-
1
-
-
84892188881
-
Why natural gradient?
-
(May)
-
Amari, S., Douglas, S.C., Why natural gradient?. Proceedings of the IEEE International Conference on Acoustics, Speech and, Signal Processing, vol. 2, 1998, 1213–1216 (May).
-
(1998)
Proceedings of the IEEE International Conference on Acoustics, Speech and, Signal Processing
, vol.2
, pp. 1213-1216
-
-
Amari, S.1
Douglas, S.C.2
-
2
-
-
3543081155
-
Variational Algorithms for Approximate Bayesian Inference
-
(PhD thesis) University College London
-
Beal, M.J., Variational Algorithms for Approximate Bayesian Inference. (PhD thesis), 2003, University College London.
-
(2003)
-
-
Beal, M.J.1
-
3
-
-
84888355781
-
Optimal tuning of the hybrid Monte Carlo algorithm
-
Beskos, Alexandros, Pillai, Natesh, Roberts, Gareth, Sanz-Serna, Jesus-Maria, Stuart, Andrew, Optimal tuning of the hybrid Monte Carlo algorithm. Bernoulli 19:5A (2013), 1501–1534.
-
(2013)
Bernoulli
, vol.19
, Issue.5A
, pp. 1501-1534
-
-
Beskos, A.1
Pillai, N.2
Roberts, G.3
Sanz-Serna, J.-M.4
Stuart, A.5
-
4
-
-
84885878770
-
The geometry of Hamiltonian Monte Carlo
-
(arXiv:1112.4118)
-
Betancourt, Michael, Stein, Leo C., The geometry of Hamiltonian Monte Carlo. 2011 (arXiv:1112.4118).
-
(2011)
-
-
Betancourt, M.1
Stein, L.C.2
-
5
-
-
84962893190
-
Optimizing the integrator step size for Hamiltonian Monte Carlo
-
(arXiv:1411.6669)
-
Betancourt, Michael, Byrne, Simon, Girolami, Mark, Optimizing the integrator step size for Hamiltonian Monte Carlo. 2015 (arXiv:1411.6669).
-
(2015)
-
-
Betancourt, M.1
Byrne, S.2
Girolami, M.3
-
6
-
-
84989782263
-
The geometric foundations of Hamiltonian Monte Carlo
-
(under review)
-
Betancourt, Michael, Byrne, Simon, Livingstone, Sam, Girolami, Mark, The geometric foundations of Hamiltonian Monte Carlo. Stat. Sci., 2015 (under review).
-
(2015)
Stat. Sci.
-
-
Betancourt, M.1
Byrne, S.2
Livingstone, S.3
Girolami, M.4
-
7
-
-
84962163387
-
Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs
-
Bischof, Christian H., Martin Bücker, H., Lang, Bruno, Rasch, A., Vehreschild, Andre, Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs. Proceedings of the Second IEEE International Workshop on Source Code Analysis and Manipulation, 2002, 65–72.
-
(2002)
Proceedings of the Second IEEE International Workshop on Source Code Analysis and Manipulation
, pp. 65-72
-
-
Bischof, C.H.1
Martin Bücker, H.2
Lang, B.3
Rasch, A.4
Vehreschild, A.5
-
8
-
-
84888128895
-
Geodesic Monte Carlo on embedded manifolds
-
Byrne, Simon, Girolami, Mark, Geodesic Monte Carlo on embedded manifolds. Scand. J. Stat. 40:4 (2013), 825–845.
-
(2013)
Scand. J. Stat.
, vol.40
, Issue.4
, pp. 825-845
-
-
Byrne, S.1
Girolami, M.2
-
9
-
-
35148901069
-
A Metropolis–Hastings algorithm for dynamic causal models
-
Chumbley, Justin R., Friston, Karl J., Fearn, Tom, Kiebel, Stefan J., A Metropolis–Hastings algorithm for dynamic causal models. NeuroImage 38:3 (2007), 478–487.
-
(2007)
NeuroImage
, vol.38
, Issue.3
, pp. 478-487
-
-
Chumbley, J.R.1
Friston, K.J.2
Fearn, T.3
Kiebel, S.J.4
-
10
-
-
0004116989
-
Introduction to Algorithms
-
2nd edition McGraw-Hill Higher Education
-
Cormen, Thomas H., Stein, Clifford, Rivest, Ronald L., Leiserson, Charles E., Introduction to Algorithms. 2nd edition, 2001, McGraw-Hill Higher Education 0070131511.
