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The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes.
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Bayes-Hermite Quadrature
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Bai, Z. and Golub, G. H · 1997
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Accurate Error Bounds for the Eigenvalues of the Kernel Matrix
Braun, M. L · 2006
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Gaussian Processes for Machine Learning
Rasmussen, C. E. and Williams, C · 2006
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Information-theoretic Metric Learning
Davis, J. V., Kulis, B., Jain, P., Sra, S., and Dhillon, I. S · 2007
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Approximate Implementation of the logarithm of the Matrix Determinant in Gaussian process Regression
Zhang, Y. and Leithead, W. E · 2007
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Borodin, A · 2009
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Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
Rue, H., Martino, S., and Chopin, N · 2009
Parameter Estimation in High Dimensional Gaussian Distributions
Aune, E., Simpson, D. P., and Eidsvik, J · 2014
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Inference for Determinantal Point Processes Without Spectral Knowledge
Bardenet, R. and Titsias, M. K · 2015
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A Randomized Algorithm for Approximating the Log Determinant of a Symmetric Positive Definite Matrix
Boutsidis, C., Drineas, P., Kambadur, P., and Zouzias, A · 2015
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Enabling Scalable Stochastic Gradient-based inference for Gaussian processes by employing the Unbiased LInear System SolvEr (ULISSE)
Filippone, M. and Engler, R · 2015
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Large-scale Log-Determinant computation through Stochastic Chebyshev Expansions
Han, I., Malioutov, D., and Shin, J · 2015
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Randomized Algorithms for Estimating the Trace of an Implicit Symmetric Positive Semi-definite Matrix
Avron, H. and Toledo, S · 2011
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Computing f(A)b via Least Squares Polynomial Approximations
Chen, J., Anitescu, M., and Saad, Y · 2011
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The University of Florida Sparse Matrix Collection
Davis, T. A. and Hu, Y · 2011
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Determinant Approximations, May 2011
Ipsen, I. C. F. and Lee, D. J · 2011
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Scalable Inference for Structured Gaussian Process Models
Saatçi, Y · 2011
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A Matrix-free Approach for Solving the Parametric Gaussian Process Maximum Likelihood Problem
Anitescu, M., Chen, J., and Wang, L · 2012
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Probabilistic Numerics and Uncertainty in Computations
Hennig, P., Osborne, M. A., and Girolami, M · 2015
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EigenGP: Gaussian Process Models with Adaptive Eigenfunctions
Peng, H. and Qi, Y · 2015
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Large-scale Log-Determinant Computation via Weighted L_2 Polynomial Approximation with Prior Distribution of Eigenvalues
Peng, W. and Wang, H · 2015
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On Spectral Distribution of Kernel Matrices related to Radial Basis functions
Wathen, A. J. and Zhu, S · 2015
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Fast Direct Methods for Gaussian Processes
Ambikasaran, S., Foreman-Mackey, D., Greengard, L., Hogg, D. W., and O’Neil, M · 2016
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Preconditioning Kernel Matrices
Cutajar, K., Osborne, M., Cunningham, J., and Filippone, M · 2016
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Improved Stochastic Trace Estimation using Mutually Unbiased Bases
Fitzsimons, J. K., Osborne, M. A., Roberts, S. J., and Fitzsimons, J. F · 2016
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Fast Estimation of tr (f (a)) via Stochastic Lanczos Quadrature
Ubaru, S., Chen, J., and Saad, Y · 2016
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