tailieunhanh - Vibration Control Part 4

Tham khảo tài liệu 'vibration control part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 64 Vibration Control Bayesian learning From the statistical point of view the concept of maximum likelihood like back-propagation algorithms is typically employed in the training procedure of MLP models for the parameter estimation. It attempts to search a single set of network parameters from a sequence of training data D with N samples through the minimization of an error function the sum of squares error between the network prediction and the corresponding target N Ed y t - y t 2 7 However during such searching training process MLP models based on the maximum likelihood approach are easily led to complex topologies which may overfit the training data. As a result such overfitted models will deteriorate the generalization performance and be unable to make predictions as well for unseen input data as for the training case. One of the feasible procedures to improve generalization is weight decay which modifies the error function 7 by involving a penalty term to S 0 pED aEe 8 M where the regularizing term Ee e2 is the sum of squares of the M network parameters weights and biases which constrains the complexity of the network by limiting the growth of the network parameters and a and p are regularization parameters which serve to balance the trade-off between the prediction accuracy and the model complexity. MacKay 1992a b has made extensive investigations on the application of a Bayesian inference technique to adapt the weights and biases through network training and meanwhile to optimize the regularization parameters in an automated fashion. Unlike the maximum likelihood approach the Bayesian inference technique considers a probability distribution over the network parameters which represents the relative degree of belief in different parameter values and is described by a prior distribution P 0 a in the absence of any data. Once the data set D is taken the posterior probability distribution for the network parameters can be expressed using the Bayes theorem

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