Results 21  30
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720
Hierarchical Gaussian process latent variable models
 In International Conference in Machine Learning
, 2007
"... The Gaussian process latent variable model (GPLVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GPLVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies ..."
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Cited by 39 (8 self)
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The Gaussian process latent variable model (GPLVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GPLVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets. 1.
Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS (NIPS20
, 2007
"... We show how to use unlabeled data and a deep belief net (DBN) to learn a good covariance kernel for a Gaussian process. We first learn a deep generative model of the unlabeled data using the fast, greedy algorithm introduced by [7]. If the data is highdimensional and highlystructured, a Gaussian ..."
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Cited by 39 (4 self)
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We show how to use unlabeled data and a deep belief net (DBN) to learn a good covariance kernel for a Gaussian process. We first learn a deep generative model of the unlabeled data using the fast, greedy algorithm introduced by [7]. If the data is highdimensional and highlystructured, a Gaussian kernel applied to the top layer of features in the DBN works much better than a similar kernel applied to the raw input. Performance at both regression and classification can then be further improved by using backpropagation through the DBN to discriminatively finetune the covariance kernel.
Topologicallyconstrained latent variable models
 In ICML ’08: Proceedings of the 25th international conference on Machine learning
, 2008
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Calculations of sobol indices for the gaussian process metamodel
 RELIABILITY ENGINEERING & SYSTEM SAFETY
, 2009
"... Global sensitivity analysis of complex numerical models can be performed by calculating variancebased importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer c ..."
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Cited by 33 (3 self)
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Global sensitivity analysis of complex numerical models can be performed by calculating variancebased importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.
Robust MultiTask Learning with tProcesses
"... Most current multitask learning frameworks ignore the robustness issue, which means that the presence of “outlier ” tasks may greatly reduce overall system performance. We introduce a robust framework for Bayesian multitask learning, tprocesses (TP), which are a generalization of Gaussian processe ..."
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Cited by 31 (0 self)
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Most current multitask learning frameworks ignore the robustness issue, which means that the presence of “outlier ” tasks may greatly reduce overall system performance. We introduce a robust framework for Bayesian multitask learning, tprocesses (TP), which are a generalization of Gaussian processes (GP) for multitask learning. TP allows the system to effectively distinguish good tasks from noisy or outlier tasks. Experiments show that TP not only improves overall system performance, but can also serve as an indicator for the “informativeness ” of different tasks. 1.
Dirichlet Process Mixtures of Generalized Linear Models
"... We propose Dirichlet Process mixtures of Generalized Linear Models (DPGLMs), a new method of nonparametric regression that accommodates continuous and categorical inputs, models a response variable locally by a generalized linear model. We give conditions for the existence and asymptotic unbiasedne ..."
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Cited by 31 (3 self)
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We propose Dirichlet Process mixtures of Generalized Linear Models (DPGLMs), a new method of nonparametric regression that accommodates continuous and categorical inputs, models a response variable locally by a generalized linear model. We give conditions for the existence and asymptotic unbiasedness of the DPGLM regression mean function estimate; we then give a practical example for when those conditions hold. We evaluate DPGLM on several data sets, comparing it to modern methods of nonparametric regression including regression trees and Gaussian processes. 1
Unfreezing the Robot: Navigation in Dense, Interacting Crowds
 In IROS
, 2010
"... AbstractIn this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the "freezing robot" problem: once the environment surpasses a certain level of complexity, the planner decides that all for ..."
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Cited by 31 (1 self)
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AbstractIn this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the "freezing robot" problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing the predictive uncertainty for individual agents by employing more informed models or heuristically limiting the predictive covariance to prevent this overcautious behavior. In this work, we demonstrate that both the individual prediction and the predictive uncertainty have little to do with the frozen robot problem. Our key insight is that dynamic agents solve the frozen robot problem by engaging in "joint collision avoidance": They cooperatively make room to create feasible trajectories. We develop IGP, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data. Our model naturally captures the nonMarkov nature of agent trajectories, as well as their goaldriven navigation. We then show how planning in this model can be efficiently implemented using particle based inference. Lastly, we evaluate our model on a dataset of pedestrians entering and leaving a building, first comparing the model with actual pedestrians, and find that the algorithm either outperforms human pedestrians or performs very similarly to the pedestrians. We also present an experiment where a covariance reduction method results in highly overcautious behavior, while our model performs desirably.
Bounded approximate decentralised coordination using the maxsum algorithm
 IN DISTRIBUTED CONSTRAINT REASONING WORKSHOP
, 2009
"... In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution qualit ..."
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Cited by 30 (9 self)
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In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the maxsum algorithm to optimally solve the resulting tree structured constraint network, providing a bounded approximation specific to the particular problem instance. We formally prove that our algorithm provides a bounded approximation of the original problem and we present an empirical evaluation in a synthetic scenario. This shows that the approximate solutions that our algorithm provides are typically within 95 % of the optimum and the approximation ratio that our algorithm provides is typically 1.23.
Fastfood — Approximating Kernel Expansions in Loglinear Time
"... Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates ..."
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Cited by 28 (1 self)
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Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such computation significantly. Key to Fastfood is the observation that Hadamard matrices when combined with diagonal Gaussian matrices exhibit properties similar to dense Gaussian random matrices. Yet unlike the latter, Hadamard and diagonal matrices are inexpensive to multiply and store. These two matrices can be used in lieu of Gaussian matrices in Random Kitchen Sinks (Rahimi & Recht, 2007) and thereby speeding up the computation for a large range of kernel functions. Specifically, Fastfood requires O(n log d) time and O(n) storage to compute n nonlinear basis functions in d dimensions, a significant improvement from O(nd) computation and storage, without sacrificing accuracy. We prove that the approximation is unbiased and has low variance. Extensive experiments show that we achieve similar accuracy to full kernel expansions and Random Kitchen Sinks while being 100x faster and using 1000x less memory. These improvements, especially in terms of memory usage, make kernel methods more practical for applications that have large training sets and/or require realtime prediction. 1.
NONPARAMETRIC FUNCTIONAL DATA ANALYSIS THROUGH BAYESIAN DENSITY ESTIMATION
, 2007
"... In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivitytemperaturedepth (CTD) data in oceanography, doseresponse models in epidemiology and timecourse microarray ..."
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Cited by 28 (6 self)
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In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivitytemperaturedepth (CTD) data in oceanography, doseresponse models in epidemiology and timecourse microarray experiments in biology and medicine. In this paper we propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent Dirichlet Process mixtures of Gaussians to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the outcome given the predictors. The resulting approach allows for flexible estimation and clustering, while borrowing information across curves. We also show that the function estimates we obtain are consistent on the space of integrable functions. As an illustration, we consider an application to the analysis of CTD data in the north Atlantic.