Sarajedini A, Hecht-Nielsen R, Chau P M
Department of Electrical and Computer Engineering, University of California, San Diego, CA 92093, USA.
IEEE Trans Neural Netw. 1999;10(2):231-8. doi: 10.1109/72.750544.
Real-world problems can often be couched in terms of conditional probability density function estimation. In particular, pattern recognition, signal detection, and financial prediction are among the multitude of applications requiring conditional density estimation. Previous developments in this direction 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 estimate the conditional distribution. Thus, the probability density of the output conditioned on the inputs is estimated using a neural network. We have derived and implemented the learning laws to train the network. We show that this network has computational advantages over a brute force ratio of joint and marginal distributions. We also compare its performance to a kernel conditional density estimator in a larger scale (higher dimensional) problem simulating more realistic conditions.
现实世界中的问题通常可以用条件概率密度函数估计来表述。特别是，模式识别、信号检测和金融预测都属于需要条件密度估计的众多应用领域。此前在这个方向上的进展已经使用神经网络来估计输入输出变量的分布统计量或边际分布或联合分布。我们对联合分布估计的 sigmoidal 神经网络进行了修改，以估计条件分布。因此，使用神经网络估计基于输入的输出的概率密度。我们推导并实现了训练网络的学习法则。我们表明，该网络在联合分布与边际分布的蛮力比值方面具有计算优势。我们还在模拟更现实条件的更大规模（更高维度）问题中，将其性能与核条件密度估计器进行了比较。
