Timezone: »
Numerical integration is an key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.
Author Information
Michael A Osborne (U Oxford)
David Duvenaud (Anthropic & U Toronto)
Roman Garnett (Washington University in St. Louis)
Carl Edward Rasmussen (University of Cambridge)
Stephen J Roberts (University of Oxford)
Zoubin Ghahramani (Uber and University of Cambridge)
Zoubin Ghahramani is Professor of Information Engineering at the University of Cambridge, where he leads the Machine Learning Group. He studied computer science and cognitive science at the University of Pennsylvania, obtained his PhD from MIT in 1995, and was a postdoctoral fellow at the University of Toronto. His academic career includes concurrent appointments as one of the founding members of the Gatsby Computational Neuroscience Unit in London, and as a faculty member of CMU's Machine Learning Department for over 10 years. His current research interests include statistical machine learning, Bayesian nonparametrics, scalable inference, probabilistic programming, and building an automatic statistician. He has held a number of leadership roles as programme and general chair of the leading international conferences in machine learning including: AISTATS (2005), ICML (2007, 2011), and NIPS (2013, 2014). In 2015 he was elected a Fellow of the Royal Society.
More from the Same Authors
-
2021 : HumBugDB: A Large-scale Acoustic Mosquito Dataset »
Ivan Kiskin · Marianne Sinka · Adam Cobb · Waqas Rafique · Lawrence Wang · Davide Zilli · Benjamin Gutteridge · Rinita Dam · Theodoros Marinos · Yunpeng Li · Dickson Msaky · Emmanuel Kaindoa · Gerard Killeen · Eva Herreros-Moya · Kathy Willis · Stephen J Roberts -
2021 : Relaxed-Responsibility Hierarchical Discrete VAEs »
Matthew Willetts · Xenia Miscouridou · Stephen J Roberts · Chris C Holmes -
2021 : On-the-fly Strategy Adaptation for ad-hoc Agent Coordination »
Jaleh Zand · Jack Parker-Holder · Stephen J Roberts -
2022 : Gaussian Process parameterized Covariance Kernels for Non-stationary Regression »
Vidhi Lalchand · Talay Cheema · Laurence Aitchison · Carl Edward Rasmussen -
2023 Poster: Bayesian Optimisation of Functions on Graphs »
Xingchen Wan · Pierre Osselin · Henry Kenlay · Binxin Ru · Michael A Osborne · Xiaowen Dong -
2022 : Panel on Open Problems in Machine Learning Systems »
Ivana Dusparic · Stephen J Roberts · Morine Amutorine · Jerome White · Murtuza Shergadwala -
2022 Poster: Sparse Gaussian Process Hyperparameters: Optimize or Integrate? »
Vidhi Lalchand · Wessel Bruinsma · David Burt · Carl Edward Rasmussen -
2022 Poster: Bezier Gaussian Processes for Tall and Wide Data »
Martin Jørgensen · Michael A Osborne -
2022 Poster: Log-Linear-Time Gaussian Processes Using Binary Tree Kernels »
Michael K. Cohen · Samuel Daulton · Michael A Osborne -
2022 Poster: Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization »
Samuel Daulton · Xingchen Wan · David Eriksson · Maximilian Balandat · Michael A Osborne · Eytan Bakshy -
2022 Poster: Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination »
Masaki Adachi · Satoshi Hayakawa · Martin Jørgensen · Harald Oberhauser · Michael A Osborne -
2021 Workshop: Bayesian Deep Learning »
Yarin Gal · Yingzhen Li · Sebastian Farquhar · Christos Louizos · Eric Nalisnick · Andrew Gordon Wilson · Zoubin Ghahramani · Kevin Murphy · Max Welling -
