D. MacKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448--472, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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A New Learning Scheme for Neural Network Ensembles - Haraldsson, Ohlsson (2002) (Correct)
....the networks are returned to the state they had before the random move; rather the temperature is used in the selection between many such updated models. III. PROPERTIES OF THE METHOD The properties and performance of the algorithm were evaluated using three test sets. The Robot Arm data set [22], 18] is an artificial regression problem, in which the outputs are simple trigonometric functions of the inputs, with a small Gaussian noise term added. The Pima Indians Diabetes Database [23] and Myocardial Scintigram data set [24] are medical classification problems with binary targets. The ....
D. J. C. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Computation, vol. 4, no. 3, pp. 448--472, 1992.
Modelling Conditional Probability Densities with Neural Networks - Husmeier (1997) (2 citations) (Correct)
....expression on the right is called the evidence for model M i , and can be used as a criterion for model selection. Section 9.2 will briefly review the Bayesian evidence scheme. This concept was originally developed by Gull [23] and was introduced to the neural network community by MacKay [42] [43], who applied it to the prediction of Gaussian conditional densities P (yjx) exp ( Gamma ) with constant precisions, fi = constant. It will be outlined, without going into mathematical detail, how this scheme can be generalised to arbitrary probability densities P (yjx) The mathematical ....
....in the constant Omega Omega s , to replace det A by fdet Ag :r . This leads to the following corrected expression for the evidence (9.31) ln P (DjM) GammaE(q) Gamma R(qjr) Gamma 2 2 lnfdet Ag :r 2 (9.53) The whole concept is illustrated in a simple example. MacKay [42] [43] considers two hyperparameters r = ff; fi) and shows that A ffff = Gamma (9.54) A fifi = Gamma (9.55) A fffi = Gamma ff fi 0 (9.56) where N denotes the size of the training set and fl the number of free parameters (to be discussed shortly) The resulting ....
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MacKay D.J.C. (1992): A practical Bayesian framework for backpropagation networks. Neural Computation 4, 448-472.
Applying MDL to Learning Best Model Granularity - Gao, Li, Vitányi (2000) (4 citations) (Correct)
....by the lengths of the two limbs, together with the angle of rotation in the first joint of the first limb, and the angle of rotation in the second joint of the second limb with respect to the first limb. The mobile end of the arm thus has two degrees of freedom given by the two angles. In [12] this standard problem is modeled using a Bayesian framework to obtain a feed forward network model. We use MDL to obtain the best number of nodes in the hidden layer of a three layer feed forward network model. The method is essentially the same as in the character recognition experiment. Just as ....
....limb (the hand so to speak) and the variables # 1 ,# 2 is given by r 1 cos(# 1 ) r 2 cos(# 1 # 2 ) r 1 sin(# 1 ) r 2 sin(# 1 # 2 ) The goal is to construct a feedforward neural network that correctly associates the (y 1 ,y 2 ) coordinates to the (# 1 ,# 2 ) coordinates. As in [12] we set r 1 2andr 2 1.3. The setup is similar to the character recognition experiment except that the data are not real world but computer generated. We generated random examples of the relation between y 1 ,y 2 and # 1 ,# 2 as in the above formula and a little Gaussian noise was added to ....
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D.J.C. MacKay, A practical Bayesian framework for backpropagation networks, Neural Computation 4 (3) (1992) 448--472.
Numerical Integration by Cubature Formulae in Bayesian.. - van Wezel, Kosters (Correct)
....Unfortunately, all usefull quantities (e.g. predictions) take the form of a multidimensional integral, approximation of which is extremely dicult. In the recent past, various authors have attempted to approximate these integrals by using various techniques, among which Gaussian approximations [4] and hybrid Markov Chain Monte Carlo (MCMC) 5] See Section 3 for a few more words on the latter technique. In this paper, which is partly based on a chapter of [7] we will attempt to approximate the integrals by using so called cubature formulae combined with a suitable transformation. A ....
....importance of the problem domain. 2 The problem: expectations in Bayesian neural networks In this section we brie y consider Bayesian inference applied to neural networks. The reader requiring more information on the subject is referred to [1] We restrict ourselves to regression problems. See [1, 4] for a description of Bayesian neural networks for classi cation. The neural network type concerned is the well known multilayer perceptron (MLP) The MLP related notation that we will use in this paper is summarized in Table 1. For notational convenience we will only consider regression problems ....
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D. J. C. MacKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448-472, 1992.
Bayesian Neural Network Learning for Prediction in .. - Macrossan.. (1999) (Correct)
....distribution for all observable and unobservable quantities in the problem. 2. Conditioning on observed data: calculating and interpreting the appropriate posterior distribution given the data. 3. Evaluating the model fit: assessing the implications of the posterior distribution. MacKay [14] and Neal [16] describe a Bayesian neural network (BNN) where a probabilistic interpretation is applied to the NN technique. This interpretation involves assigning a meaning to the functions and parameters already in use. In the Bayesian approach to NN prediction, the objective is to use the ....
