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Bayesian Compressive Sensing
, 2007
"... The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing ..."
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Cited by 327 (24 self)
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The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing is a framework whereby one does not measure one of the aforementioned Ndimensional signals directly, but rather a set of related measurements, with the new measurements a linear combination of the original underlying Ndimensional signal. The number of required compressivesensing measurements is typically much smaller than N, offering the potential to simplify the sensing system. Let f denote the unknown underlying Ndimensional signal, and g a vector of compressivesensing measurements, then one may approximate f accurately by utilizing knowledge of the (underdetermined) linear relationship between f and g, in addition to knowledge of the fact that f is compressible in B. In this paper we employ a Bayesian formalism for estimating the underlying signal f based on compressivesensing measurements g. The proposed framework has the following properties: (i) in addition to estimating the underlying signal f, “error bars ” are also estimated, these giving a measure of confidence in the inverted signal; (ii) using knowledge of the error bars, a principled means is provided for determining when a sufficient
Sparse multinomial logistic regression: fast algorithms and generalization bounds
 IEEE Trans. on Pattern Analysis and Machine Intelligence
"... Abstract—Recently developed methods for learning sparse classifiers are among the stateoftheart in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsitypromoting priors encouraging the weight estimates to be either significantly larg ..."
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Cited by 190 (1 self)
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Abstract—Recently developed methods for learning sparse classifiers are among the stateoftheart in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsitypromoting priors encouraging the weight estimates to be either significantly large or exactly zero. From a learningtheoretic perspective, these methods control the capacity of the learned classifier by minimizing the number of basis functions used, resulting in better generalization. This paper presents three contributions related to learning sparse classifiers. First, we introduce a true multiclass formulation based on multinomial logistic regression. Second, by combining a bound optimization approach with a componentwise update procedure, we derive fast exact algorithms for learning sparse multiclass classifiers that scale favorably in both the number of training samples and the feature dimensionality, making them applicable even to large data sets in highdimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsitypromoting prior. Third, we show how nontrivial generalization bounds can be derived for our classifier in the binary case. Experimental results on standard benchmark data sets attest to the accuracy, sparsity, and efficiency of the proposed methods.
A new view of automatic relevance determination
 In NIPS 20
, 2008
"... Automatic relevance determination (ARD) and the closelyrelated sparse Bayesian learning (SBL) framework are effective tools for pruning large numbers of irrelevant features leading to a sparse explanatory subset. However, popular update rules used for ARD are either difficult to extend to more gene ..."
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Cited by 68 (9 self)
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Automatic relevance determination (ARD) and the closelyrelated sparse Bayesian learning (SBL) framework are effective tools for pruning large numbers of irrelevant features leading to a sparse explanatory subset. However, popular update rules used for ARD are either difficult to extend to more general problems of interest or are characterized by nonideal convergence properties. Moreover, it remains unclear exactly how ARD relates to more traditional MAP estimationbased methods for learning sparse representations (e.g., the Lasso). This paper furnishes an alternative means of expressing the ARD cost function using auxiliary functions that naturally addresses both of these issues. First, the proposed reformulation of ARD can naturally be optimized by solving a series of reweighted ℓ1 problems. The result is an efficient, extensible algorithm that can be implemented using standard convex programming toolboxes and is guaranteed to converge to a local minimum (or saddle point). Secondly, the analysis reveals that ARD is exactly equivalent to performing standard MAP estimation in weight space using a particular feature and noisedependent, nonfactorial weight prior. We then demonstrate that this implicit prior maintains several desirable advantages over conventional priors with respect to feature selection. Overall these results suggest alternative cost functions and update procedures for selecting features and promoting sparse solutions in a variety of general situations. In particular, the methodology readily extends to handle problems such as nonnegative sparse coding and covariance component estimation. 1
Fast Bayesian compressive sensing using Laplace priors
 in IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc. (ICASSP09
, 2009
"... In this paper we model the components of the compressive sensing (CS) problem using the Bayesian framework by utilizing a hierarchical form of the Laplace prior to model sparsity of the unknown signal. This signal prior includes some of the existing models as special cases and achieves a high degree ..."