2021 : HumBugDB: A Large-scale Acoustic Mosquito Dataset »
Ivan Kiskin · Marianne Sinka · Adam Cobb · Waqas Rafique · Lawrence Wang · Davide Zilli · Benjamin Gutteridge · Rinita Dam · Theodoros Marinos · Yunpeng Li · Dickson Msaky · Emmanuel Kaindoa · Gerard Killeen · Eva Herreros-Moya · Kathy Willis · Stephen J Roberts -
2021 Poster: Meta-learning to Improve Pre-training »
Aniruddh Raghu · Jonathan Lorraine · Simon Kornblith · Matthew McDermott · David Duvenaud -
2021 Poster: Tuning Mixed Input Hyperparameters on the Fly for Efficient Population Based AutoRL »
Jack Parker-Holder · Vu Nguyen · Shaan Desai · Stephen J Roberts -
2021 Poster: On Pathologies in KL-Regularized Reinforcement Learning from Expert Demonstrations »
Tim G. J. Rudner · Cong Lu · Michael A Osborne · Yarin Gal · Yee Teh -
2021 Poster: Adversarial Attacks on Graph Classifiers via Bayesian Optimisation »
Xingchen Wan · Henry Kenlay · Robin Ru · Arno Blaas · Michael A Osborne · Xiaowen Dong -
2021 Poster: Kernel Identification Through Transformers »
Fergus Simpson · Ian Davies · Vidhi Lalchand · Alessandro Vullo · Nicolas Durrande · Carl Edward Rasmussen -
2021 Poster: Marginalised Gaussian Processes with Nested Sampling »
Fergus Simpson · Vidhi Lalchand · Carl Edward Rasmussen -
2021 Poster: Deep Neural Networks as Point Estimates for Deep Gaussian Processes »
Vincent Dutordoir · James Hensman · Mark van der Wilk · Carl Henrik Ek · Zoubin Ghahramani · Nicolas Durrande -
2020 : Combining variational autoencoder representations with structural descriptors improves prediction of docking scores »
Miguel Garcia-Ortegon · Carl Edward Rasmussen · Hiroshi Kajino -
2020 Poster: Effective Diversity in Population Based Reinforcement Learning »
Jack Parker-Holder · Aldo Pacchiano · Krzysztof M Choromanski · Stephen J Roberts -
2020 Poster: Gaussian Process Bandit Optimization of the Thermodynamic Variational Objective »
Vu Nguyen · Vaden Masrani · Rob Brekelmans · Michael A Osborne · Frank Wood -
2020 Spotlight: Effective Diversity in Population Based Reinforcement Learning »
Jack Parker-Holder · Aldo Pacchiano · Krzysztof M Choromanski · Stephen J Roberts -
2020 Poster: Explicit Regularisation in Gaussian Noise Injections »
Alexander Camuto · Matthew Willetts · Umut Simsekli · Stephen J Roberts · Chris C Holmes -
2020 Poster: Bayesian Optimization for Iterative Learning »
Vu Nguyen · Sebastian Schulze · Michael A Osborne -
2020 Poster: Ensembling geophysical models with Bayesian Neural Networks »
Ushnish Sengupta · Matt Amos · Scott Hosking · Carl Edward Rasmussen · Matthew Juniper · Paul Young -
2020 Poster: Provably Efficient Online Hyperparameter Optimization with Population-Based Bandits »
Jack Parker-Holder · Vu Nguyen · Stephen J Roberts -
2019 : Poster Session »
Gergely Flamich · Shashanka Ubaru · Charles Zheng · Josip Djolonga · Kristoffer Wickstrøm · Diego Granziol · Konstantinos Pitas · Jun Li · Robert Williamson · Sangwoong Yoon · Kwot Sin Lee · Julian Zilly · Linda Petrini · Ian Fischer · Zhe Dong · Alexander Alemi · Bao-Ngoc Nguyen · Rob Brekelmans · Tailin Wu · Aditya Mahajan · Alexander Li · Kirankumar Shiragur · Yair Carmon · Linara Adilova · SHIYU LIU · Bang An · Sanjeeb Dash · Oktay Gunluk · Arya Mazumdar · Mehul Motani · Julia Rosenzweig · Michael Kamp · Marton Havasi · Leighton P Barnes · Zhengqing Zhou · Yi Hao · Dylan Foster · Yuval Benjamini · Nati Srebro · Michael