On the bias of predictive distribution in pattern recognition

To estimate distribution from training samples, maximum likelihood estimation treats the unknown parameter of the distribution as a constant. On the other hand, Bayesian estimation treats the parameter as a random variable. In pattern recognition, Bayesian estimation has been known to improve recognition accuracy. However, it was pointed out that Bayesian estimation is not effective due to the bias of the likelihood when sample sizes of classes are not the same. In this paper, we show that recognition accuracy is improved by modifying the bias of the likelihood when sample sizes are not the same. This indicates that the cause of the ineffectiveness is the bias. We derive the formula of the bias of Geisser's predictive distribution without any approximation, and show a way of modification of the bias of the likelihood. We confirm the effectiveness of the proposed method in experiments. In addition, the derived formula gives the theoretical background of a known empirical knowledge.