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Cited by 66 (11 self)
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In this paper we model the components of the compressive sensing (CS) problem using the Bayesian framework by utilizing a hierarchical form of the Laplace prior to model sparsity of the unknown signal. This signal prior includes some of the existing models as special cases and achieves a high degree of sparsity. We develop a constructive (greedy) algorithm resulting from this formulation where necessary parameters are estimated solely from the observation and therefore no userintervention is needed. We provide experimental results with synthetic 1D signals and images, and compare with the stateoftheart CS reconstruction algorithms demonstrating the superior performance of the proposed approach. Index Terms — Bayesian methods, compressive sensing, inverse problems, sparse Bayesian learning, relevance vector machine
Sparse Bayesian learning for efficient visual tracking
 IEEE Trans. Pattern Anal. Mach. Intell
, 2005
"... This paper extends the use of statistical learning algorithms for object localization. It has been shown that object recognizers using kernelSVMs can be elegantly adapted to localization by means of spatial perturbation of the SVM. Whilst this SVM applies to each frame of a video independently of ..."
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Cited by 66 (6 self)
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This paper extends the use of statistical learning algorithms for object localization. It has been shown that object recognizers using kernelSVMs can be elegantly adapted to localization by means of spatial perturbation of the SVM. Whilst this SVM applies to each frame of a video independently of other frames, the benefits of temporal fusion of data are well known. This is addressed here by using a fully probabilistic Relevance Vector Machine (RVM) to generate observations with Gaussian distributions that can be fused over time. Rather than adapting a recognizer, we build a displacement expert which directly estimates displacement from the target region. An object detector is used in tandem, for object verification, providing the capability for automatic initialization and recovery. This approach is demonstrated in realtime tracking systems where the sparsity of the RVM means that only a fraction of CPU time is required to track at frame rate. An experimental evaluation compares 1 this approach to the state of the art showing it to be a viable method for longterm region tracking.
Outputassociative rvm regression for dimensional and continuous emotion prediction
 in Proc. of IEEE FG
, 2011
"... Abstract — Many problems in machine learning and computer vision consist of predicting multidimensional output vectors given a specific set of input features. In many of these problems, there exist inherent temporal and spacial dependencies between the output vectors, as well as repeating output pa ..."
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Cited by 28 (6 self)
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Abstract — Many problems in machine learning and computer vision consist of predicting multidimensional output vectors given a specific set of input features. In many of these problems, there exist inherent temporal and spacial dependencies between the output vectors, as well as repeating output patterns and inputoutput associations, that can provide more robust and accurate predictors when modelled properly. With this intrinsic motivation, we propose a novel OutputAssociative Relevance Vector Machine (OARVM) regression framework that augments the traditional RVM regression by being able to learn nonlinear input and output dependencies. Instead of depending solely on the input patterns, OARVM models output structure and covariances within a predefined temporal window, thus capturing past, current and future context. As a result, output patterns manifested in the training data are captured within a formal probabilistic framework, and subsequently used during inference. As a proof of concept, we target the highly challenging problem of dimensional and continuous prediction of emotions from naturalistic facial expressions. We demonstrate the advantages of the proposed OARVM regression by performing both subjectdependent and subjectindependent experiments using the SAL database. The experimental results show that OARVM regression outperforms the traditional RVM and SVM regression approaches in prediction accuracy, generating more robust and accurate models.
On the Roles of Eye Gaze and Head Dynamics in Predicting Driver’s Intent to Change Lanes
, 2009
"... Driver behavioral cues may present a rich source of information and feedback for future intelligent advanced driverassistance systems (ADASs). With the design of a simple and robust ADAS in mind, we are interested in determining the most important driver cues for distinguishing driver intent. Eye g ..."
