Preconditioning an Artificial Neural Network Using Naive Bayes
Logistic Regression (LR) is a workhorse of the statistics community and a state-of-the-art machine learning classifier. It learns a linear model from inputs to outputs trained by optimizing the Conditional Log-Likelihood (CLL) of the data. Recently, it has been shown that preconditioning LR using a Naive Bayes (NB) model speeds up LR learning many-fold. One can, however, train a linear model by optimizing the mean-square-error (MSE) instead of CLL. This leads to an Artificial Neural Network (ANN) with no hidden layer. In this work, we study the effect of NB preconditioning on such an ANN classifier. Optimizing MSE instead of CLL may lead to a lower bias classifier and hence result in better performance on big datasets. We show that this NB preconditioning can speed-up convergence significantly. We also show that optimizing a linear model with MSE leads to a lower bias classifier than optimizing with CLL. We also compare the performance to state-of-the-art classifier Random Forest.
KeywordsLogistic regression Preconditioning Conditional log-likelihood Mean-square-error WANBIA-C Artificial neural networks
This research has been supported by the Australian Research Council under grants DP120100553 and DP140100087, and Asian Office of Aerospace Research and Development, Air Force Office of Scientific Research under contracts FA2386-15-1-4007 and FA2386-15-1-4017.
- 2.Minka, T.P.: A comparison of numerical optimizers for logistic regression (2003)Google Scholar
- 4.Zaidi, N.A., Carman, M.J., Cerquides, J., Webb, G.I.: Naive-bayes inspired effective pre-conditioners for speeding-up logistic regression. In: IEEE International Conference on Data Mining (2014)Google Scholar
- 5.Martinez, A., Chen, S., Webb, G.I., Zaidi, N.A.: Scalable learning of Bayesian network classifiers. J. Mach. Learn. Res. (2015) (in press)Google Scholar
- 6.Zaidi, N.A., Webb, G.I., Carman, M.J., Petitjean, F.: Deep broad learning - Big models for Big data (2015). arxiv:1509.01346
- 7.Kohavi, R., Wolpert, D.: Bias plus variance decomposition for zero-one loss functions. In: ICML, pp. 275–283 (1996)Google Scholar
- 9.Brain, D., Webb, G.I.: The need for low bias algorithms in classification learning from small data sets. In: PKDD, pp. 62–73 (2002)Google Scholar
- 14.Brain, D., Webb, G.: On the effect of data set size on bias and variance in classification learning. In: Proceedings of the Fourth Australian Knowledge Acquisition Workshop, pp. 117–128. University of New South Wales (1999)Google Scholar