M. Sahami. Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks. In AAAI Press, editor, Proceedings of the Eleventh National Conference on Artificial Inteligence, pages 335--341, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... trees have only very recently begun to attract the attention of researchers in the machine learning community [BU, 1992; 1994] Furthermore, we show how any such TLU trees can be mechanically transformed into a three layer neural network as first suggested by Brent [BR, 1990] and developed by Sahami [SA, 1993]. In our investigation, we compare several different methods for learning the linear discriminant at each node of the tree and compare these with ID3 s univariate approach and a naive Bayesian method for learning multivariate tests. 2 The TLU Tree Algorithm The tree building algorithm is ....

Sahami, M. 1993. Learning Non-Linearly Separable Boolean Functions With Linear Threshold Unit Trees and Madaline-Style Networks. In Proceedings of the 11th National Conference on Artificial Intelligence, 335-41. Menlo Park, CA: AAAI Press.

....[403] describe a method that constructs Boolean features using lookahead, and uses the constructed feature combinations as tests at tree nodes. Lookahead for construction of Boolean feature combinations is also considered in [515] Linear threshold unit trees for Boolean functions are described in [418]. Decision trees having first order predicate calculus representations, with Horn clauses as tests at internal nodes, are considered in [497] Subsample selection Feature subset selection attempts to choose useful features. Similarly, subsample selection attempts to choose appropriate training ....

M. Sahami. Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks. In AAAI-93 [8], pages 335--341.

....coefficients in the tree by defining the model likelihood and using the EM algorithm (Dempster, Laird Rubin 1977) for optimization. Soft splits are used not only for tree construction but also during classification. However, their method requires the user to specify the tree structure a priori. Sahami (1993) investigates various optimization algorithms for finding an errorminimizing discriminant at each node in a decision tree. Bichsel Seitz (1989) gives an algorithm for training a tree structured net very similar to the approach by Heath, Kasif Salzberg (1993) using simulated annealing to ....

Sahami, M. (1993), Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks, in "AAAI-93: Proceedings of the Eleventh National Conference on Artificial Intelligence", American Association for Artificial Intelligence, AAAI Press/MIT Press, pp. 335--341.

....coefficients in the tree by defining the model likelihood and using the EM algorithm (Dempster, Laird Rubin 1977) for optimization. Soft splits are used not only for tree construction but also during classification. However, their method requires the user to specify the tree structure a priori. Sahami (1993) investigates various optimization algorithms for finding error minimizing linear discriminants at each node in a decision tree. Bichsel Seitz (1989) give an algorithm for training a tree structured net very similar to the approach by Heath, Kasif Salzberg (1993) using simulated annealing to ....

Sahami, M. (1993), Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks, in "AAAI-93: Proceedings of the Eleventh National Conference on Artificial Intelligence", AAAI Press/MIT Press, pp. 335--341.

....[310] describe a method that constructs Boolean features using lookahead, and uses the constructed feature combinations as tests at tree nodes. Lookahead for construction of Boolean feature combinations is also considered in [389] Linear threshold unit trees for Boolean functions are described in [321]. Decision trees having first order predicate calculus representations, with Horn clauses as tests at internal nodes, are considered in [375] 5.1.3. Subsample selection Feature subset selection attempts to choose useful features. Similarly, subsample selection attempts to choose appropriate ....

M. Sahami. Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks. In AAAI-93 [2], pages 335--341.

....still preliminary and conflicting results have also been reported [12] This report helps to address these issues as well. Furthermore, we show how any such TLU tree can be mechanically transformed into a three layer neural network as first suggested by Brent [1] and further developed by Sahami [10, 11]. Such transformed networks, which have two hidden layers and one output layer (the input layer is not counted) can often by trained much more quickly by building the TLU tree and transforming it into a network than attempting to train the corresponding network using the standard Back Propagation ....

....to get to it. Thus each node in the second hidden layer represents a single distinct path through T by being connected to those nodes in the first layer which 1 Notation in the description of the TLU tree algorithm is similar to that presented in [1] The algorithm presented here closely follows [10]. correspond to the nodes that were traversed along the given path. Since the nodes in the second hidden layer are merely AND gates, the inputs coming from the first hidden layer must first be inverted if a left branch was traversed in T at the node corresponding to a given input from the first ....

Sahami, M. 1993. Learning Non-Linearly Separable Boolean Functions With Linear Threshold Unit Trees and Madaline-Style Networks. In AAAI-93 Proceedings of the Eleventh National Conference on Artificial Intelligence, 335-41. Menlo Park, CA: AAAI Press.

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M. Sahami. Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks. In AAAI Press, editor, Proceedings of the Eleventh National Conference on Artificial Inteligence, pages 335--341, 1993.

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M. Sahami. Learning non-linearly separable boolean functions with linear threshold unit trees and madaline-style networks. In AAAI-93 #2#, pages 335#341.

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