TJ of the gradient updates is held constant (simple backpropagation).

E (0,00), remains in spite of many real (and 459 460 Finnoff imagined)deficiencies the most widely used network training algorithm, and a vast body of literature documents its general applicability and robustness. In this paper we will draw on the highly developed literature of stochastic approximation theory todemonstrate several asymptotic properties of simple backpropagation.

One method proposed for improving the generalization capability of a feedforward network trained with the backpropagation algorithm is to use artificial training vectors which are obtained by adding noise to the original training vectors. We discuss the connection of such backpropagation training with noise to kernel density and kernel regression estimation. We compare by simulated examples (1) backpropagation, (2) backpropagation with noise, and (3) kernel regression in mapping estimation and pattern classification contexts.

One method proposed for improving the generalization capability of a feedforward network trained with the backpropagation algorithm is to use artificial training vectors which are obtained by adding noise to the original training vectors. We discuss the connection of such backpropagation training with noise to kernel density and kernel regression estimation. We compare by simulated examples (1) backpropagation, (2) backpropagation with noise, and (3) kernel regression in mapping estimation and pattern classification contexts.

One method proposed for improving the generalization capability of a feedforward networktrained with the backpropagation algorithm is to use artificial training vectors which are obtained by adding noise to the original trainingvectors. We discuss the connection of such backpropagation training with noise to kernel density and kernel regression estimation. We compare by simulated examples (1) backpropagation, (2) backpropagation with noise, and (3) kernel regression in mapping estimation and pattern classification contexts.

We describe a closed-form technique for mapping the output of a trained backpropagation network int.o input activity space. The mapping is an verse in mapping in the sense that, when the image of the mapping in input activity space is propagat.ed

We describe a closed-form technique for mapping the output of a trained backpropagation network int.o input activity space. The mapping is an verse in mapping in the sense that, when the image of the mapping in input activity space is propagat.ed

We describe a closed-form technique for mapping the output of a trained backpropagation network int.o input activity space. The mapping is an inverse mappingin the sense that, when the image of the mapping in input activity space is propagat.ed

We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm for networks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections for networks with hidden units. Other transfer functions may lead to a 8lower polynomial rate of convergence. Our analytic calculations were presented in (Tesauro, He & Ahamd, 1989). Here we focus in more detail on our empirical measurements of the convergence rate in numerical simulations, which confirm our analytic results.

In this paper we compare regression and classification systems. A regression system can generate an output f for an input X, where both X and f are continuous and, perhaps, multidimensional. A classification system can generate an output class, C, for an input X, where X is continuous and multidimensional and C is a member of a finite alphabet. The statistical technique of Classification And Regression Trees (CART) was developed during the years 1973 (Meisel and Michalpoulos) through 1984 (Breiman el al).