|Title:||On the Role of Partial Differentiation in Probabilistic Inference|
|Series:||Linköping Electronic Articles
in Computer and Information Science
|Issue:||Vol. 5 (2000), No. 028|
|Abstract:|| We present in this paper one of the simplest, yet most comprehensive
frameworks for inference in Bayesian networks. According to this framework,
one compiles a Bayesian network into a polynomial -- in which variables
correspond to potential evidence and network parameters -- and then computes
the partial derivatives of this polynomial with respect to each variable.
Once such derivatives are made available, one can compute in constant-time
answers to a large class of probabilistic queries, which are central to
classical inference, parameter estimation, model validation and sensitivity
analysis. We show a number of key results relating to this framework.
First, given a Bayesian network of size n and an elimination order of
width w, we present an elimination algorithm for compiling the polynomial
Next, given some evidence and parameter setting, we show that the compiled
polynomial can be evaluated, and all its first partial derivatives computed
Finally, we show that second partial derivatives can all be computed
The proposed framework provides new insights into the role of partial differentiation in probabilistic inference. Moreover, its combined simplicity, comprehensiveness and computational complexity appear to be unique among existing frameworks for inference in Bayesian networks.
|In ETAI Newsletter and Decision and Reasoning under Uncertainty|
| Original publication
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