  Prediction markets are used in real life to predict outcomes of interest such
as presidential elections. This paper presents a mathematical theory of
artificial prediction markets for supervised learning of conditional
probability estimators. The artificial prediction market is a novel method for
fusing the prediction information of features or trained classifiers, where the
fusion result is the contract price on the possible outcomes. The market can be
trained online by updating the participants' budgets using training examples.
Inspired by the real prediction markets, the equations that govern the market
are derived from simple and reasonable assumptions. Efficient numerical
algorithms are presented for solving these equations. The obtained artificial
prediction market is shown to be a maximum likelihood estimator. It generalizes
linear aggregation, existent in boosting and random forest, as well as logistic
regression and some kernel methods. Furthermore, the market mechanism allows
the aggregation of specialized classifiers that participate only on specific
instances. Experimental comparisons show that the artificial prediction markets
often outperform random forest and implicit online learning on synthetic data
and real UCI datasets. Moreover, an extensive evaluation for pelvic and
abdominal lymph node detection in CT data shows that the prediction market
improves adaboost's detection rate from 79.6% to 81.2% at 3 false
positives/volume.
