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yap-6.3/CLPBN/clpbn/gibbs.yap

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%
% each variable is represented by a node in a binary tree.
% each node contains:
% key,
% current_value
% Markov Blanket
%
:- module(gibbs, [gibbs/3,
check_if_gibbs_done/1]).
:- use_module(library(rbtrees),
[new/1,
insert/4,
lookup/3]).
:- use_module(library(lists),
[member/2,
append/3,
delete/3]).
:- use_module(library(ordsets),
[ord_subtract/3]).
:- use_module(library('clpbn/discrete_utils'), [
project_from_CPT/3,
reorder_CPT/5]).
:- use_module(library('clpbn/utils'), [
check_for_hidden_vars/3]).
:- dynamic gibbs_params/3.
:- dynamic implicit/1.
gibbs([],_,_) :- !.
gibbs(LVs,Vs0,_) :-
clean_up,
check_for_hidden_vars(Vs0, Vs0, Vs1),
sort(Vs1,Vs),
(clpbn:output(xbif(XBifStream)) -> clpbn2xbif(XBifStream,vel,Vs) ; true),
(clpbn:output(gviz(XBifStream)) -> clpbn2gviz(XBifStream,vel,Vs,LVs) ; true),
initialise(Vs, Graph, LVs, OutputVars, VarOrder),
% write(Graph),nl,
process(VarOrder, Graph, OutputVars, Estimates),
write(Estimates),nl,
clean_up.
initialise(LVs, Graph, GVs, OutputVars, VarOrder) :-
init_keys(Keys0),
gen_keys(LVs, 0, VLen, Keys0, Keys),
functor(Graph,graph,VLen),
graph_representation(LVs, Graph, 0, Keys, TGraph),
compile_graph(Graph),
topsort(TGraph, VarOrder),
show_sorted(VarOrder, Graph),
add_output_vars(GVs, Keys, OutputVars).
init_keys(Keys0) :-
new(Keys0).
gen_keys([], I, I, Keys, Keys).
gen_keys([V|Vs], I0, If, Keys0, Keys) :-
clpbn:get_atts(V,[evidence(_)]), !,
gen_keys(Vs, I0, If, Keys0, Keys).
gen_keys([V|Vs], I0, If, Keys0, Keys) :-
I is I0+1,
insert(Keys0,V,I,KeysI),
gen_keys(Vs, I, If, KeysI, Keys).
graph_representation([],_,_,_,[]).
graph_representation([V|Vs], Graph, I0, Keys, TGraph) :-
clpbn:get_atts(V,[evidence(_)]), !,
clpbn:get_atts(V, [dist(Vals,Table,Parents)]),
get_sizes(Parents, Szs),
length(Vals,Sz),
project_evidence_out([V|Parents],[V|Parents],Table,[Sz|Szs],Variables,NewTable),
% all variables are parents
propagate2parents(Variables, NewTable, Variables, Graph, Keys),
graph_representation(Vs, Graph, I0, Keys, TGraph).
graph_representation([V|Vs], Graph, I0, Keys, [I-IParents|TGraph]) :-
I is I0+1,
clpbn:get_atts(V, [dist(Vals,Table,Parents)]),
get_sizes(Parents, Szs),
length(Vals,Sz),
project_evidence_out([V|Parents],[V|Parents],Table,[Sz|Szs],Variables,NewTable),
Variables = [V|NewParents],
sort_according_to_indices(NewParents,Keys,SortedNVs,SortedIndices),
reorder_CPT(Variables,NewTable,[V|SortedNVs],NewTable2,_),
add2graph(V, Vals, NewTable2, SortedIndices, Graph, Keys),
propagate2parents(NewParents, NewTable, Variables, Graph,Keys),
parent_indices(NewParents, Keys, IVariables0),
sort(IVariables0, IParents),
arg(I, Graph, var(_,_,_,_,_,_,_,NewTable2,SortedIndices)),
graph_representation(Vs, Graph, I, Keys, TGraph).
get_sizes([], []).
get_sizes([V|Parents], [Sz|Szs]) :-
clpbn:get_atts(V, [dist(Vals,_,_)]),
length(Vals,Sz),
get_sizes(Parents, Szs).
parent_indices([], _, []).
parent_indices([V|Parents], Keys, [I|IParents]) :-
lookup(V, I, Keys),
parent_indices(Parents, Keys, IParents).
