Conditional probability density function estimation with sigmoidal neural networks

Real-world problems can often be couched in terms of conditional probabilit y density function estimation. In particular, pattern recognition, signal d etection, and financial prediction are among the multitude of applications requiring conditional density estimation. Previous developments in this dir ection have used neural nets to estimate statistics of the distribution or the marginal or joint distributions of the input-output variables. We have modified the joint distribution estimating sigmoidal neural network to esti mate the conditional distribution. Thus, the probability density of the out put conditioned on the inputs is estimated using a neural network. We have derived and implemented the learning laws to train the network, We show tha t this network has computational advantages over a brute force ratio of joi nt and marginal distributions. We also compare its performance to a kernel conditional density estimator in a larger scale (higher dimensional) proble m simulating more realistic conditions.