Leaning Causal Models with Conditional Causal Probabilities from Data
Department of Management and Information Systems Science, Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, Niigata, 940-2188 Japan
We propose a way to lean probabilistic causal models using conditional causal probabilities (CCPs) to represent uncertainty of causalities. The CCP is a probability devised by Peng and Reggia representing the uncertainty that a cause actually causes an effect given the cause. The main advantage of using CCPs is that they represent exact probabilities of causalities that people recognize mentally, and that the number of probabilities used in the causal model is far smaller than that of conditional probabilities by all combinations of possible causes. Thus, Peng and Reggia assumed that CCPs are given by human experts as subjective ones, and did not discuss how to calculate them from data when a dataset was available. We address this problem, starting from a discussion about properties of data frequently given in practical problems, and shows that prior probabilities that should be learned may differ from those derived by counting data. We then discuss and propose how to learn prior probabilities and CCPs from data, and evaluate the proposed method through numerical experiments and analyze results to show that the precision of leaned models is satisfactory.