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3.4 Inference

To perform inference, run the infer executable, e.g., ALCHDIR/bin/infer -i univ-out.mln -e univ-test.db -r univ.results -q advisedBy;student;professor -c -maxSteps 20000.

-i specifies the input .mln file. In that file all formulas must be preceded by a weight or terminated by a period (but not both). Each formula in the input .mln file is converted to CNF. If a weight precedes the formula, it is divided equally among its CNF clauses. If the formula is terminated by a period (i.e., the formula is hard), each of its CNF clauses is given a default weight that is twice the maximum soft clause weight.

-e specifies the evidence .db file; a comma-separated list can be used to specify more than one .db file. -r specifies the output file which contains the inference results.

-q specifies the query formulas, separated by a semi-colon. You can specify more than one query formula, and restrict the query to particular groundings, e.g.,

-q advisedBy(x,Ida);advisedBy(Ida,Geri). (Depending on the shell you are using, you may have to enclose the query predicates in quotes because of the presence of parentheses.) If free variables are present, then a probability / MAP state is computed for each grounding, e.g., student(x) (or student) produces a probability for each grounding of x.

Alternatively, you can use the -c option followed by the query formulas. In this case, if free variables are present, then counts are computed over all groundings of them, e.g., student(x) (or student) produces a count representing the average number of students in each sampled state.

You can also use the -f option to specify a file containing the query formulas you are interested in. (You may use both -q and -f together.)

An evidence predicate is defined as a predicate of which the .db evidence file contains at least one grounding; all evidence predicates are closed-world by default. All non-evidence predicates are open-world by default. The user may specify that some evidence predicates are open-world by listing them with the -ow option. Also, the user may specify that some non-evidence predicates are closed-world by listing them with the -cw option. This effectively turns them into evidence predicates with all false groundings. If a ground atom is listed as a query atom on the command line or in the query file, or is specified as unknown in the evidence file, this overrides any closed-world defaults or options. If a first-order predicate is listed as a query predicate and the evidence file contains at least one of its groundings, the predicate is open-world. In other words, the openness of query predicates overrides the closedness of evidence ones. If a predicate is simultaneously listed as a query predicate and as closed-world with the -cw option, or appears in both -cw and -ow lists, an error message is returned to the user. If a predicate is closed-world and some of its atoms are query atoms, the predicate is treated as closed-world except for the query atoms. If the user specifies an evidence predicate as closed with the -cw option or a non-evidence one as open with -ow, a warning message is returned, as these are the defaults. Type ALCHDIR/bin/infer without any parameters to see all available options.

Alchemy supports two basic types of inference: probabilistic and MAP/MPE. The current implementation contains four probabilistic inference algorithms: (Lifted) Belief Propagation [13] (option -bp), MC-SAT [8] (option -ms), Gibbs sampling (option -p) and simulated tempering [6] (option -simtp). When probabilistic inference is run, the probabilities that the query atoms are true are written to the output file specified. -maxSteps is used to specify the maximum number of steps in the algorithm.

As mentioned, lifted inference can be run. This has potential advantages in terms of running time and memory usage when compared to the fully grounded network. Currently, this option -lifted can only be combined with Belief Propagation.

To use MAP inference instead, specify either the -m or -a option. The former only returns the true ground atoms, while the latter returns both true and false ones. For MAP inference, the output file also contains the weight assigned to a hard ground clause, fraction of hard ground clauses that are satisfied, the sum of their weights, and the sum of the weights of satisfied soft ground clauses. During MAP inference, each hard clause (derived from a hard formula with a terminating period) is given a weight that is the sum of the soft clause weights plus 10.

The MAP inference engine used in Alchemy attempts to satisfy clauses with positive weights (just as in the original MaxWalkSat algorithm) and keep clauses with negative weights unsatisfied. As an extension to the MaxWalkSat algorithm, when a clause with a negative weight is chosen to fix, one true atom in that clause is chosen at random to be set to false.

If no inference algorithm is specified, then Lifted Belief Propagation -lifted -bp is used.



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next up previous
Next: 3.4.1 Memory-efficient inference Up: 3 Quick Start Previous: 3.3 Structure Learning
Marc Sumner 2010-01-22