Efficient Reinforcement Learning for Motor Control (2009)
Deisenroth, Marc, Rasmussen, Carl Edward
Artificial learners often require many more trials than humans or animals when learning motor control tasks in the absence of expert knowledge. We implement two key ingredients of biological learning...
Nonparametric mixtures of factor analyzers (2009)
Gorur, Dilan, Rasmussen, Carl Edward
The mixtures of factor analyzers (MFA) model allows data to be modeled as a mixture of Gaussians with a reduced parametrization. We present the formulation of a nonparametric form of the MFA model,...
Joaquin Quiñonero C, Agathe Girard, Jan Larsen, Carl Edward Rasmussen
The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables evaluation of forecasted values and their uncertainties. In this paper we focus on reliably...
Gaussian Process Dynamic Programming (2009)
Deisenroth, Marc, Rasmussen, Carl Edward, Peters, Jan
Reinforcement learning (RL) and optimal control of systems with continuous states and actions require approximation techniques in most interesting cases. In this article, we introduce Gaussian...
Evaluating Predictive Uncertainty Challenge (2008)
Joaquin Quiñonero-c, Carl Edward Rasmussen, Fabian Sinz, Olivier Bousquet, Bernhard Schölkopf
Abstract. This Chapter presents the PASCAL 1 Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a...
98 Analysis of Some Methods for Reduced Rank Gaussian Process Regression (2008)
Joaquin Quiñonero-c, Carl Edward Rasmussen
Abstract. While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them...
Probabilistic Inference for Fast Learning in Control (2008)
Rasmussen, Carl Edward, Deisenroth, Marc
We provide a novel framework for very fast model-based reinforcement learning in continuous state and action spaces. The framework requires probabilistic models that explicitly characterize their...
MIT Press (2000) The Infinite Gaussian Mixture Model (2008)
In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the...
Approximate Dynamic Programming with Gaussian Processes (2008)
Deisenroth, Marc, Peters, Jan, Rasmussen, Carl Edward
In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The...
The Need for Open Source Software in Machine Learning (2008)
Sören Sonnenburg, Mikio L. Braun, Samy Bengio, Leon Bottou, Geoffrey Holmes, Yann Lecun, ...
Nonstationary Gaussian Process Regression using a Latent Extension of the Input Space ∗ (2008)
Tobias Pfingsten, Malte Kuss, Carl Edward Rasmussen
Introduction Gaussian Processes (GPs) can be used to specify a prior over latent functions in non-parametric Bayesian models, e.g. for regression and classification. For this abstract we assume...
Model-based Reinforcement Learning with Continuous States and Actions (2008)
Deisenroth, Marc, Rasmussen, Carl Edward, Peters, Jan
Finding an optimal policy in a reinforcement learning (RL) framework with continuous state and action spaces is challenging. Approximate solutions are often inevitable. GPDP is an approximate dynamic...
MIT Press (2000) The Infinite Gaussian Mixture Model (2008)
In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the...
MIT Press (2000) The Infinite Gaussian Mixture Model (2008)
In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the...
MIT Press (2000) Bayesian modelling of fMRI time series (2008)
Lars K. Hansen, Carl Edward Rasmussen
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is...
Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals (2008)
J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, ...
Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of...
Joaquin Quiñonero C, Agathe Girard, Jan Larsen, Carl Edward Rasmussen
The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables evaluation of forecasted values and their uncertainties. In this paper we focus on reliably...
Agathe Girard, Joaquin Quiñonero Candela, Roderick Murray-smith, Carl Edward Rasmussen
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model.-step ahead forecasting of a discrete-time non-linear dynamic system can...
Agathe Girard, Joaquin Quiñonero Candela, Roderick Murray-smith, Carl Edward Rasmussen
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model.�-step ahead forecasting of a discrete-time non-linear dynamic system...
Approximations for Binary Gaussian Process Classification (2008)
Nickisch, Hannes, Rasmussen, Carl Edward
We provide a comprehensive overview of many recent algorithms for approximate inference in Gaussian process models for probabilistic binary classification. The relationships between several...
Agathe Girard, Carl Edward Rasmussen, Roderick Murray-smith
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time nonlinear dynamic system...
Agathe Girard, Carl Edward Rasmussen, Math Modelling
The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables evaluation of forecasted values and their uncertainties. In this paper we focus on reliably...
Monte Carlo, Carl Edward Rasmussen, Zoubin Ghahramani
We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the...