%
% first, remove nodes that have evidence from tables.
%
project_evidence_out([],Deps,Table,_,Deps,Table).
project_evidence_out([V|Parents],Deps,Table,Szs,NewDeps,NewTable) :-
clpbn:get_atts(V,[evidence(_)]), !,
NTab =.. [t|Table],
project_from_CPT(V,tab(NTab,Deps,Szs),tab(ITable,IDeps,ISzs)),
ITable =.. [_|LITable],
project_evidence_out(Parents,IDeps,LITable,ISzs,NewDeps,NewTable).
project_evidence_out([_Par|Parents],Deps,Table,Szs,NewDeps,NewTable) :-
project_evidence_out(Parents,Deps,Table,Szs,NewDeps,NewTable).
propagate2parents([], _, _, _, _).
propagate2parents([V|NewParents], Table, Variables, Graph, Keys) :-
delete(Variables,V,NVs),
sort_according_to_indices(NVs,Keys,SortedNVs,SortedIndices),
reorder_CPT(Variables,Table,[V|SortedNVs],NewTable,_),
add2graph(V, _, NewTable, SortedIndices, Graph, Keys),
propagate2parents(NewParents,Table, Variables, Graph, Keys).
add2graph(V, Vals, Table, IParents, Graph, Keys) :-
lookup(V, Index, Keys),
(var(Vals) -> true ; length(Vals,Sz)),
arg(Index, Graph, var(V,Index,_,Vals,Sz,VarSlot,_,_,_)),
member(tabular(Table,Index,IParents), VarSlot), !.
sort_according_to_indices(NVs,Keys,SortedNVs,SortedIndices) :-
vars2indices(NVs,Keys,ToSort),
keysort(ToSort, Sorted),
split_parents(Sorted, SortedNVs,SortedIndices).
split_parents([], [], []).
split_parents([I-V|Sorted], [V|SortedNVs],[I|SortedIndices]) :-
split_parents(Sorted, SortedNVs, SortedIndices).
vars2indices([],_,[]).
vars2indices([V|Parents],Keys,[I-V|IParents]) :-
lookup(V, I, Keys),
vars2indices(Parents,Keys,IParents).
compact_table(NewTable, RepTable) :-
NewTable = [_|_], !,
RepTable =.. [t|NewTable].
%
% This is the really cool bit.
%
compile_graph(Graph) :-
Graph =.. [_|VarsInfo],
compile_vars(VarsInfo,Graph).
compile_vars([],_).
compile_vars([var(_,I,_,Vals,Sz,VarSlot,Parents,_,_)|VarsInfo],Graph)
:-
compile_var(I,Vals,Sz,VarSlot,Parents,Graph),
compile_vars(VarsInfo,Graph).
compile_var(I,Vals,Sz,VarSlot,Parents,Graph) :-
fetch_all_parents(VarSlot,Graph,[],Parents,[],Sizes),
mult_list(Sizes,1,TotSize),
compile_var(TotSize,I,Vals,Sz,VarSlot,Parents,Sizes,Graph).
fetch_all_parents([],_,Parents,Parents,Sizes,Sizes).
fetch_all_parents([tabular(_,_,Ps)|CPTs],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
merge_these_parents(Ps,Graph,Parents0,ParentsI,Sizes0,SizesI),
fetch_all_parents(CPTs,Graph,ParentsI,ParentsF,SizesI,SizesF).