-
(2001)
-
-
Cormen, T.H.1
Stein, C.2
Rivest, R.L.3
Leiserson, C.E.4
-
11
-
-
0030539336
-
Markov Chain Monte Carlo convergence diagnostics: A comparative review
-
Cowles, M.K., Carlin, B.P., Markov Chain Monte Carlo convergence diagnostics: A comparative review. J. Am. Stat. Assoc. 91:434 (1996), 883–904.
-
(1996)
J. Am. Stat. Assoc.
, vol.91
, Issue.434
, pp. 883-904
-
-
Cowles, M.K.1
Carlin, B.P.2
-
12
-
-
33745183321
-
Mechanisms of evoked and induced responses in MEG/EEG
-
David, Olivier, Kilner, James M., Friston, Karl J., Mechanisms of evoked and induced responses in MEG/EEG. NeuroImage 31:4 (2006), 1580–1591.
-
(2006)
NeuroImage
, vol.31
, Issue.4
, pp. 1580-1591
-
-
David, O.1
Kilner, J.M.2
Friston, K.J.3
-
13
-
-
4243137056
-
Hybrid Monte Carlo
-
Duane, S., Kennedy, A.D., Pendleton, B.J., Roweth, D., Hybrid Monte Carlo. Phys. Lett. B 195 (1987), 216–222.
-
(1987)
Phys. Lett. B
, vol.195
, pp. 216-222
-
-
Duane, S.1
Kennedy, A.D.2
Pendleton, B.J.3
Roweth, D.4
-
14
-
-
76749113376
-
Statistically optimal perception and learning: from behavior to neural representations
-
(Mar)
-
Fiser, József, Berkes, Pietro, Orbán, Gergo, Lengyel, Máté, Statistically optimal perception and learning: from behavior to neural representations. Trends Cogn. Sci. 14:3 (2010), 119–130 (Mar).
-
(2010)
Trends Cogn. Sci.
, vol.14
, Issue.3
, pp. 119-130
-
-
Fiser, J.1
Berkes, P.2
Orbán, G.3
Lengyel, M.4
-
15
-
-
33751115761
-
Variational free energy and the Laplace approximation
-
Friston, K., Mattout, J., Trujillo-Barreto, N., Ashburner, J., Penny, W., Variational free energy and the Laplace approximation. NeuroImage 34 (2007), 220–234.
-
(2007)
NeuroImage
, vol.34
, pp. 220-234
-
-
Friston, K.1
Mattout, J.2
Trujillo-Barreto, N.3
Ashburner, J.4
Penny, W.5
-
16
-
-
0041924877
-
Dynamic causal modelling
-
Friston, K.J., Harrison, L., Penny, W., Dynamic causal modelling. NeuroImage 19:4 (2003), 1273–1302.
-
(2003)
NeuroImage
, vol.19
, Issue.4
, pp. 1273-1302
-
-
Friston, K.J.1
Harrison, L.2
Penny, W.3
-
17
-
-
84972492387
-
Inference from iterative simulation using multiple sequences
-
Gelman, Andrew, Rubin, Donald B., Inference from iterative simulation using multiple sequences. Stat. Sci. 7:4 (1992), 457–472.
-
(1992)
Stat. Sci.
, vol.7
, Issue.4
, pp. 457-472
-
-
Gelman, A.1
Rubin, D.B.2
-
18
-
-
0001032163
-
Evaluating the accuracy of sampling-based approaches to calculating posterior moments
-
J.M. Bernardo J. Berger A.P. Dawid J.F.M. Smith Oxford University Press Oxford
-
Geweke, J., Evaluating the accuracy of sampling-based approaches to calculating posterior moments. Bernardo, J.M., Berger, J., Dawid, A.P., Smith, J.F.M., (eds.) Bayesian Statistics 4, 1992, Oxford University Press, Oxford, 169–193.
