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11,827
Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
Abstract

Cited by 721 (17 self)
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. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them
A Practical Bayesian Framework for Backprop Networks
 Neural Computation
, 1991
"... A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures ..."
Abstract

Cited by 496 (20 self)
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A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures
"GrabCut”  interactive foreground extraction using iterated graph cuts
 ACM TRANS. GRAPH
, 2004
"... The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently ..."
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Cited by 1140 (36 self)
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The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently, an approach based on optimization by graphcut has been developed which successfully combines both types of information. In this paper we extend the graphcut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power of the iterative algorithm is used to simplify substantially the user interaction needed for a given quality of result. Thirdly, a robust algorithm for “border matting ” has been developed to estimate simultaneously the alphamatte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vector machine' (RVM), a model of identical functional form to the popular and stateoftheart `support vector machine' (SVM). We demonstrate that by exploiting a probabilistic Bayesian learning framework, we can derive accurate prediction models which typically utilise dramatically fewer basis functions than a comparable SVM while oering a number of additional advantages. These include the benets of probabilistic predictions, automatic estimation of `nuisance' parameters, and the facility to utilise arbitrary basis functions (e.g. non`Mercer' kernels).
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
InformationBased Objective Functions for Active Data Selection
 Neural Computation
"... Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed which measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain infor ..."
Abstract

Cited by 429 (5 self)
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Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed which measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain
A hidden Markov model for predicting transmembrane helices in protein sequences
 In Proceedings of the 6th International Conference on Intelligent Systems for Molecular Biology (ISMB
, 1998
"... A novel method to model and predict the location and orientation of alpha helices in membrane spanning proteins is presented. It is based on a hidden Markov model (HMM) with an architecture that corresponds closely to the biological system. The model is cyclic with 7 types of states for helix core, ..."
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Cited by 367 (9 self)
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A novel method to model and predict the location and orientation of alpha helices in membrane spanning proteins is presented. It is based on a hidden Markov model (HMM) with an architecture that corresponds closely to the biological system. The model is cyclic with 7 types of states for helix core, helix caps on either side, loop on the cytoplasmic side, two loops for the noncytoplasmic side, and a globular domain state in the middle of each loop. The two loop paths on the noncytoplasmic side are used to model short and long loops separately, which corresponds biologically to the two known different membrane insertions mechanisms. The close mapping between the biological and computational states allows us to infer which parts of the model architecture are important to capture the information that encodes the membrane topology, and to gain a better understanding of the mechanisms and constraints involved. Models were estimated both by maximum likelihood and a discriminative method, and a method for reassignment of the membrane helix boundaries were developed. In a cross validated test on single sequences, our transmembrane HMM, TMHMM, correctly predicts the entire topology for 77 % of the sequencesin a standard dataset of 83 proteins with known topology. The same accuracy was achieved on a larger dataset of 160 proteins. These results compare favourably with existing methods.
Support Vector Machines for Classification and Regression
 UNIVERSITY OF SOUTHAMPTON, TECHNICAL REPORT
, 1998
"... The problem of empirical data modelling is germane to many engineering applications.
In empirical data modelling a process of induction is used to build up a model of the
system, from which it is hoped to deduce responses of the system that have yet to be observed.
Ultimately the quantity and qualit ..."
Abstract

Cited by 342 (5 self)
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The problem of empirical data modelling is germane to many engineering applications.
In empirical data modelling a process of induction is used to build up a model of the
system, from which it is hoped to deduce responses of the system that have yet to be observed.
Ultimately the quantity and quality of the observations govern the performance
of this empirical model. By its observational nature data obtained is finite and sampled;
typically this sampling is nonuniform and due to the high dimensional nature of the
problem the data will form only a sparse distribution in the input space. Consequently
the problem is nearly always ill posed (Poggio et al., 1985) in the sense of Hadamard
(Hadamard, 1923). Traditional neural network approaches have suffered difficulties with
generalisation, producing models that can overfit the data. This is a consequence of the
optimisation algorithms used for parameter selection and the statistical measures used
to select the ’best’ model. The foundations of Support Vector Machines (SVM) have
been developed by Vapnik (1995) and are gaining popularity due to many attractive
features, and promising empirical performance. The formulation embodies the Structural
Risk Minimisation (SRM) principle, which has been shown to be superior, (Gunn
et al., 1997), to traditional Empirical Risk Minimisation (ERM) principle, employed by
conventional neural networks. SRM minimises an upper bound on the expected risk,
as opposed to ERM that minimises the error on the training data. It is this difference
which equips SVM with a greater ability to generalise, which is the goal in statistical
learning. SVMs were developed to solve the classification problem, but recently they
have been extended to the domain of regression problems (Vapnik et al., 1997). In the
literature the terminology for SVMs can be slightly confusing. The term SVM is typically
used to describe classification with support vector methods and support vector
regression is used to describe regression with support vector methods. In this report
the term SVM will refer to both classification and regression methods, and the terms
Support Vector Classification (SVC) and Support Vector Regression (SVR) will be used
for specification. This section continues with a brief introduction to the structural risk
Results 1  10
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