Hybrid Monte Carlo for Expensive Bayesian Integrals (2007)
J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, Carl Edward Rasmussen
Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of...
dynamic systems-- A Gaussian Process (2007)
Agathe Girard, Carl Edward Rasmussen, Roderick Murray-smith
Multiple-step ahead prediction for non linear
intensive method has shown encouraging performance in (Neal 1996) and in a study using several datasets in (Rasmussen 1996). For a full description of the method the reader is referred to (Neal...
MIT Press (2000) Bayesian modelling of fMRI time series (2007)
Lars K. Hansen, Carl Edward Rasmussen
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is...
Agathe Girard, Joaquin Quiñonero Candela, Roderick Murray-smith, Carl Edward Rasmussen
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. �-step ahead forecasting of a discrete-time non-linear dynamic system...
The Need for Open Source Software in Machine Learning (2007)
Sonnenburg, Sören, Braun, Mikio, Ong, Cheng Soon, Bengio, Samy, Bottou, Leon, Holmes, Geoffrey, ...
Open source tools have recently reached a level of maturity which makes them suitable for building large-scale real-world systems. At the same time, the field of machine learning has developed a...
Approximation Methods for Gaussian Process Regression (2006)
Quinonero Candela, Joaquin, Rasmussen, Carl Edward, Williams, Christopher
A wealth of computationally efficient approximation methods for Gaussian process regression have been recently proposed. We give a unifying overview of sparse approximations, fol lowing...
MCMC inference in (Conditionally) Conjugate Dirichlet Process Gaussian Mixture Models (2006)
Rasmussen, Carl Edward, Gorur, Dilan
We compare the predictive accuracy of the Dirichlet Process Gaussian mixture models using conjugate and conditionally conjugate priors and show that better density models result from using the wider...
A Choice Model with Infinitely Many Latent Features (2006)
Gorur, Dilan, Jäkel, Frank, Rasmussen, Carl Edward
Elimination by aspects (EBA) is a probabilistic choice model describing how humans decide between several options. The options from which the choice is made are characterized by binary features and...
Sampling for Non-conjugate Infinite Latent Feature Models (2006)
Gorur, Dilan, Rasmussen, Carl Edward
Latent variable models are powerful tools to model the underlying structure in data. Infinite latent variable models can be defined using Bayesian nonparametrics. Dirichlet process (DP) models...
A Choice Model with Infinitely Many Latent Features (2006)
Gorur, Dilan, Jäkel, Frank, Rasmussen, Carl Edward
Elimination by aspects (EBA) is a probabilistic choice model describing how humans decide between several options. The options from which the choice is made are characterized by binary features and...
Gaussian Processes for Machine Learning (2006)
Rasmussen, Carl Edward, Williams, Christopher
Publisher's description: Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning...
Model-based Design Analysis and Yield Optimization (2006)
Pfingsten, Tobias, Herrmann, Daniel, Rasmussen, Carl Edward
Fluctuations are inherent to any fabrication process. Integrated circuits and micro-electro-mechanical systems are particularly affected by these variations, and due to high quality requirements the...
A Choice Model with Infinitely Many Latent Features (2006)
Gorur, Dilan, Jäkel, Frank, Rasmussen, Carl Edward
Elimination by aspects (EBA) is a probabilistic choice model describing how humans decide between several options. The options from which the choice is made are characterized by binary features and...
A Choice Model with Infinitely Many Latent Features (2006)
Dilan Görür, Frank Jäkel, Carl Edward Rasmussen
Elimination by aspects (EBA) is a probabilistic choice model describing how humans decide between several options. The options from which the choice is made are characterized by binary features and...
Gaussian processes for machine learning (2006)
Abstract. We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions....
A Unifying View of Sparse Approximate Gaussian Process Regression (2005)
Quinonero Candela, Joaquin, Rasmussen, Carl Edward
We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the...
Assessing Approximate Inference for Binary Gaussian Process Classification (2005)
Kuss, Malte, Rasmussen, Carl Edward
Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques...
Healing the Relevance Vector Machine through Augmentation (2005)
Rasmussen, Carl Edward, Quinonero Candela, Joaquin
The Relevance Vector Machine (RVM) is a sparse approximate Bayesian kernel method. It provides full predictive distributions for test cases. However, the predictive uncertainties have the unintuitive...
Assesing approximations for gaussian process classification (2005)
Malte Kuss, Carl Edward Rasmussen
Gaussian processes are attractive models for probabilistic classification but unfortunately exact inference is analytically intractable. We compare Laplace’s method and Expectation Propagation (EP)...
A unifying view of sparse approximate Gaussian process regression (2005)
Joaquin Quiñonero-candela, Carl Edward Rasmussen, Ralf Herbrich
We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the...
Assesing approximations for gaussian process classification (2005)
Malte Kuss, Carl Edward Rasmussen
Gaussian processes are attractive models for probabilistic classification but unfortunately exact inference is analytically intractable. We compare Laplace’s method and Expectation Propagation (EP)...