-
(1992)
Bayesian Statistics 4
, pp. 169-193
-
-
Geweke, J.1
-
19
-
-
84972511893
-
Practical Markov Chain Monte Carlo
-
Geyer, Charles J., Practical Markov Chain Monte Carlo. Stat. Sci. 08834237, 7(4), 1992, 473–483.
-
(1992)
Stat. Sci.
, vol.7
, Issue.4
, pp. 473-483
-
-
Geyer, C.J.1
-
20
-
-
79952295497
-
Riemann manifold Langevin and Hamiltonian Monte Carlo methods
-
(03)
-
Girolami, Mark, Calderhead, Ben, Riemann manifold Langevin and Hamiltonian Monte Carlo methods. J. R. Stat. Soc. Ser. B 73:2 (2011), 123–214 (03).
-
(2011)
J. R. Stat. Soc. Ser. B
, vol.73
, Issue.2
, pp. 123-214
-
-
Girolami, M.1
Calderhead, B.2
-
21
-
-
0004236492
-
Matrix Computations
-
3rd ed. Johns Hopkins University Press Baltimore, MD, USA
-
Golub, Gene H., Van Loan, Charles F., Matrix Computations. 3rd ed., 2012, Johns Hopkins University Press, Baltimore, MD, USA.
-
(2012)
-
-
Golub, G.H.1
Van Loan, C.F.2
-
22
-
-
0038563932
-
An adaptive Metropolis algorithm
-
Haario, H., Saksman, E., Tamminen, J., An adaptive Metropolis algorithm. Bernoulli 7:2 (2001), 223–242.
-
(2001)
Bernoulli
, vol.7
, Issue.2
, pp. 223-242
-
-
Haario, H.1
Saksman, E.2
Tamminen, J.3
-
23
-
-
84937937938
-
Fast sampling-based inference in balanced neuronal networks
-
Hennequin, G., Aitchison, L., Lengyel, M., Fast sampling-based inference in balanced neuronal networks. Advances in Neural Information Processing Systems, 27, 2014.
-
(2014)
Advances in Neural Information Processing Systems
, vol.27
-
-
Hennequin, G.1
Aitchison, L.2
Lengyel, M.3
-
24
-
-
28944439329
-
User Documentation for CVODES, and ODE Solver with Sensitivity Analysis Capabilities
-
Centre for Applied Scientific Computing, Lawrence Livermore National Laboratory
-
Hindmarsh, A., Serban, R., User Documentation for CVODES, and ODE Solver with Sensitivity Analysis Capabilities. Technical Report, 2002, Centre for Applied Scientific Computing, Lawrence Livermore National Laboratory.
-
(2002)
Technical Report
-
-
Hindmarsh, A.1
Serban, R.2
-
25
-
-
84901687683
-
The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo
-
Hoffman, Matthew D., Gelman, Andrew, The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15:1 (2014), 1593–1623.
-
(2014)
J. Mach. Learn. Res.
, vol.15
, Issue.1
, pp. 1593-1623
-
-
Hoffman, M.D.1
Gelman, A.2
-
26
-
-
84969229610
-
Stochastic Analysis on Manifolds. Graduate Studies in Mathematics
-
American Mathematical Society Providence, RI
-
Hsu, Elton P., Stochastic Analysis on Manifolds. Graduate Studies in Mathematics. 2002, American Mathematical Society, Providence, RI.
-
(2002)
-
-
Hsu, E.P.1
-
27
-
-
84919914124
-
Hamiltonian Monte Carlo without detailed balance
-
Tony Jebara Eric P. Xing
-
Mudigonda, Mayur, Sohl-Dickstein, Jascha, Deweese, Michael, Hamiltonian Monte Carlo without detailed balance. Jebara, Tony, Xing, Eric P., (eds.) Proceedings of the 31st International Conference on Machine Learning (ICML-14) JMLR Workshop and Conference Proceedings, 2014, 719–726.
-
(2014)
Proceedings of the 31st International Conference on Machine Learning (ICML-14), JMLR Workshop and Conference Proceedings
, pp. 719-726
-
-
Mudigonda, M.1
Sohl-Dickstein, J.2
Deweese, M.3
-
28
-
-
85045318750
-
Spherical Hamiltonian Monte Carlo for constrained target distributions
-
Lan, Shiwei, Zhou, Bo, Shahbaba, Babak, Spherical Hamiltonian Monte Carlo for constrained target distributions. ICML, vol. 31, 2014, 629–637.
