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165
T.: Sparse probabilistic regression for activityindependent human pose inference
 In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR
, 2008
"... Discriminative approaches to human pose inference involve mapping visual observations to articulated body configurations. Current probabilistic approaches to learn this mapping have been limited in their ability to handle domains with a large number of activities that require very large training set ..."
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Cited by 58 (10 self)
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Discriminative approaches to human pose inference involve mapping visual observations to articulated body configurations. Current probabilistic approaches to learn this mapping have been limited in their ability to handle domains with a large number of activities that require very large training sets. We propose an online probabilistic regression scheme for efficient inference of complex, highdimensional, and multimodal mappings. Our technique is based on a local mixture of Gaussian Processes, where locality is defined based on both appearance and pose, and where the mapping hyperparameters can vary across local neighborhoods to better adapt to specific regions in the pose space. The mixture components are defined online in very small neighborhoods, so learning and inference is extremely efficient. When the mapping is onetoone, we derive a bound on the approximation error of local regression (vs. global regression) for monotonically decreasing covariance functions. Our method can determine when training examples are redundant given the rest of the database, and use this criteria for pruning. We report results on synthetic (Poser) and real (Humaneva) pose databases, obtaining fast and accurate pose estimates using training set sizes up to 105. 1.
Variational learning of inducing variables in sparse Gaussian processes
 In Artificial Intelligence and Statistics 12
, 2009
"... Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound ..."
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Cited by 57 (6 self)
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Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood. The key property of this formulation is that the inducing inputs are defined to be variational parameters which are selected by minimizing the KullbackLeibler divergence between the variational distribution and the exact posterior distribution over the latent function values. We apply this technique to regression and we compare it with other approaches in the literature. 1
Sparse incremental learning for interactive robot control policy estimation
 in Intl. Conf. on Robotics and Automation
, 2008
"... Abstract — We are interested in transferring control policies for arbitrary tasks from a human to a robot. Using interactive demonstration via teleoperation as our transfer scenario, we cast learning as statistical regression over sensoractuator data pairs. Our desire for interactive learning neces ..."
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Cited by 35 (6 self)
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Abstract — We are interested in transferring control policies for arbitrary tasks from a human to a robot. Using interactive demonstration via teleoperation as our transfer scenario, we cast learning as statistical regression over sensoractuator data pairs. Our desire for interactive learning necessitates algorithms that are incremental and realtime. We examine Locally Weighted Projection Regression, a popular robotic learning algorithm, and Sparse Online Gaussian Processes in this domain on one synthetic and several robotgenerated data sets. We evaluate each algorithm in terms of function approximation, learned task performance, and scalability to large data sets. I. INTRODUCTION AND RELATED WORK In this paper we address the problem of Policy transfer, how a control policy (π) for some unknown task, latent in the mind of a human, can be transitioned onto a robot. The
Kernels for VectorValued Functions: a Review
, 2011
"... Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kern ..."
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Cited by 32 (2 self)
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Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
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
Sparse Spectrum Gaussian Process Regression
"... We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the spectral representation of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable tradeoffs between predictive accuracy and computational requiremen ..."
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Cited by 28 (2 self)
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We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the spectral representation of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable tradeoffs between predictive accuracy and computational requirements, and show that these are typically superior to existing stateoftheart sparse approximations. We discuss both the weight space and function space representations, and note that the new construction implies priors over functions which are always stationary, and can approximate any covariance function in this class.
Approximation Methods for Gaussian Process Regression
, 2007
"... A wealth of computationally efficient approximation methods for Gaussian process regression have been recently proposed. We give a unifying overview of sparse approximations, following QuiñoneroCandela and Rasmussen (2005), and a brief review of approximate matrixvector multiplication methods. 1 ..."
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Cited by 27 (4 self)
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A wealth of computationally efficient approximation methods for Gaussian process regression have been recently proposed. We give a unifying overview of sparse approximations, following QuiñoneroCandela and Rasmussen (2005), and a brief review of approximate matrixvector multiplication methods. 1
Computationally efficient convolved multiple output gaussian processes
 Journal of Machine Learning Research
"... Recently there has been an increasing interest in regression methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appr ..."
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Cited by 27 (2 self)
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Recently there has been an increasing interest in regression methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semidefinite, captures the dependencies between all the data points and across all the outputs. One approach to account for nontrivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different efficient approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in school exams score prediction, pollution prediction and gene expression data.
An information theoretic approach of designing sparse kernel adaptive filters
 IEEE Transactions on Neural Networks
, 2009
"... Abstract—This paper discusses an information theoretic approach of designing sparse kernel adaptive filters. To determine useful data to be learned and remove redundant ones, a subjective information measure called surprise is introduced. Surprise captures the amount of information a datum contain ..."
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Cited by 23 (3 self)
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Abstract—This paper discusses an information theoretic approach of designing sparse kernel adaptive filters. To determine useful data to be learned and remove redundant ones, a subjective information measure called surprise is introduced. Surprise captures the amount of information a datum contains which is transferable to a learning system. Based on this concept, we propose a systematic sparsification scheme, which can drastically reduce the time and space complexity without harming the performance of kernel adaptive filters. Nonlinear regression, short term chaotic timeseries prediction, and long term timeseries forecasting examples are presented. Index Terms—Information measure, kernel adaptive filters, online Gaussian processes, online kernel learning, sparsification, surprise. I.