Learning Bayesian Networks with qualitative constraints

Graphical models such as Bayesian Networks (BNs) are being increasingly applied to various computer vision problems. One bottleneck in using BN is that learning the BN model parameters often requires a large amount of reliable and representative training data, which proves to be difficult to acquire for many computer vision tasks. On the other hand, there is often available qualitative prior knowledge about the model. Such knowledge comes either from domain experts based on their experience or from various physical or geometric constraints that govern the objects we try to model. Unlike the quantitative prior, the qualitative prior is often ignored due to the difficulty of incorporating them into the model learning process. In this paper, we introduce a closed-form solution to systematically combine the limited training data with some generic qualitative knowledge for BN parameter learning. To validate our method, we compare it with the Maximum Likelihood (ML) estimation method under sparse data and with the Expectation Maximization (EM) algorithm under incomplete data respectively. To further demonstrate its applications for computer vision, we apply it to learn a BN model for facial Action Unit (AU) recognition from real image data. The experimental results show that with simple and generic qualitative constraints and using only a small amount of training data, our method can robustly and accurately estimate the BN model parameters.