Assessing approximate inference for binary Gaussian process classification (2005)
Malte Kuss, Carl Edward Rasmussen, Ralf Herbrich
Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques...
Healing the relevance vector machine through augmentation (2005)
The Relevance Vector Machine (RVM) is a sparse approximate Bayesian kernel method. It provides full predictive distributions for test cases. However, the predictive uncertainties have the unintuitive...
Analysis of Some Methods for Reduced Rank Gaussian Process Regression (2004)
Quinonero Candela, Joaquin, Rasmussen, Carl Edward
While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical...
Learning Depth From Stereo. Pattern Recognition (2004)
Sinz, Fabian, Quinonero Candela, Joaquin, Bakir, Goekhan Hasan, Rasmussen, Carl Edward, Franz, Matthias
We compare two approaches to the problem of estimating the depth of a point in space from observing its image position in two different cameras: 1. The classical photogrammetric approach explicitly...
Semi-supervised kernel regression using whitened function classes (2004)
Franz, Matthias, Kwon, Y., Rasmussen, Carl Edward, Schölkopf, Bernhard
The use of non-orthonormal basis functions in ridge regression leads to an often undesired non-isotropic prior in function space. In this study, we investigate an alternative regularization technique...
Warped Gaussian processes (2004)
Snelson, Ed, Rasmussen, Carl Edward, Ghahramani, Zoubin
We generalise the Gaussian process (GP) framework for regression by learning a nonlinear transformation of the GP outputs. This allows for non-Gaussian processes and non-Gaussian noise. The learning...
Modelling Spikes with Mixtures of Factor Analysers (2004)
Gorur, Dilan, Rasmussen, Carl Edward, Tolias, Andreas S., Sinz, Fabian, Logothetis, Nikos K.
Identifying the action potentials of individual neurons from extracellular recordings, known as spike sorting, is a challenging problem. We consider the spike sorting problem using a generative...
Analysis of some methods for reduced rank gaussian process regression (2004)
Joaquin Quiñonero-c, Carl Edward Rasmussen
Abstract. While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them...
Prediction on spike data using kernel algorithms (2004)
Jan Eichhorn, Andreas Tolias, Er Zien, Malte Kuss, Carl Edward Rasmussen, Jason Weston, ...
We report and compare the performance of different learning algorithms based on data from cortical recordings. The task is to predict the orientation of visual stimuli from the activity of a...
Gaussian Processes in Reinforcement Learning (2004)
Carl Edward Rasmussen, Malte Kuss
We exploit some useful properties of Gaussian process (GP) regression models for reinforcement learning in continuous state spaces and discrete time. We demonstrate how the GP model allows evaluation...
Gaussian Processes in Reinforcement Learning (2004)
Carl Edward Rasmussen, Malte Kuss
We exploit some useful properties of Gaussian process (GP) regression models for reinforcement learning in continuous state spaces and discrete time. We demonstrate how the GP model allows evaluation...
Predictive control with Gaussian process models (2003)
Jus Kocijan, Roderick Murray-Smith, Carl Edward Rasmussen, Bojan Likar
This paper describes model-based predictive control based on Gaussian processes. Gaussian process models provide a probabilistic nonparametric modelling approach for black-box identification of...
Adaptive, cautious, predictive control with Gaussian process priors (2003)
Roderick Murray-Smith, Daniel Sbarbaro, Carl Edward Rasmussen, Agathe Girard
Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made...
Gaussian process priors with uncertain inputs: Multiple-step ahead prediction (2003)
Agathe Girard, Carl Edward Rasmussen, Mathematical Modelling, Roderick Murray-smith
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system...
Carl Edward Rasmussen, Zoubin Ghahramani
We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the...
Predictive control with Gaussian process models (2003)
Roderick Murray-smith, Carl Edward Rasmussen, Bojan Likar, Nova Gorica Polytechnic, Nova Gorica
Abstract—This paper describes model-based predictive control based on Gaussian processes. Gaussian process models provide a probabilistic nonparametric modelling approach for black-box...
Gaussian Processes in Reinforcement Learning (2003)
Carl Edward Rasmussen, Malte Kuss
We exploit some useful properties of Gaussian process (GP) regression models for reinforcement learning in continuous state spaces and discrete time. We demonstrate how the GP model allows evaluation...
Prediction on Spike Data Using Kernel Algorithms (2003)
Jan Eichhorn, Andreas Tolias, Alexander Zien, Er Zien, Malte Kuss, Carl Edward Rasmussen, ...
