B.T. Zhang, P. Ohm, H. Muhlenbein, Evolutionary induction of sparse neural trees, Evolutionary Computation 5 (1997) 213--236.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....The results are encouraging. The numerical result indicates that control of the weight factor can substantially reduce the amount of computation. For Bayesian network we have not yet experimented with control strategies. We have intensively studied the problem in the context of neural networks [ZOM97]. 7 The System Dynamics Approach to Optimization We have shown that Wright s equations converge to some local optima of the fitness function at the boundary. We might ask ourselves: Why not using the difference equations directly, without generating a population This approach is callled the ....

Byoung-Tak Zhang, Peter Ohm, and Heinz Muhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5:213--236, 1997.

....the theoretical estimate. The numerical result indicates that control of the weight factor ff can substantially reduce the amount of computation. For Bayesian network we have not yet experimented with control strategies. We have intensively studied the problem in the context of neural networks [15]. The method will be discussed in section 1.6. Network Equivalence and Optimality Many Bayesian networks represent the same probability. These networks are called equivalent. Let us discuss a simple example. p(x) p(x 1 )p(x 2 jx 1 )p(x 3 jx 2 ; x 1 )p(x 4 jx 3 ) 1.22) The independence ....

....of the error and size of the subtrees. Other criteria for subtree evaluation proposed in the literature include the error of the subtree, error difference, frequency of subtrees, use of the average fitness of population, correlation based selection, combination of frequency and error difference [15]. Mutation and adding of library functions is also discussed there. 1.7 MDL Based Fitness Function The goal is to find a neural tree or model A whose evaluation fA (x) best approximates the unknown relation y = f(x) given an input x. The goodness of the program for the dataset D is measured by ....

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Byoung-Tak Zhang, Peter Ohm, and Heinz Muhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5:213--236,

.... [1] to option pricing [2] and modeling of the dynamics underlying nancial markets [4] Approaches to time series prediction based on GP can be roughly classi ed into three strands: approaches which use GP or another evolutionary algorithm to optimize a neural network model of the time series [15,3,16]; GP evolving some ad hoc structure representing in an indirect way knowledge or informations about the time series, such as decision trees [13] GP evolving an expression or simple program which computes future values of the time series based on a number of past values [14,12,11,10,7] The ....

B. Zhang, P. Ohm, and H. Mhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5(2):213236, 1997.

....method well suited for fine tuning already evolved expressions and so completing the work of the evolutionary process. Possible fields of application may include GP for time series modeling [19] multiple interacting programs (MIPs) 3] and the training of higher order ANNs or neural trees [28]. In the next section, we investigate the usefulness of employing the gradient based operators during the evolutionary process by investigating the absolute benefit of different coefficient adaptation strategies. 5.2 Experiments We used a toy problem to analyze the operators. The task was to ....

B.-T. Zhang, P. Ohm, and H. Muhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5(2):213--236, 1997.

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Zhang, Byoung-Tak, Ohm, Peter, & Muhlenbein, Heinz. 1997. Evolutionary Induction of Sparse Neural Trees. Evolutionary Computation, 5, 213-236.

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Zhang, B.-T. & Ohm, P. & Muhlenbein, H. (1997). Evolutionary Induction of Sparse Neural Trees, Evolutionary Computation, 5:pp. 213--236.

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Zhang, B.-T., Ohm, P., and Muehlenbein, H. (1997). Evolutionary induction of sparse neural trees, Evolutionary Computation, 5(2), 213-236.

....over generation. In order to improve the performance of the networks we deal with complexity of networks as well as the method to select data points. In evolving MLPs we use neural trees (NTs) that represent higher order neural networks (HONNs) as a generalization of the multilayer perceptrons [4]. The paper is organized as follows. Section 2 describes the evolutionary neural trees for designing and training MLPs. Section 3 describes active data selection in general. Sections 4 describes active data inheritance in more detail. Section 5 presents the experimental setup and results on ....

....the experimental setup and results on benchmark problems from the Santa Fe time series competition database and the UCI machine learning database. Section 6 concludes this paper. 2 Evolutionary Neural Trees for Neural Net Learning A neural tree consists of nonterminal nodes and terminal nodes [4] (see Fig. 1) The nonter minal nodes represent neural units and the neuron type is an element of the basis function set r : neuron types . Each terminal node is la beled with an element from the terminal set 7 : Xl,X2, Xn , where X i is the ith component of the external input x. Each link ....

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B.-T. Zhang, P. Ohm, and H. Mfihlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, Vol. 5, No. 1, pp. 213-236, 1997.

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) Zhang, B.-T. & Ohm, P. & Muhlenbein, H. (1997). Evolutionary Induction of Sparse Neural Trees, Evolutionary Computation, 5:pp. 213-236.

