Sensitivities: An Alternative to Conditional Probabilities for Bayesian Belief Networks

We show an alternative way of represent­ ing a Bayesian belief network by sensitivities and probability distributions. This represen­ tation is equivalent to the traditional rep­ resentation by conditional probabilities, but makes dependencies between nodes apparent and intuitively easy to understand. We also propose a QR matrix representation for the sensitivities and/ or conditional probabilities which is more efficient, in both memory re­ quirements and computational speed, than the traditional representation for computer­ based implementations of probabilistic infer­ ence. We use sensitivities to show that for a certain class of binary networks, the com­ putation time for approximate probabilistic inference with any positive upper bound on the error of the result is independent of the size of the network. Finally, as an alternative to traditional algorithms that use conditional probabilities, we describe an exact algorithm for probabilistic inference that uses the QR­ representation for sensitivities and updates probability distributions of nodes in a net­ work according to messages from the neigh­ bors.