merge_these_parents([],_,Parents,Parents,Sizes,Sizes).
merge_these_parents([I|Ps],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
member(I,Parents0), !,
merge_these_parents(Ps,Graph,Parents0,ParentsF,Sizes0,SizesF).
merge_these_parents([I|Ps],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
arg(I,Graph,var(_,I,_,Vals,_,_,_,_,_)),
length(Vals, Sz),
add_parent(Parents0,I,ParentsI,Sizes0,Sz,SizesI),
merge_these_parents(Ps,Graph,ParentsI,ParentsF,SizesI,SizesF).
add_parent([],I,[I],[],Sz,[Sz]).
add_parent([P|Parents0],I,[I,P|Parents0],Sizes0,Sz,[Sz|Sizes0]) :-
P > I, !.
add_parent([P|Parents0],I,[P|ParentsI],[S|Sizes0],Sz,[S|SizesI]) :-
add_parent(Parents0,I,ParentsI,Sizes0,Sz,SizesI).
mult_list([],Mult,Mult).
mult_list([Sz|Sizes],Mult0,Mult) :-
MultI is Sz*Mult0,
mult_list(Sizes,MultI,Mult).
% compile node as set of facts, faster execution
compile_var(TotSize,I,_Vals,Sz,CPTs,Parents,_Sizes,Graph) :-
TotSize < 1024, TotSize > 0, !,
multiply_all(I,Parents,CPTs,Sz,Graph).
compile_var(_,I,_,_,_,_,_,_) :-
assert(implicit(I)).
multiply_all(I,Parents,CPTs,Sz,Graph) :-
markov_blanket_instance(Parents,Graph,Values),
multiply_all(CPTs,Sz,Graph,Probs),
store_mblanket(I,Values,Probs),
fail.
multiply_all(_,_,_,_,_).
% note: what matters is how this predicate instantiates the temp
% slot in the graph!
markov_blanket_instance([],_,[]).
markov_blanket_instance([I|Parents],Graph,[Pos|Values]) :-
arg(I,Graph,var(_,I,Pos,Vals,_,_,_,_,_)),
fetch_val(Vals,0,Pos),
markov_blanket_instance(Parents,Graph,Values).
% backtrack through every value in domain
%
fetch_val([_|_],Pos,Pos).
fetch_val([_|Vals],I0,Pos) :-
I is I0+1,
fetch_val(Vals,I,Pos).
multiply_all(CPTs,Size,Graph,Probs) :-
init_factors(Size,Factors0),
mult_factors(CPTs,Size,Graph,Factors0,Factors),
normalise_factors(Factors,0,_,Probs,_).
init_factors(0,[]) :- !.
init_factors(I0,[1|Factors]) :-
I is I0-1,
init_factors(I,Factors).
mult_factors([],_,_,Factors,Factors).
mult_factors([tabular(Table,_,Parents)|CPTs],Size,Graph,Factors0,Factors) :-
functor(Table,_,CPTSize),
Off is CPTSize//Size,
factor(Parents,Table,Graph,0,Off,Indx0),
Indx is Indx0+1,
mult_with_probs(Factors0,Indx,Off,Table,FactorsI),
mult_factors(CPTs,Size,Graph,FactorsI,Factors).
factor([],_,_,Arg,_,Arg).
factor([I|Parents],Table,Graph,Pos0,Weight0,Pos) :-
arg(I,Graph,var(_,I,CurPos,_,Sz,_,_,_,_)),
NWeight is Weight0 // Sz,
PosI is Pos0+(NWeight*CurPos),
factor(Parents,Table,Graph,PosI,NWeight,Pos).
mult_with_probs([],_,_,_,[]).
mult_with_probs([F0|Factors0],Indx,Off,Table,[F|Factors]) :-
arg(Indx,Table,P1),
F is F0*P1,
Indx1 is Indx+Off,
mult_with_probs(Factors0,Indx1,Off,Table,Factors).
