Bayes in Wonderland! Predictive Supervised Classification Inference Hits Unpredictability

The marginal Bayesian predictive classifiers (mBpc), as opposed to the simultaneous (sBpc), handle each data separately and, hence, tacitly assume independence of observations. Due saturation in learning generative model parameters, adverse effect this false assumption on accuracy mBpc tends wear out face an increasing amount training data, guaranteeing convergence these two under de Finetti type exchangeability. This result, however, is far from trivial for sequences generated Partition Exchangeability (PE), where even umpteen does not rule possibility unobserved outcome (Wonderland!). We provide a computational scheme that allows generation PE. Based that, with controlled increase we show sBpc and mBpc. underlies use simpler yet computationally more efficient instead simultaneous. also parameter estimation giving rise partition exchangeable sequence well testing paradigm equality across different samples. package supervised classifications, hypothesis Ewens sampling formula deposited CRAN PEkit package.