Get access
IMA Journal of Numerical Analysis, Volume 37, Issue 3, July 2017, Pages 1468–1495, https://doi.org/10.1093/imanum/drw032
Published: 22 July 2016
... positive-definite linear functionals. Its mathematical context is extremely rich, with orthogonal polynomials, continued fractions and Padé approximation on one (functional analytic or approximation theory) side, and the method of moments,(real) Jacobi matrices, spectral decompositions and the Lanczos...