normalise_factors([],Sum,Sum,[],1.0) :- Sum > 0.0.
normalise_factors([F|Factors],S0,S,[P0|Probs],PF) :-
Si is S0+F,
normalise_factors(Factors,Si,S,Probs,P0),
PF is P0-F/S.
store_mblanket(I,Values,Probs) :-
append(Values,Probs,Args),
Rule =.. [mblanket,I|Args],
assert(Rule).
add_output_vars([], _, []).
add_output_vars([V|LVs], Keys, [I|OutputVars]) :-
lookup(V, I, Keys),
add_output_vars(LVs, Keys, OutputVars).
process(VarOrder, Graph, OutputVars, Estimates) :-
gibbs_params(NChains,BurnIn,NSamples),
functor(Graph,_,Len),
init_chains(NChains,VarOrder,Len,Graph,Chains0),
init_estimates(NChains,OutputVars,Graph,Est0),
process_chains(BurnIn,VarOrder,BurnedIn,Chains0,Graph,Len,Est0,_),
process_chains(NSamples,VarOrder,_,BurnedIn,Graph,Len,Est0,Estimates).
%
% I use an uniform distribution to generate the initial sample.
%
init_chains(0,_,_,_,[]) :- !.
init_chains(I,VarOrder,Len,Graph,[Chain|Chains]) :-
init_chain(VarOrder,Len,Graph,Chain),
I1 is I-1,
init_chains(I1,VarOrder,Len,Graph,Chains).
init_chain(VarOrder,Len,Graph,Chain) :-
functor(Chain,sample,Len),
gen_sample(VarOrder,Graph,Chain).
gen_sample([],_,_) :- !.
gen_sample([I|Vs],Graph,Chain) :-
arg(I,Graph,var(_,I,_,_,Sz,_,_,Table,IPars)),
functor(Table,_,CPTSize),
Off is CPTSize//Sz,
iparents_pos_sz(IPars, Chain, IPos, Graph, ISz),
R is random,
project(IPos, ISz, Table,0,Off,Indx0),
Indx is Indx0+1,
fetch_from_dist(Table,R,Indx,Off,0,Pos),
arg(I,Chain,Pos),
gen_sample(Vs,Graph,Chain).
project([],[],_,Arg,_,Arg).
project([CurPos|Parents],[Sz|Sizes],Table,Pos0,Weight0,Pos) :-
NWeight is Weight0 // Sz,
PosI is Pos0+(NWeight*CurPos),
project(Parents,Sizes,Table,PosI,NWeight,Pos).
fetch_from_dist(Table,R,Indx,Off,IPos,Pos) :-
arg(Indx,Table,P),
( P >= R ->
Pos = IPos
;
NR is R-P,
NIndx is Indx+Off,
NPos is IPos+1,
fetch_from_dist(Table,NR,NIndx,Off,NPos,Pos)
).
iparents_pos_sz([], _, [], _, []).
iparents_pos_sz([I|IPars], Chain, [P|IPos], Graph, [Sz|Sizes]) :-
arg(I,Chain,P),
arg(I,Graph, var(_,I,_,_,Sz,_,_,_,_)),
iparents_pos_sz(IPars, Chain, IPos, Graph, Sizes).
init_estimates(0,_,_,[]) :- !.
init_estimates(NChains,OutputVars,Graph,[Est|Est0]) :-
NChainsI is NChains-1,
init_estimate(OutputVars,Graph,Est),
init_estimates(NChainsI,OutputVars,Graph,Est0).
init_estimate([],_,[]).
init_estimate([V|OutputVars],Graph,[[I|E0L]|Est]) :-
arg(V,Graph,var(_,I,_,_,Sz,_,_,_,_)),
gen_e0(Sz,E0L),
init_estimate(OutputVars,Graph,Est).
gen_e0(0,[]) :- !.
