"AI systems–like people–must often act despite partial and uncertain information. First, the information received may be unreliable (e.g., a patient may mis-remember when a disease started, or may not have noticed a symptom that is important to a diagnosis). In addition, rules connecting real-world events can never include all the factors that might determine whether their conclusions really apply (e.g., the correctness of basing a diagnosis on a lab test depends whether there were conditions that might have caused a false positive, on the test being done correctly, on the results being associated with the right patient, etc.) Thus in order to draw useful conclusions, AI systems must be able to reason about the probability of events, given their current knowledge." – from David Leake, Reasoning Under Uncertainty
In addition to being a challenging problem due to the super-exponentially large search space, learning a single DAG structure from data may also lead to confident but incorrect predictions (Madigan et al.,
Our first contribution addresses this shortcoming by introducing the CatLog-Derivative trick-a variation of the Log-Derivative trick tailored towards categorical distributions.