Expert domain knowledge is usually qualitative, not quantitative, and thus, eliciting probability numbers from experts is usually very difficult. One of the core goals of the KI-Learn project is to use
qualitative knowledge, and we attempt this with a language whose qualitative statements
- are easy and natural to write by domain experts
- have well-defined semantics for probability distributions which correspond to experts' intuitions
However, things aren't so simple. Suppose our training data contradicts an expert's qualitative statement. The proper posterior depends on how much we believe in our domain knowledge and how much data we have. In fact, the question is: how strong is our expert's prior? This is where we are forced right back into specifying quantitative aspects of our model (i.e., the numbers that parameterize the expert's prior).
So here is my question: is it ever possible to specify purely qualitative domain knowledge? I suppose the answer is: only if you assume the knowledge is true with probability 1 (which of course is simply making the quantitative part implicit). This is nasty, though. Nobody wants to state something is true with probability 1, but nobody wants to specify probabilities, either. Is there any alternative to picking the lesser of these two evils? It seems the answer is no...?