Tschannen · Paul Rubenstein · Sylvain Gelly · John Duchi · Aaron Sidford · Robin Ru · Stefan Zohren · Murtaza Dalal · Michael A Osborne · Stephen J Roberts · Moses Charikar · Jayakumar Subramanian · Xiaodi Fan · Max Schwarzer · Nicholas Roberts · Simon Lacoste-Julien · Vinay Prabhu · Aram Galstyan · Greg Ver Steeg · Lalitha Sankar · Yung-Kyun Noh · Gautam Dasarathy · Frank Park · Ngai-Man (Man) Cheung · Ngoc-Trung Tran · Linxiao Yang · Ben Poole · Andrea Censi · Tristan Sylvain · R Devon Hjelm · Bangjie Liu · Jose Gallego-Posada · Tyler Sypherd · Kai Yang · Jan Nikolas Morshuis -
2019 : Poster Session »
Eduard Gorbunov · Alexandre d'Aspremont · Lingxiao Wang · Liwei Wang · Boris Ginsburg · Alessio Quaglino · Camille Castera · Saurabh Adya · Diego Granziol · Rudrajit Das · Raghu Bollapragada · Fabian Pedregosa · Martin Takac · Majid Jahani · Sai Praneeth Karimireddy · Hilal Asi · Balint Daroczy · Leonard Adolphs · Aditya Rawal · Nicolas Brandt · Minhan Li · Giuseppe Ughi · Orlando Romero · Ivan Skorokhodov · Damien Scieur · Kiwook Bae · Konstantin Mishchenko · Rohan Anil · Vatsal Sharan · Aditya Balu · Chao Chen · Zhewei Yao · Tolga Ergen · Paul Grigas · Chris Junchi Li · Jimmy Ba · Stephen J Roberts · Sharan Vaswani · Armin Eftekhari · Chhavi Sharma -
2019 Workshop: Bayesian Deep Learning »
Yarin Gal · José Miguel Hernández-Lobato · Christos Louizos · Eric Nalisnick · Zoubin Ghahramani · Kevin Murphy · Max Welling -
2019 Poster: Bayesian Learning of Sum-Product Networks »
Martin Trapp · Robert Peharz · Hong Ge · Franz Pernkopf · Zoubin Ghahramani -
2018 Workshop: Bayesian Deep Learning »
Yarin Gal · José Miguel Hernández-Lobato · Christos Louizos · Andrew Wilson · Zoubin Ghahramani · Kevin Murphy · Max Welling -
2018 Poster: MetaGAN: An Adversarial Approach to Few-Shot Learning »
Ruixiang ZHANG · Tong Che · Zoubin Ghahramani · Yoshua Bengio · Yangqiu Song -
2017 : Panel Session »
Neil Lawrence · Finale Doshi-Velez · Zoubin Ghahramani · Yann LeCun · Max Welling · Yee Whye Teh · Ole Winther -
2017 Workshop: Bayesian Deep Learning »
Yarin Gal · José Miguel Hernández-Lobato · Christos Louizos · Andrew Wilson · Andrew Wilson · Diederik Kingma · Zoubin Ghahramani · Kevin Murphy · Max Welling -
2017 : Cost-sensitive detection with variational autoencoders for environmental acoustic sensing »
Yunpeng Li · Stephen J Roberts -
2017 : Panel: On the Foundations and Future of Approximate Inference »
David Blei · Zoubin Ghahramani · Katherine Heller · Tim Salimans · Max Welling · Matthew D. Hoffman -
2017 : Contributed talk: Safe Policy Search with Gaussian Process Models »
Kyriakos Polymenakos · Stephen J Roberts -
2017 : Panel: "Should we prioritize research on human-like AI or something different?" »
Cynthia Dwork · David Runciman · Zoubin Ghahramani -
2017 Symposium: Kinds of intelligence: types, tests and meeting the needs of society »
José Hernández-Orallo · Zoubin Ghahramani · Tomaso Poggio · Adrian Weller · Matthew Crosby -
2017 Poster: Convolutional Gaussian Processes »
Mark van der Wilk · Carl Edward Rasmussen · James Hensman -
2017 Oral: Convolutional Gaussian Processes »
Mark van der Wilk · Carl Edward Rasmussen · James Hensman -
2017 Poster: Data-Efficient Reinforcement Learning in Continuous State-Action Gaussian-POMDPs »
Rowan McAllister · Carl Edward Rasmussen -
