An integrated generative and discriminative Bayesian model for binary classification
published: Nov. 8, 2010, recorded: October 2010, views: 3232
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much smaller number of samples. Analysing such data is statistically challenging, as the covariates are highly correlated, which results in unstable parameter estimates and inaccurate prediction. To alleviate this problem, we have developed a statistical model which uses a small number of meta-covariates inferred from the data through a Gaussian mixture model, rather than all the original covariates, to classify samples via a probit regression model. A graphical overview of our model is presented in Figure 1 below. The novelty of our approach is that our meta-covariates are formed considering predictor-outcome correlations as well as inter-predictor correlations. This idea was partly inspired by recent empirical research that has shown that optimum predictive performance often corresponds to an intermediate trade-off between the purely generative and purely discriminative approaches to classification . The main advantage over using a sparse classification model  is that we can extract a much larger subset of covariates with essential predictive power and partition this subset into groups, within which the covariates are similar.
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