-
(2014)
ICML
, vol.31
, pp. 629-637
-
-
Lan, S.1
Zhou, B.2
Shahbaba, B.3
-
29
-
-
28844494719
-
Simulating Hamiltonian dynamics
-
Cambridge University Press
-
Leimkuhler, B., Reich, Sebastian, Simulating Hamiltonian dynamics. 2004, Cambridge University Press.
-
(2004)
-
-
Leimkuhler, B.1
Reich, S.2
-
30
-
-
84940084249
-
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
-
Livingstone, S., Girolami, M., Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions. Entropy 16 (2014), 3074–3102.
-
(2014)
Entropy
, vol.16
, pp. 3074-3102
-
-
Livingstone, S.1
Girolami, M.2
-
31
-
-
0030551974
-
Rates of convergence of the Hastings and Metropolis algorithms
-
Mengersen, K.L., Tweedie, R.L., Rates of convergence of the Hastings and Metropolis algorithms. Ann. Stat. 1 (1996), 101–121.
-
(1996)
Ann. Stat.
, vol.1
, pp. 101-121
-
-
Mengersen, K.L.1
Tweedie, R.L.2
-
32
-
-
0002702476
-
The imbedding problem for Riemannian manifolds
-
Nash, John, The imbedding problem for Riemannian manifolds. Ann. Math. 63:1 (1956), 20–63.
-
(1956)
Ann. Math.
, vol.63
, Issue.1
, pp. 20-63
-
-
Nash, J.1
-
34
-
-
0003982971
-
Numerical Optimization
-
2nd edition Springer New York
-
Nocedal, J., Wright, S.J., Numerical Optimization. 2nd edition, 2006, Springer, New York.
-
(2006)
-
-
Nocedal, J.1
Wright, S.J.2
-
35
-
-
77949374261
-
Adaptively scaling the Metropolis algorithm using expected squared jumped distance
-
Pasarica, Cristian, Gelman, Andrew, Adaptively scaling the Metropolis algorithm using expected squared jumped distance. Stat. Sin. 20 (2010), 343–364.
-
(2010)
Stat. Sin.
, vol.20
, pp. 343-364
-
-
Pasarica, C.1
Gelman, A.2
-
36
-
-
69549089778
-
Dynamic causal models for phase coupling
-
(Sep)
-
Penny, W.D., Litvak, V., Fuentemilla, L., Duzel, E., Friston, K., Dynamic causal models for phase coupling. J. Neurosci. Methods 183:1 (2009), 19–30 (Sep).
-
(2009)
J. Neurosci. Methods
, vol.183
, Issue.1
, pp. 19-30
-
-
Penny, W.D.1
Litvak, V.2
Fuentemilla, L.3
Duzel, E.4
Friston, K.5
-
37
-
-
0000759236
-
How many iterations in the Gibbs sampler?
-
Oxford University Press
-
Raftery, Adrian E., Lewis, Steven, How many iterations in the Gibbs sampler?. Bayesian Statistics 4, 1992, Oxford University Press, 763–773.
-
(1992)
Bayesian Statistics 4
, pp. 763-773
-
-
Raftery, A.E.1
Lewis, S.2
-
38
-
-
25444448065
-
Gaussian Processes for Machine Learning
-
The MIT Press
-
Rasmussen, Carl Edward, Williams, Christopher K.I., Gaussian Processes for Machine Learning. 2005, The MIT Press.
-
(2005)
-
-
Rasmussen, C.E.1
Williams, C.K.I.2
-
39
-
-
84977551116
-
Monte Carlo Statistical Methods
-
Springer-Verlag New York, Inc. Secaucus, NJ, USA
-
Robert, Christian P., Casella, George, Monte Carlo Statistical Methods. 2005, Springer-Verlag New York, Inc., Secaucus, NJ, USA 0387212396.
-
(2005)
-
-
Robert, C.P.1
Casella, G.2
-
40
-
-
85132364916
-
Exponential convergence of Langevin distributions and their discrete approximations
-
Roberts, G., Tweedie, R., Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2:4 (1996), 341–363.