2017 Poster: Interpolated Policy Gradient: Merging On-Policy and Off-Policy Gradient Estimation for Deep Reinforcement Learning »
Shixiang (Shane) Gu · Timothy Lillicrap · Richard Turner · Zoubin Ghahramani · Bernhard Schölkopf · Sergey Levine -
2016 : Generating Class-conditional Images with Gradient-based Inference »
David Duvenaud -
2016 : David Duvenaud – No more mini-languages: The power of autodiffing full-featured Python »
David Duvenaud -
2016 : Automatic Discovery of the Statistical Types of Variables in a Dataset »
Isabel Valera · Zoubin Ghahramani -
2016 : History of Bayesian neural networks »
Zoubin Ghahramani -
2016 Workshop: Bayesian Deep Learning »
Yarin Gal · Christos Louizos · Zoubin Ghahramani · Kevin Murphy · Max Welling -
2016 Workshop: Towards an Artificial Intelligence for Data Science »
Charles Sutton · James Geddes · Zoubin Ghahramani · Padhraic Smyth · Chris Williams -
2016 : How Machine Learning Research Can Address Key Societal and Governance Issues »
Zoubin Ghahramani -
2016 Workshop: People and machines: Public views on machine learning, and what this means for machine learning researchers »
Susannah Odell · Peter Donnelly · Jessica Montgomery · Sabine Hauert · Zoubin Ghahramani · Katherine Gorman -
2016 Workshop: Reliable Machine Learning in the Wild »
Dylan Hadfield-Menell · Adrian Weller · David Duvenaud · Jacob Steinhardt · Percy Liang -
2016 Poster: A Theoretically Grounded Application of Dropout in Recurrent Neural Networks »
Yarin Gal · Zoubin Ghahramani -
2016 Poster: Bayesian Optimization for Probabilistic Programs »
Thomas Rainforth · Tuan Anh Le · Jan-Willem van de Meent · Michael A Osborne · Frank Wood -
2016 Poster: Understanding Probabilistic Sparse Gaussian Process Approximations »
Matthias Bauer · Mark van der Wilk · Carl Edward Rasmussen -
2016 Poster: Composing graphical models with neural networks for structured representations and fast inference »
Matthew Johnson · David Duvenaud · Alex Wiltschko · Ryan Adams · Sandeep R Datta -
2016 Poster: Distributed Flexible Nonlinear Tensor Factorization »
Shandian Zhe · Kai Zhang · Pengyuan Wang · Kuang-chih Lee · Zenglin Xu · Yuan Qi · Zoubin Ghahramani -
2016 Poster: Probing the Compositionality of Intuitive Functions »
Eric Schulz · Josh Tenenbaum · David Duvenaud · Maarten Speekenbrink · Samuel J Gershman -
2015 : Bayesian Optimization »
Zoubin Ghahramani · Bobak Shahriari -
2015 Workshop: Black box learning and inference »
Josh Tenenbaum · Jan-Willem van de Meent · Tejas Kulkarni · S. M. Ali Eslami · Brooks Paige · Frank Wood · Zoubin Ghahramani -
2015 : *David Duvenaud* Automatic Differentiation: The most criminally underused tool in probabilistic numerics »
David Duvenaud -
2015 Workshop: Probabilistic Integration »
Michael A Osborne · Philipp Hennig -
2015 Symposium: Algorithms Among Us: the Societal Impacts of Machine Learning »
Michael A Osborne · Adrian Weller · Murray Shanahan -
2015 Poster: Convolutional Networks on Graphs for Learning Molecular Fingerprints »
David Duvenaud · Dougal Maclaurin · Jorge Iparraguirre · Rafael Bombarell · Timothy Hirzel · Alan Aspuru-Guzik · Ryan Adams -
2015 Poster: Particle Gibbs for Infinite Hidden Markov Models »
Nilesh Tripuraneni · Shixiang (Shane) Gu · Hong Ge · Zoubin Ghahramani -
2015 Poster: Neural Adaptive Sequential Monte Carlo »
Shixiang (Shane) Gu · Zoubin Ghahramani · Richard Turner -
2015 Poster: MCMC for Variationally Sparse Gaussian Processes »
