This article proves that the task of computing near-optimal weights for sigmoidal nodes under the L_1 regression norm is NP-Hard. For the special case where the sigmoid is piecewise linear, we prove a lightly stronger result: that computing the optimal weights is NP-Hard. These results parallel that for the one-node pattern recognition problem-that deter- mining the optimal weights for a threshold logic node is also intractable. Our results have important consequences for constructive algorithms That build a regression model one node at a time.
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