Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: An important subclass of hybrid Bayesian networks are those that represent Conditional Linear Gaussian (CLG) distributionsa distribution with a multivari­ ate Gaussian component for each instantiation of the discrete variables. In this paper we explore the prob­ lem of inference in CLGs, and provide complexity re­ sults for an important class of CLGs, which includes Switching Kalman Filters. In particular, we prove that even if the CLG is restricted to an extremely simple structure of a polytree, the inference task is NP-hard. Furthermore, we show that, unless P=NP, even ap­ proximate inference on these simple networks is in­ tractable. Given the often prohibitive computational cost of even approximate inference, we must take advantage of spe­ cial domain properties which may enable efficient in­ ference. We concentrate on the fault diagnosis domain, and explore several approximate inference algorithms. These algorithms try to find a small subset of Gaus­ sians which are a good approximation to the full mix­ ture distribution. We consider two Monte Carlo ap­ proaches and a novel approach that enumerates mix­ ture components in order of prior probability. We com­ pare these methods on a variety of problems and show that our novel algorithm is very promising for large, hybrid diagnosis problems.

Inference in Hybrid Networks: Theoretical Limits and Practical Algorithms