-
(1996)
Bernoulli
, vol.2
, Issue.4
, pp. 341-363
-
-
Roberts, G.1
Tweedie, R.2
-
41
-
-
84904092156
-
Efficient gradient computation for dynamical models
-
Sengupta, B., Friston, K.J., Penny, W.D., Efficient gradient computation for dynamical models. NeuroImage 98 (2014), 521–527.
-
(2014)
NeuroImage
, vol.98
, pp. 521-527
-
-
Sengupta, B.1
Friston, K.J.2
Penny, W.D.3
-
42
-
-
84989802320
-
-
(in preparation)
-
Sengupta, Biswa, Friston Karl, J., Penny Will, D., Second order MCMC for dynamic causal modelling, 2015 (in preparation).
-
(2015)
Second order MCMC for dynamic causal modelling
-
-
Sengupta, B.1
Friston Karl, J.2
Penny Will, D.3
-
43
-
-
84937764183
-
Gradient-free MCMC methods for dynamic causal modelling
-
(Mar)
-
Sengupta, Biswa, Friston, Karl J., Penny, Will D., Gradient-free MCMC methods for dynamic causal modelling. NeuroImage 15:112 (2015), 375–381 (Mar).
-
(2015)
NeuroImage
, vol.15
, Issue.112
, pp. 375-381
-
-
Sengupta, B.1
Friston, K.J.2
Penny, W.D.3
-
44
-
-
77956501313
-
Gaussian process optimization in the bandit setting: No regret and experimental design
-
Srinivas, Niranjan, Krause, Andreas, Kakade, Sham, Seeger, Matthias, Gaussian process optimization in the bandit setting: No regret and experimental design. ICML, vol. 27, 2010, 1015–1022.
-
(2010)
ICML
, vol.27
, pp. 1015-1022
-
-
Srinivas, N.1
Krause, A.2
Kakade, S.3
Seeger, M.4
-
45
-
-
84860236413
-
Information-theoretic regret bounds for Gaussian process optimization in the bandit setting
-
Srinivas, Niranjan, Krause, Andreas, Kakade, Sham, Seeger, Matthias, Information-theoretic regret bounds for Gaussian process optimization in the bandit setting. IEEE Trans. Inf. Theory 58:5 (2012), 3250–3265.
-
(2012)
IEEE Trans. Inf. Theory
, vol.58
, Issue.5
, pp. 3250-3265
-
-
Srinivas, N.1
Krause, A.2
Kakade, S.3
Seeger, M.4
-
46
-
-
85003226669
-
Stan Modeling Language Users Guide and Reference Manual, Version 2.5.0
-
Stan Development Team, Stan Modeling Language Users Guide and Reference Manual, Version 2.5.0. 2014.
-
(2014)
-
-
Stan Development Team1
-
47
-
-
65749118363
-
Graphical models, exponential families, and variational inference
-
Wainwright, Martin J., Jordan, Michael I., Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1935-8237, 1(1-2), 2008, 1–305.
-
(2008)
Found. Trends Mach. Learn.
, vol.1
, Issue.1-2
, pp. 1-305
-
-
Wainwright, M.J.1
Jordan, M.I.2
-
48
-
-
84919794312
-
Adaptive Hamiltonian and Riemann manifold Monte Carlo
-
Wang, Ziyu, Mohamed, Shakir, de Freitas, Nando, Adaptive Hamiltonian and Riemann manifold Monte Carlo. ICML, vol. 28, 2013, 1462–1470.
-
(2013)
ICML
, vol.28
, pp. 1462-1470
-
-
Wang, Z.1
Mohamed, S.2
de Freitas, N.3
-
49
-
-
84898817029
-
Langevin diffusions and the Metropolis-adjusted Langevin algorithm
-
Xifara, T., Sherlock, C., Livingstone, S., Byrne, S., Girolami, M., Langevin diffusions and the Metropolis-adjusted Langevin algorithm. Statistics & Probability Letters. 91 (2014), 14–19.
-
(2014)
Statistics & Probability Letters.
, vol.91
, pp. 14-19
-
-
Xifara, T.1
Sherlock, C.2
Livingstone, S.3
Byrne, S.4
Girolami, M.5
|