Contextual Variable Elimination |

This section introduces an abstract nondeterministic version of CVE. Section * presents a more concrete version where we explain how to resolve much of the nondeterminism.

The input to CVE is:

- a multiset of confactors that consists of the union of the confactors that represent the conditional probability distribution of each variable given its predecessors
- a set of query variables
- an observation that is a conjunction of assignments of values to some of the variables

Initially and after the elimination of each variable, we maintain a multiset of confactors with the following **program invariant**:

The probability of a context *c* on the non-eliminated variables can be
obtained by multiplying the values of context *c* associated with confactors that
are applicable in context *c*. For each complete context on the
non-eliminated variables and for each variable there is at least one
confactor containing that variable that is applicable in that
context^{7}.

Like VE, the abstract algorithm is made up of the primitive operations of summing out a variable and multiplying confactors, and also includes a primitive operation of confactor splitting that enables the other two operations. All of these operations locally preserve this program invariant. They are described in the next subsections.

- Multiplying Contextual Factors
- Summing Out A Variable That Appears In The Table
- Summing Out A Variable In The Body Of Confactors
- Confactor Splitting
- Examples of Eliminating Variables
- When to Split
- Evidence
- Extracting the Answer
- The Abstract Contextual Variable Elimination Algorithm
- Ones
- Multi-Valued Variables
- Why CVE Does More Than Representing Factors As Trees
- CVE Compared To VE

David Poole and Nevin Lianwen Zhang,Exploiting Contextual Independence In Probabilistic Inference, Journal of Artificial Intelligence Research, 18, 2003, 263-313.

Contextual Variable Elimination |