Approximate Learning with Multiple Machines

Abstract

In this paper we define two new inference classes Team Density and Team Uniform Density. The team density class turns out to be the “most powerful” of all the inference classes that have been defined and studied so far. We compare these classes to previously defined classes. We obtain necessary and sufficient conditions for one team density class to be a subset of another team density class. Similar results are obtained for team uniform density class. We also have compare team density and team uniform density classes and obtained necessary and sufficient conditions for one class to be a subset of another. Most importantly we show that team density, the “most powerfull” class, cannot cover the BC class. From this result we obtain several theorems as corollaries that have been proved in earlier papers.