....the objective evaluation of a number of issues involved in complex modelling including the choice between alternative network architectures (e.g. the number of hidden units and the activation function) the stopping rules for network training and the effective number of parameters used. MacKay [14] postulates that the overall effect of the Bayesian framework should be realised in the reduction in the high cost of the learning process in terms of the time needed for the learning to take place. The framework allows for the full use of the limited and often expensive data set for training the ....
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D.J.C. MacKay. A practical bayesian framework for backpropagation networks. Neural Computation, 4:448--472, 1992.
A New Bayesian Design Method For Support Vector Classification - Wei Chu Sathiya (Correct)
....determine the values of these parameters. Moreover, Bayesian methods can also provide probabilistic class prediction that is more desirable than just deterministic classification. There is some literature on Bayesian interpretations of classical SVC. Kwok [3] built up MacKay s evidence framework [4] using a weight space interpretation. The unnormalized evidence may cause inaccuracy in Bayesian inference. Sollich [6] pointed out that the normalization issue in Wei Chu gratefully acknowledges the financial support provided by the National University of Singapore through Research Scholarship. ....
....idea about the suitable values of # before training data are available, we assume a flat distribution for P(#) i.e. is greatly insensitive to the values of #. Therefore, P(D #) known as the evidence of #, can be used to assign a preference to alternative values of the hyperparameters # [4]. The evidence could be calculated by an explicit formula after using a Laplacian approximation at f MP , and then hyperparameter inference may be done by gradient based optimization methods. We can get the evidence by an integral over all f : P(D #, f)P(f #) df . Using the definitions ....
D. J. C. MacKay, A practical Bayesian framework for back propagation networks. Neural Computation, 4(3), 448-472, 1992.
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D. MacKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448--472, 1992.
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D. J. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Comput., vol. 4, pp. 448--472, 1992.
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D.J.C. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Comput., vol 4, pp. 448-472, 1992.
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D. J. C. MacKay. A practical Bayesian framework for back propagation networks. Neural Computation, 4(3):448--472, 1992.
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MacKay, D. J. C., 1992b. A practical Bayesian framework for backpropagation networks. Neural Computation, 4, 448--472.
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MACKAY, D.J.C., A practical Bayesian framework for backpropagation networks, in Neural Computation,4(3) (1992),p.448-472.
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A Dynamical System Perspective of Structural Learning with.. - Miller, Zurada (1998) (1 citation) (Correct)
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D. J. C. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Computa., vol. 4, pp. 448--472, 1992.
Training Context-Sensitive Neural Networks with Few .. - Stricker, Vichot.. (2000) (1 citation) (Correct)
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D. J. C. MacKay. A Practical Bayesian Framework for Backpropagation Networks. Neural Computation, 4(3), 448-472, 1992.
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D. J. C. MacKay. A practical Bayesian framework for back-propagation networks. Neural Computation, 4(3):448-472, 1992.
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D. J. C. MacKay. A Practical Bayesian Framework for Backpropagation Networks. Neural Computation, 4:448-472, 1992.
Computational Intelligence Methods for Rule-Based Data.. - Duch, Setiono, Zurada (2004) (Correct)
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D. J. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Comput., vol. 4, pp. 448--472, 1992.
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D. MacKay. A practical Bayesian framework for backpropagation networks. Neural Computation, 4:448-472, 1992.
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MacKay DJC. A practical Bayesian framework for back-propagation networks. Neural Computation 1992; 4: 448--472
Numerical Integration by Cubature Formulae in Bayesian.. - van Wezel, Kosters (2003) (Correct)
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D. J. C. MacKay, "A practical Bayesian framework for backpropagation networks," Neural Computation, vol. 4, no. 3, pp. 448--472, 1992.
Studies of Model Selection and Regularization for Generalization in .. - Guo (Correct)
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D. J. C. MacKay, "A Practical Bayesian Framework for Backpropagation Networks, " Neural Computation, vol. 4, no. 3, pp. 448--472, 1992.
Applying Machine Learning to Solve an Estimation Problem .. - Ragg, Padberg.. (2002) (Correct)
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MacKay : "A practical bayesian framework for backpropagation networks" , Neural Computation 4:3 (1992) 448-472
A Tutorial on Learning With Bayesian Networks - Heckerman (1996) (218 citations) (Correct)
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MacKay, D. (1992b). A practical Bayesian framework for backpropagation networks. Neural Computation, 4:448--472.
A Tutorial on Learning With Bayesian Networks - Heckerman (1996) (218 citations) (Correct)
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MacKay, D. (1992b). A practical Bayesian framework for backpropagation networks. Neural Computation, 4:448-472.
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