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A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support.
Joint measures and cross-covariance operators
Baker, C · 1973
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Efficient Metropolis jumping rules
Gelman, A., Roberts, G. O., and Gilks, W. R · 1996
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Integral transforms, reproducing kernels, and their applications
Saitoh, S · 1997
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Nonlinear component analysis as a kernel eigenvalue problem
Schölkopf, B., Smola, A. J., and Müller, K.-R · 1998
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Bayesian classification with Gaussian processes
Williams, C.K.I. and Barber, D · 1998
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Adaptive Proposal Distribution for Random Walk Metropolis Algorithm
Haario, H., Saksman, E., and Tamminen, J · 1999
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An adaptive Metropolis algorithm
Haario, H., Saksman, E., and Tamminen, J · 2001
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Regularized principal manifolds
Smola, A. J., Mika, S., Schölkopf, B., and Williamson, R. C · 2001
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Learning to find pre-images
Bakir, G., Weston, J., and Schölkopf, B · 2003
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Langevin diffusions and Metropolis-Hastings algorithms
Roberts, G.O. and Stramer, O · 2003
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Reproducing Kernel Hilbert Spaces in Probability and Statistics
Berlinet, A. and Thomas-Agnan, C · 2004
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Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces
Fukumizu, K., Bach, F. R., and Jordan, M. I · 2004
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Integrating structured biological data by kernel maximum mean discrepancy
Borgwardt, K. M., Gretton, A., Rasch, M. J., Kriegel, H.-P., Schölkopf, B., and Smola, A. J · 2006
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A kernel method for the two-sample problem
Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., and Smola, A · 2007
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Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms
Roberts, G.O. and Rosenthal, J.S · 2007
The pseudo-marginal approach for efficient Monte Carlo computations
Andrieu, C. and Roberts, G.O · 2009
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Hilbert space embeddings and metrics on probability measures
Sriperumbudur, B., Gretton, A., Fukumizu, K., Lanckriet, G., and Schölkopf, B · 2010
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Riemann manifold Langevin and Hamiltonian Monte Carlo methods
Girolami, M. and Calderhead, B · 2011
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Universality, characteristic kernels and RKHS embedding of measures
Sriperumbudur, B., Fukumizu, K., and Lanckriet, G · 2011
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Bayesian learning via stochastic gradient Langevin dynamics
Welling, M. and Teh, Y.W · 2011
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Slice sampling covariance hyperparameters of latent Gaussian models
Murray, I. and Adams, R.P · 2012
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A tutorial on adaptive MCMC
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Steinwart, I. and Christmann, A · 2008
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