James Hensman · Alexander Matthews · Maurizio Filippone · Zoubin Ghahramani -
2015 Poster: Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions »
Amar Shah · Zoubin Ghahramani -
2015 Poster: Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees »
François-Xavier Briol · Chris Oates · Mark Girolami · Michael A Osborne -
2015 Spotlight: Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees »
François-Xavier Briol · Chris Oates · Mark Girolami · Michael A Osborne -
2015 Invited Talk: Probabilistic Machine Learning: Foundations and Frontiers »
Zoubin Ghahramani -
2015 Poster: Statistical Model Criticism using Kernel Two Sample Tests »
James R Lloyd · Zoubin Ghahramani -
2014 Workshop: Bayesian Optimization in Academia and Industry »
Zoubin Ghahramani · Ryan Adams · Matthew Hoffman · Kevin Swersky · Jasper Snoek -
2014 Poster: Distributed Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models »
Yarin Gal · Mark van der Wilk · Carl Edward Rasmussen -
2014 Poster: Probabilistic ODE Solvers with Runge-Kutta Means »
Michael Schober · David Duvenaud · Philipp Hennig -
2014 Poster: Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature »
Tom Gunter · Michael A Osborne · Roman Garnett · Philipp Hennig · Stephen J Roberts -
2014 Oral: Probabilistic ODE Solvers with Runge-Kutta Means »
Michael Schober · David Duvenaud · Philipp Hennig -
2014 Poster: Predictive Entropy Search for Efficient Global Optimization of Black-box Functions »
José Miguel Hernández-Lobato · Matthew Hoffman · Zoubin Ghahramani -
2014 Poster: Gaussian Process Volatility Model »
Yue Wu · José Miguel Hernández-Lobato · Zoubin Ghahramani -
2014 Poster: Variational Gaussian Process State-Space Models »
Roger Frigola · Yutian Chen · Carl Edward Rasmussen -
2014 Spotlight: Predictive Entropy Search for Efficient Global Optimization of Black-box Functions »
José Miguel Hernández-Lobato · Matthew Hoffman · Zoubin Ghahramani -
2014 Poster: General Table Completion using a Bayesian Nonparametric Model »
Isabel Valera · Zoubin Ghahramani -
2013 Workshop: Constructive Machine Learning »
Thomas Gaertner · Roman Garnett · Andrea Passerini -
2013 Workshop: Bayesian Optimization in Theory and Practice »
Matthew Hoffman · Jasper Snoek · Nando de Freitas · Michael A Osborne · Ryan Adams · Sebastien Bubeck · Philipp Hennig · Remi Munos · Andreas Krause -
2013 Workshop: Probabilistic Models for Big Data »
Neil D Lawrence · Joaquin Quiñonero-Candela · Tianshi Gao · James Hensman · Zoubin Ghahramani · Max Welling · David Blei · Ralf Herbrich -
2013 Poster: Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC »
Roger Frigola · Fredrik Lindsten · Thomas Schön · Carl Edward Rasmussen -
2013 Session: Oral Session 5 »
Zoubin Ghahramani -
2012 Workshop: Probabilistic Numerics »
Philipp Hennig · John P Cunningham · Michael A Osborne -
2012 Workshop: Bayesian Optimization and Decision Making »
Javad Azimi · Roman Garnett · Frank R Hutter · Shakir Mohamed -
2012 Poster: Collaborative Gaussian Processes for Preference Learning »
Neil Houlsby · José Miguel Hernández-Lobato · Ferenc Huszar · Zoubin Ghahramani -
2012 Poster: A nonparametric variable clustering model »
David A Knowles · Konstantina Palla · Zoubin Ghahramani -
2012 Poster: Random function priors for exchangeable graphs and arrays »
James R Lloyd · Daniel Roy · Peter Orbanz · Zoubin Ghahramani -
