/usr/share/Yap/clpbn/vel.yap is in yap 5.1.3-6.
This file is owned by root:root, with mode 0o644.
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Variable Elimination in Prolog
How to do it
Three steps:
build the graph:
- for all variables, find out
all tables they connect to;
multiply their size
order by size
*********************************/
:- module(vel, [vel/3,
check_if_vel_done/1]).
:- attribute size/1, all_diffs/1.
:- use_module(library(ordsets), [ord_union/3]).
:- use_module(library('clpbn/xbif'), [clpbn2xbif/3]).
:- use_module(library('clpbn/graphviz'), [clpbn2gviz/4]).
:- use_module(library('clpbn/dists'),
[
get_dist_domain_size/2,
get_dist_matrix/5]).
:- use_module(library('clpbn/utils'), [
clpbn_not_var_member/2,
check_for_hidden_vars/3]).
:- use_module(library('clpbn/display'), [
clpbn_bind_vals/3]).
:- use_module(library('clpbn/matrix_cpt_utils'),
[project_from_CPT/3,
reorder_CPT/5,
multiply_CPTs/4,
normalise_CPT/2,
list_from_CPT/2]).
:- use_module(library(lists),
[
append/3
]).
check_if_vel_done(Var) :-
get_atts(Var, [size(_)]), !.
%
% implementation of the well known variable elimination algorithm
%
vel([],_,_) :- !.
vel(LVs,Vs0,AllDiffs) :-
check_for_hidden_vars(Vs0, Vs0, Vs1),
sort(Vs1,Vs),
% LVi will have a list of CLPBN variables
% Tables0 will have the full data on each variable
find_all_clpbn_vars(Vs, LV0, LVi, Tables0),
% construct the graph
find_all_table_deps(Tables0, LV0),
(clpbn:output(xbif(XBifStream)) -> clpbn2xbif(XBifStream,vel,Vs) ; true),
(clpbn:output(gviz(XBifStream)) -> clpbn2gviz(XBifStream,vel,Vs,LVs) ; true),
% variable elimination proper
process(LVi, LVs, tab(Dist,_,_)),
% move from potentials back to probabilities
normalise_CPT(Dist,Ps),
% from array to list
list_from_CPT(Ps, LPs),
% bind Probs back to variables so that they can be output.
clpbn_bind_vals(LVs,LPs,AllDiffs).
%
% just get a list of variables plus associated tables
%
find_all_clpbn_vars([], [], [], []) :- !.
find_all_clpbn_vars([V|Vs], [Var|LV], ProcessedVars, [table(I,Table,Parents,Sizes)|Tables]) :-
var_with_deps(V, Table, Parents, Sizes, Ev, Vals), !,
% variables with evidence should not be processed.
(var(Ev) ->
Var = var(V,I,Sz,Vals,Parents,Ev,_,_),
vel_get_dist_size(V,Sz),
ProcessedVars = [Var|ProcessedVars0]
;
ProcessedVars = ProcessedVars0
),
find_all_clpbn_vars(Vs, LV, ProcessedVars0, Tables).
var_with_deps(V, Table, Deps, Sizes, Ev, Vals) :-
clpbn:get_atts(V, [dist(Id,Parents)]),
get_dist_matrix(Id,Parents,_,Vals,TAB0),
( clpbn:get_atts(V, [evidence(Ev)]) -> true ; true),
% set CPT in canonical form
reorder_CPT([V|Parents],TAB0,Deps0,TAB1,Sizes1),
% remove evidence.
simplify_evidence(Deps0, TAB1, Deps0, Sizes1, Table, Deps, Sizes).
find_all_table_deps(Tables0, LV) :-
find_dep_graph(Tables0, DepGraph0),
sort(DepGraph0, DepGraph),
add_table_deps_to_variables(LV, DepGraph).
find_dep_graph([], []).
find_dep_graph([table(I,Tab,Deps,Sizes)|Tables], DepGraph) :-
add_table_deps(Deps, I, Deps, Tab, Sizes, DepGraph0, DepGraph),
find_dep_graph(Tables, DepGraph0).
add_table_deps([], _, _, _, _, DepGraph, DepGraph).
add_table_deps([V|Deps], I, Deps0, Table, Sizes, DepGraph0, [V-tab(Table,Deps0,Sizes)|DepGraph]) :-
add_table_deps(Deps, I, Deps0, Table, Sizes, DepGraph0, DepGraph).
add_table_deps_to_variables([], []).
add_table_deps_to_variables([var(V,_,_,_,_,_,Deps,K)|LV], DepGraph) :-
steal_deps_for_variable(DepGraph, V, NDepGraph, Deps),
compute_size(Deps,[],K),
% ( clpbn:get_atts(V,[key(Key)]) -> format('~w:~w~n',[Key,K]) ; true),
add_table_deps_to_variables(LV, NDepGraph).
steal_deps_for_variable([V-Info|DepGraph], V0, NDepGraph, [Info|Deps]) :-
V == V0, !,
steal_deps_for_variable(DepGraph, V0, NDepGraph, Deps).