We report and compare the performance of different learning algorithms based on data from cortical recordings. The task is to predict the orientation of visual stimuli from the activity of a...
Agathe Girard, Carl Edward Rasmussen
We consider in this report non-linear models that map an input D-dimensional column vector x into a single dimensional output f(x). The non-linear mapping f() is implemented by means of a Gaussian...
Observations on the Nyström method for Gaussian process prediction (2002)
Carl Edward Rasmussen, Anton Schwaighofer, Volker Tresp
A number of methods for speeding up Gaussian Process (GP) prediction have been proposed, including the Nystrom method of Williams and Seeger (2001). In this paper we focus on two issues (1) the...
Infinite mixtures of Gaussian process experts (2002)
Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process,...
Infinite mixtures of Gaussian process experts (2002)
Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using a input dependent adaptation of the Dirichlet Process, we...
Infinite mixtures of Gaussian process experts (2002)
Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process,...
Infinite mixtures of Gaussian process experts (2002)
Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process,...
Infinite mixtures of Gaussian process experts (2002)
Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process,...
Carl Edward Rasmussen, Zoubin Ghahramani
The Bayesian paradigm apparently only sometimes gives rise to Occam's Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are...
Carl Edward Rasmussen, Zoubin Ghahramani
The Bayesian paradigm apparently only sometimes gives rise to Occam’s Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are...
Carl Edward Rasmussen, Zoubin Ghahramani
The Bayesian paradigm apparently only sometimes gives rise to Occam’s Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are...
Carl Edward Rasmussen, Zoubin Ghahramani
The Bayesian paradigm apparently only sometimes gives rise to Occam’s Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are...
Bayesian Modelling of fMRI Time Series (2000)
Lars K. Hansen, Carl Edward Rasmussen
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trail fMRI activation experiments with blocked task paradigms. Inference is...
The Infinite Gaussian Mixture Model (2000)
In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the...
Bayesian modelling of fMRI time series (2000)
Pedro Højen-Sørensen, Lars Kai Hansen, Carl Edward Rasmussen
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is...
The Countably Infinite Bayesian Gaussian Mixture Density Model (1999)
In a Bayesian mixture model, there is no need a priori to restrict the number of components to be finite. Infinite mixture models sidestep the problem of finding the "correct" number of...
Evaluation of Gaussian processes and other methods for non-linear regression (1997)
grantor: University of Toronto
Factorial hidden Markov models (1997)
Matthew J. Beal, Zoubin Ghahramani, Carl Edward Rasmussen
We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the...
Factorial hidden Markov models (1997)
Matthew J. Beal, Zoubin Ghahramani, Carl Edward Rasmussen
We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the...
Factorial hidden Markov models (1997)
Matthew J. Beal, Zoubin Ghahramani, Carl Edward Rasmussen
m.beal,zoubin,edward¡ We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly...
Evaluation of Gaussian Processes and other Methods for Non-Linear Regression (1996)
Carl Edward Rasmussen, Carl Edward Rasmussen
A thesis submitted in conformity with the requirements
Gaussian processes for regression (1996)
The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process...
A Practical Monte Carlo Implementation of Bayesian Learning (1996)
A practical method for Bayesian training of feed-forward neural networks using sophisticated Monte Carlo methods is presented and evaluated. In reasonably small amounts of computer time this approach...
Function Minimization Using Conjugate Gradients: Conj (1996)
This document describes the utility function conj which optimizes network weights using a conjugent gradient method. The function has a private function lns for doing line-searches.
Gaussian Processes for Regression (1996)
Christopher Williams Neural, Carl Edward Rasmussen
The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process...
K Nearest Neighbors for Regression knn-cv-1 (1996)
sure closeness; I will use the simple and common choice of Euclidean distance. Many extensions of nearest neighbor algorithms exist which attempt to adapt the distance metric (Lowe 1995; Hastie and...
Pruning from Adaptive Regularization (1994)
Lars Kai Hansen, Carl Edward Rasmussen
Inspired by the recent upsurge of interest in Bayesian methods we consider adaptive regularization. A generalization based scheme for adaptation of regularization parameters is introduced and...
Generalization in Neural Networks (1993)
Abstract 1 This report is concerned with methods for optimizing the generalization ability of neural networks. The framework is developed to deal with regression type problems, where the networks are...
Carl Edward Rasmussen, David J. Willshaw, Buccleuch Place
The development of the nervous system involves in many cases interactions on a local scale rather than the execution of a fully specified genetic blueprint. The problem is to discover the nature of...
in Advances in Neural Information Processing Systems 14, MIT Press (2002). (1989)
Infinite Mixtures Of, Carl Edward Rasmussen, Zoubin Ghahramani
We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process,...