ProbLog1

Probabilistic Inference

Go to the directory ~/yap-6/packages/ProbLog/problog_examples/ and start YAP. Then type ?- [graph]. This query loads the example file below which contains a small probabilistic graph encoded as a ProbLog program.

:- use_module(library(problog)).

% probabilistic facts
0.9::dir_edge(1,2).
0.8::dir_edge(2,3).
0.6::dir_edge(3,4).
0.7::dir_edge(1,6).
0.5::dir_edge(2,6).
0.4::dir_edge(6,5).
0.7::dir_edge(5,3).
0.2::dir_edge(5,4).

% Now comes the background knowledge
% definition of acyclic path using list of visited nodes
path(X,Y) :- path(X,Y,[X],_).

path(X,X,A,A).
path(X,Y,A,R) :- 
	X\==Y, 
	edge(X,Z), 
	absent(Z,A), 
	path(Z,Y,[Z|A],R).

% using directed edges in both directions
edge(X,Y) :- dir_edge(Y,X).
edge(X,Y) :- dir_edge(X,Y).

% checking whether node hasn't been visited before
absent(_,[]).
absent(X,[Y|Z]):-X \= Y, absent(X,Z).

ProbLog provides several predicates to evaluate the probability of queries. In the following we always use the query path(1,4) which ask whether there is a cycle-free undirected path between node 1 and 4.

explanation probability (and facts involved)

?- problog_max(path(1,4),Prob,FactsUsed).
  FactsUsed = [dir_edge(1,2),dir_edge(2,3),dir_edge(3,4)],
  Prob = 0.432 ?
  yes

success probability

?- problog_exact(path(1,4),Prob,Status).
  8 proofs
  Prob = 0.53864,
  Status = ok ?
  yes

lower bound using 4 best proofs

?- problog_kbest(path(1,4),4,Prob,Status).
  4 proofs
  Prob = 0.517344,
  Status = ok ?
  yes

approximation using monte carlo, to reach 95%-confidence interval width 0.01

?- problog_montecarlo(path(1,4),0.01,Prob).
  Prob = 0.537525 ?
  yes

upper and lower bound using iterative deepening, final interval width 0.01

?- problog_delta(path(1,4),0.01,Bound_low,Bound_up,Status).
  Bound_low = 0.5354096,
  Bound_up = 0.53864,
  Status = ok ?
  yes

upper and lower bound obtained cutting the sld tree at probability 0.1 for each branch

?- problog_threshold(path(1,4),0.1,Bound_low,Bound_up,Status).
  4 proofs
  Bound_low = 0.517344,
  Bound_up = 0.563728,
  Status = ok ?
  yes

lower bound obtained cutting the sld tree at probability 0.2 for each branch

?- problog_low(path(1,4),0.2,Bound_low,Status).
  1 proofs
  Bound_low = 0.432,
  Status = ok ?
  yes

Settings for Inference (problog.yap)

Both the learning and the inference module have various parameters to play around with.
For the inference module, use :-problog_flags. to get an overview of all options, :-set_problog_flag(Name,Value). to change an option and :-problog_flag(Name,Value). to obtain the current value for a flag.

Continue with the tutorial on parameter learning from queries.