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) Zhang, B.-T. & Ohm, P. & Muhlenbein, H. (1997). Evolutionary Induction of Sparse Neural Trees, Evolutionary Computation, 5:pp. 213-236.

....the theoretical estimate. The numerical result indicates that control of the weight factor # can substantially reduce the amount of computation. For Bayesian network we have not yet experimented with control strategies. We have intensively studied the problem in the context of neural networks [33]. 10 Conclusion We have shown that evolutionary algorithms can be approximated by an algorithm which keeps the population in linkage equilibrium. This algorithm, called UMDA, transforms the discrete optimization problem maxf (x) into a continuous one defined by max W(p 1 , p n ) 0 # ....

Byoung-Tak Zhang, Peter Ohm, and Heinz Mhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5:213--236, 1997.

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B.-T. Zhang, P. Ohm, and H. Muhlenbein, "Evolutionary induction of sparse neural trees," Z. Evolutionary Computation, Vol. 5 1 pp. 213#236, 1997.

.... algorithms can be helpful for the design of ANNs, what may consistute an effective design of EANN To address this question, two setups are taken, which also distinguish this study from [1] Firstly, the evolutionary algorithm employed in this paper, namely, evolutionary nerual trees ( 4] [5]) is more rich in its content than the one used by [1] This richness will enable us to ask address several important aspects of EANNs which may be difficult to be done in the framework of [1] such as complexity regulation, more flexible architectures, and hybridizing global search with local ....

....unit. The duplication does not necessarily mean more space requirements in trees than network representations since frequentlyused fit submodules can be stored and multiply reused. This leads to the construction of modular structures and reduces memory requirements for representing the population [5]. Neural trees do not require decoding for their fitness evaluation. Training and evaluation of fitness can be performed directly on the genotype since both the genotype and phenotype are equivalent. Since subtree crossover used in genetic programming may be applied without modification to this ....

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Zhang, B.-T., Ohm, P. and Muehlenbein, H. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5(2): 213-236. 1997.

....formal description of this procedure is given in Figure 18.3. The initial population is created with random individuals. Then, the fitness values of individual A i at generation t for the training set D, F (i) t : E(DjA i ) are evaluated as described above. Based on the adaptive Occam method [Zhang et al. 1997] a complexity term was used in all experiments to penalize large trees: F (i) E(DjA i ) fiC(A i ) where C(A i ) is the complexity measured in the number of nodes in tree A i and fi is a small constant. This measure is based on the minimum description length (MDL) principle, i.e. it ....

Zhang, B.-T., Ohm, P., and Muhlenbein, H. (1997), "Evolutionary induction of sparse neural trees," Evolutionary Computation, 5(2):213--236.

....use the machine layout problem as a testbed for this comparative study. This problem provides a useful benchmark due to its importance in engineering design, scalability of problem complexity, and its characteristic as a mixed discrete and continuous optimization task (Zhang and Mhlenbein, 1995; Zhang et al. 1997). The paper is organized as follows. Section 2 defines the machine layout problem. Section 3 describes the evolutionary optimization approach to this problem and presents the selection methods to be compared. Experimental results are given in Section 4. Section 5 compares the empirical results ....

Zhang B.T., Ohm P. & Mhlenbein H. (1997) Evolutionary induction of sparse neural trees, Evolutionary Computation, 5(2):213-236.

....measured as the sum of errors and complexity of individual A i : F (A i ) E(A i ) C(A i ) 4) E(A i ) is usually measured by the misclassi cation rate or the sum of squared errors on the data set D. The parameter is the Occam factor that controls the accuracy and complexity of individuals [15]. C(A i ) is based on the number of nodes and depth. 4 Byoung Tak Zhang and Je Gun Joung 3.2 Evolving Committees The goal of stage 2 is to nd an optimal committee, optimal in the sense of the size and members. We use the symbol V k (g) to denote the kth committee at generation g. The ....

Zhang, B.-T., Ohm, P. and Muehlenbein, H.: Evolutionary Induction of Sparse Neural Trees. Evolutionary Computation, 5(2) (1997) 213-236.

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B.T. Zhang, P. Ohm, H. Muhlenbein, Evolutionary induction of sparse neural trees, Evolutionary Computation 5 (1997) 213--236.

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Byoung-Tak Zhang, Peter Ohm, and Heinz Muhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5:213--236, 1997.

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Byoung-Tak Zhang, Peter Ohm, and Heinz Muhlenbein. Evolutionary induction of sparse neural trees. Evolutionary Computation, 5:213--236, 1997.

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B.-T. Zhang, P. Ohm, and H. Muhlenbein, "Evolutionary Induction of Sparse Neural Trees," Evolutionary Computation, 5 (2), pp. 213237, 1997.

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