2012 Poster: Continuous Relaxations for Discrete Hamiltonian Monte Carlo »
Zoubin Ghahramani · Yichuan Zhang · Charles Sutton · Amos Storkey -
2012 Spotlight: Continuous Relaxations for Discrete Hamiltonian Monte Carlo »
Zoubin Ghahramani · Yichuan Zhang · Charles Sutton · Amos Storkey -
2011 Workshop: Copulas in Machine Learning »
Gal Elidan · Zoubin Ghahramani · John Lafferty -
2011 Workshop: Bayesian optimization, experimental design and bandits: Theory and applications »
Nando de Freitas · Roman Garnett · Frank R Hutter · Michael A Osborne -
2011 Poster: Gaussian Process Training with Input Noise »
Andrew McHutchon · Carl Edward Rasmussen -
2011 Poster: Testing a Bayesian Measure of Representativeness Using a Large Image Database »
Joshua T Abbott · Katherine Heller · Zoubin Ghahramani · Tom Griffiths -
2011 Poster: Additive Gaussian Processes »
David Duvenaud · Hannes Nickisch · Carl Edward Rasmussen -
2010 Workshop: Transfer Learning Via Rich Generative Models. »
Russ Salakhutdinov · Ryan Adams · Josh Tenenbaum · Zoubin Ghahramani · Tom Griffiths -
2010 Talk: Unifying Views in Unsupervised Learning »
Zoubin Ghahramani -
2010 Oral: Tree-Structured Stick Breaking for Hierarchical Data »
Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Poster: Tree-Structured Stick Breaking for Hierarchical Data »
Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Spotlight: Copula Processes »
Andrew Wilson · Zoubin Ghahramani -
2010 Poster: Copula Processes »
Andrew Wilson · Zoubin Ghahramani -
2009 Workshop: Nonparametric Bayes »
Dilan Gorur · Francois Caron · Yee Whye Teh · David B Dunson · Zoubin Ghahramani · Michael Jordan -
2009 Workshop: Probabilistic Approaches for Control and Robotics »
Marc Deisenroth · Hilbert J Kappen · Emo Todorov · Duy Nguyen-Tuong · Carl Edward Rasmussen · Jan Peters -
2009 Poster: Large Scale Nonparametric Bayesian Inference: Data Parallelisation in the Indian Buffet Process »
Shakir Mohamed · David A Knowles · Zoubin Ghahramani · Finale P Doshi-Velez -
2008 Poster: The Infinite Factorial Hidden Markov Model »
Jurgen Van Gael · Yee Whye Teh · Zoubin Ghahramani -
2008 Poster: Bayesian Exponential Family PCA »
Shakir Mohamed · Katherine Heller · Zoubin Ghahramani -
2008 Spotlight: Bayesian Exponential Family PCA »
Shakir Mohamed · Katherine Heller · Zoubin Ghahramani -
2008 Spotlight: The Infinite Factorial Hidden Markov Model »
Jurgen Van Gael · Yee Whye Teh · Zoubin Ghahramani -
2007 Poster: Hidden Common Cause Relations in Relational Learning »
Ricardo Silva · Wei Chu · Zoubin Ghahramani -
2007 Spotlight: Hidden Common Cause Relations in Relational Learning »
Ricardo Silva · Wei Chu · Zoubin Ghahramani -
2006 Poster: Bayesian Image Super-resolution, Continued »
Lyndsey C Pickup · David Capel · Stephen J Roberts · Andrew Zisserman -
2006 Poster: Relational Learning with Gaussian Processes »
Wei Chu · Vikas Sindhwani · Zoubin Ghahramani · Sathiya Selvaraj Keerthi -
2006 Spotlight: Bayesian Image Super-resolution, Continued »
Lyndsey C Pickup · David Capel · Stephen J Roberts · Andrew Zisserman -
2006 Poster: Modeling Dyadic Data with Binary Latent Features »
Ted Meeds · Zoubin Ghahramani · Radford M Neal · Sam T Roweis -
2006 Spotlight: Modeling Dyadic Data with Binary Latent Features »
Ted Meeds · Zoubin Ghahramani · Radford M Neal · Sam T Roweis -
2006 Tutorial: Advances in Gaussian Processes »
Carl Edward Rasmussen