Learning stochastic finite automata from experts

We present in this paper a new learning problem called learning distributions from experts. In the case we study the experts are stochastic deterministic finite automata (sdfa). We deal with the situation arising when wanting to learn sdfa from unrepeated examples. This is intended to model the situation where the data is not generated automatically, but in an order dependent of its probability, as would be the case with the data presented by a human expert. It is then impossible to use frequency measures directly in order to construct the underlying automaton or to adjust its probabilities. In this paper we prove that although a polynomial identification with probability one is not always possible, a wide class of automata can successfully, and for this criterion, be identified. As the framework is new the problem leads to a variety of open problems.