steal_deps_for_variable(DepGraph, _, DepGraph, []).
compute_size([],Vs,K) :-
% use sizes now
% length(Vs,K).
multiply_sizes(Vs,1,K).
compute_size([tab(_,Vs,_)|Tabs],Vs0,K) :-
ord_union(Vs,Vs0,VsI),
compute_size(Tabs,VsI,K).
multiply_sizes([],K,K).
multiply_sizes([V|Vs],K0,K) :-
vel_get_dist_size(V, Sz),
KI is K0*Sz,
multiply_sizes(Vs,KI,K).
process(LV0, InputVs, Out) :-
find_best(LV0, V0, -1, V, WorkTables, LVI, InputVs),
V \== V0, !,
% format('1 ~w: ~w~n',[V,WorkTables]),
multiply_tables(WorkTables, tab(Tab0,Deps0,_)),
reorder_CPT(Deps0,Tab0,Deps,Tab,Sizes),
Table = tab(Tab,Deps,Sizes),
% format('2 ~w: ~w~n',[V,Table]),
project_from_CPT(V,Table,NewTable),
% format('3 ~w: ~w~n',[V,NewTable]),
include(LVI,NewTable,V,LV2),
process(LV2, InputVs, Out).
process(LV0, _, Out) :-
fetch_tables(LV0, WorkTables),
multiply_tables(WorkTables, Out).
find_best([], V, _TF, V, _, [], _).
%:-
% clpbn:get_atts(V,[key(K)]), write(chosen:K:TF), nl.
% root_with_single_child
%find_best([var(V,I,_,_,[],Ev,[Dep],K)|LV], _, _, V, [Dep], LVF, Inputs) :- !.
find_best([var(V,I,Sz,Vals,Parents,Ev,Deps,K)|LV], _, Threshold, VF, NWorktables, LVF, Inputs) :-
( K < Threshold ; Threshold < 0),
clpbn_not_var_member(Inputs, V), !,
find_best(LV, V, K, VF, WorkTables,LV0, Inputs),
(V == VF ->
LVF = LV0, Deps = NWorktables
;
LVF = [var(V,I,Sz,Vals,Parents,Ev,Deps,K)|LV0], WorkTables = NWorktables
).
find_best([V|LV], V0, Threshold, VF, WorkTables, [V|LVF], Inputs) :-
find_best(LV, V0, Threshold, VF, WorkTables, LVF, Inputs).
multiply_tables([Table], Table) :- !.
multiply_tables([TAB1, TAB2| Tables], Out) :-
multiply_CPTs(TAB1, TAB2, TAB, _),
multiply_tables([TAB| Tables], Out).
simplify_evidence([], Table, Deps, Sizes, Table, Deps, Sizes).
simplify_evidence([V|VDeps], Table0, Deps0, Sizes0, Table, Deps, Sizes) :-
clpbn:get_atts(V, [evidence(_)]), !,
project_from_CPT(V,tab(Table0,Deps0,Sizes0),tab(NewTable,Deps1,Sizes1)),
simplify_evidence(VDeps, NewTable, Deps1, Sizes1, Table, Deps, Sizes).
simplify_evidence([_|VDeps], Table0, Deps0, Sizes0, Table, Deps, Sizes) :-
simplify_evidence(VDeps, Table0, Deps0, Sizes0, Table, Deps, Sizes).
fetch_tables([], []).
fetch_tables([var(_,_,_,_,_,_,Deps,_)|LV0], Tables) :-
append(Deps,Tables0,Tables),
fetch_tables(LV0, Tables0).
%
include([],_,_,[]).
include([var(V,P,VSz,D,Parents,Ev,Tabs,Est)|LV],tab(T,Vs,Sz),V1,[var(V,P,VSz,D,Parents,Ev,Tabs,Est)|NLV]) :-
clpbn_not_var_member(Vs,V), !,
include(LV,tab(T,Vs,Sz),V1,NLV).
include([var(V,P,VSz,D,Parents,Ev,Tabs,_)|LV],Table,NV,[var(V,P,VSz,D,Parents,Ev,NTabs,NEst)|NLV]) :-
update_tables(Tabs,NTabs,Table,NV),
compute_size(NTabs, [], NEst),
include(LV,Table,NV,NLV).
update_tables([],[Table],Table,_).
update_tables([tab(Tab0,Vs,Sz)|Tabs],[tab(Tab0,Vs,Sz)|NTabs],Table,V) :-
clpbn_not_var_member(Vs,V), !,
update_tables(Tabs,NTabs,Table,V).
update_tables([_|Tabs],NTabs,Table,V) :-
update_tables(Tabs,NTabs,Table,V).
vel_get_dist_size(V,Sz) :-
get_atts(V, [size(Sz)]), !.
vel_get_dist_size(V,Sz) :-
clpbn:get_atts(V,dist(Id,_)), !,
get_dist_domain_size(Id,Sz),
put_atts(V, [size(Sz)]).
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