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Cited by 26 (15 self)
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Driver behavioral cues may present a rich source of information and feedback for future intelligent advanced driverassistance systems (ADASs). With the design of a simple and robust ADAS in mind, we are interested in determining the most important driver cues for distinguishing driver intent. Eye gaze may provide a more accurate proxy than head movement for determining driver attention, whereas the measurement of head motion is less cumbersome and more reliable in harsh driving conditions. We use a lanechange intentprediction system (McCall et al., 2007) to determine the relative usefulness of each cue for determining intent. Various combinations of input data are presented to a discriminative classifier, which is trained to output a prediction of probable lanechange maneuver at a particular point in the future. Quantitative results from a naturalistic driving study are presented and show that head motion, when combined with lane position and vehicle dynamics, is a reliable cue for lanechange intent prediction. The addition of eye gaze does not improve performance as much as simpler head dynamics cues. The advantage of head data over eye data is shown to be statistically significant (p <0.01) 3 s ahead of lanechange situations, indicating that there may be a biological basis for head motion to begin earlier than eye motion during “lanechange”related gaze shifts.
Sparse Event Detection in Wireless Sensor Networks using Compressive Sensing
"... Abstract — Compressive sensing is a revolutionary idea proposed recently to achieve much lower sampling rate for sparse signals. For large wireless sensor networks, the events are relatively sparse compared with the number of sources. Because of deployment cost, the number of sensors is limited, and ..."
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Cited by 24 (3 self)
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Abstract — Compressive sensing is a revolutionary idea proposed recently to achieve much lower sampling rate for sparse signals. For large wireless sensor networks, the events are relatively sparse compared with the number of sources. Because of deployment cost, the number of sensors is limited, and due to energy constraint, not all the sensors are turned on all the time. In this paper, the first contribution is to formulate the problem for sparse event detection in wireless sensor networks as a compressive sensing problem. The number of (wakeup) sensors can be greatly reduced to the similar level of the number of sparse events, which is much smaller than the total number of sources. Second, we suppose the event has the binary nature, and employ the Bayesian detection using this prior information. Finally, we analyze the performance of the compressive sensing algorithms under the Gaussian noise. From the simulation results, we show that the sampling rate can reduce to 25 % without sacrificing performance. With further decreasing the sampling rate, the performance is gradually reduced until 10 % of sampling rate. Our proposed detection algorithm has much better performance than the l1magic algorithm proposed in the literature. I.
Fast algorithms for large scale conditional 3D prediction
 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR
, 2008
"... The potential success of discriminative learning approaches to 3D reconstruction relies on the ability to efficiently train predictive algorithms using sufficiently many examples that are representative of the typical configurations encountered in the application domain. Recent research indicates th ..."
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Cited by 23 (4 self)
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The potential success of discriminative learning approaches to 3D reconstruction relies on the ability to efficiently train predictive algorithms using sufficiently many examples that are representative of the typical configurations encountered in the application domain. Recent research indicates that sparse conditional Bayesian Mixture of Experts (cMoE) models (e.g. BME [21]) are adequate modeling tools that not only provide contextual 3D predictions for problems like human pose reconstruction, but can also represent multiple interpretations that result from depth ambiguities or occlusion. However, training conditional predictors requires sophisticated doubleloop algorithms that scale unfavorably with the input dimension and the training set size, thus limiting their usage to 10,000 examples of less, so far. In this paper we present largescale algorithms, referred to as f BME, that combine forward feature selection and bound optimization in order to train probabilistic, BME models, with one order of magnitude more data (100,000 examples and up) and more than one order of magnitude faster. We present several large scale experiments, including monocular evaluation on the HumanEva dataset [19], demonstrating how the proposed methods overcome the scaling limitations of existing ones. 1.
Bayesian Regression and Classification
 Advances in Learning Theory: Methods, Models and Applications
, 2003
"... Abstract In recent years Bayesian methods have become widespread in many domains including computer vision, signal processing, information retrieval and genome data analysis. The availability of fast computers allows the required computations to be performed in reasonable time, and thereby makes the ..."
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Cited by 22 (0 self)
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Abstract In recent years Bayesian methods have become widespread in many domains including computer vision, signal processing, information retrieval and genome data analysis. The availability of fast computers allows the required computations to be performed in reasonable time, and thereby makes the benefits of a Bayesian treatment