gen_e0(Sz,[0|E0L]) :-
Sz1 is Sz-1,
gen_e0(Sz1,E0L).
process_chains(0,_,F,F,_,_,Est,Est) :- !.
process_chains(ToDo,VarOrder,End,Start,Graph,Len,Est0,Estf) :-
process_chains(Start,VarOrder,Int,Graph,Len,Est0,Esti),
%cvt2problist(Esti, Probs), format('done ~d: ~w~n',[ToDo,Probs]),
ToDo1 is ToDo-1,
process_chains(ToDo1,VarOrder,End,Int,Graph,Len,Esti,Estf).
process_chains([], _, [], _, _,[],[]).
process_chains([Sample0|Samples0], VarOrder, [Sample|Samples], Graph, SampLen,[E0|E0s],[Ef|Efs]) :-
functor(Sample,sample,SampLen),
do_sample(VarOrder,Sample,Sample0,Graph),
% format('~w ',[Sample]),
update_estimate(E0,Sample,Ef),
process_chains(Samples0, VarOrder, Samples, Graph, SampLen,E0s,Efs).
do_sample([],_,_,_).
do_sample([I|VarOrder],Sample,Sample0,Graph) :-
do_var(I,Sample,Sample0,Graph),
do_sample(VarOrder,Sample,Sample0,Graph).
do_var(I,Sample,Sample0,Graph) :-
arg(I,Graph,var(_,I,_,_,Sz,CPTs,Parents,_,_)),
( implicit(I) ->
fetch_parents(Parents,I,Sample,Sample0,Bindings,[]),
multiply_all_in_context(Parents,Bindings,CPTs,Sz,Graph,Vals)
;
length(Vals,Sz),
fetch_parents(Parents,I,Sample,Sample0,Args,Vals),
Goal =.. [mblanket,I|Args],
call(Goal)
),
X is random,
pick_new_value(Vals,X,0,Val),
arg(I,Sample,Val).
multiply_all_in_context(Parents,Args,CPTs,Sz,Graph,Vals) :-
set_pos(Parents,Args,Graph),
multiply_all(CPTs,Sz,Graph,Vals),
assert(mall(Vals)),
fail.
multiply_all_in_context(_,_,_,_,_,Vals) :-
retract(mall(Vals)).
set_pos([],[],_).
set_pos([I|Is],[Pos|Args],Graph) :-
arg(I,Graph,var(_,I,Pos,_,_,_,_,_,_)),
set_pos(Is,Args,Graph).
fetch_parents([],_,_,_,Args,Args).
fetch_parents([P|Parents],I,Sample,Sample0,[VP|Args],Vals) :-
arg(P,Sample,VP),
nonvar(VP), !,
fetch_parents(Parents,I,Sample,Sample0,Args,Vals).
fetch_parents([P|Parents],I,Sample,Sample0,[VP|Args],Vals) :-
arg(P,Sample0,VP),
fetch_parents(Parents,I,Sample,Sample0,Args,Vals).
pick_new_value([V|_],X,Val,Val) :-
X < V, !.
pick_new_value([_|Vals],X,I0,Val) :-
I is I0+1,
pick_new_value(Vals,X,I,Val).
update_estimate([],_,[]).
update_estimate([[I|E]|E0],Sample,[[I|NE]|Ef]) :-
arg(I,Sample,V),
update_estimate_for_var(V,E,NE),
update_estimate(E0,Sample,Ef).
update_estimate_for_var(0,[X|T],[X1|T]) :- !, X1 is X+1.
update_estimate_for_var(V,[E|Es],[E|NEs]) :-
V1 is V-1,
update_estimate_for_var(V1,Es,NEs).
check_if_gibbs_done(Var) :-
get_atts(Var, [dist(_)]), !.
clean_up :-
current_predicate(mblanket,P),
retractall(P),
fail.
clean_up :-
retractall(implicit(_)),
fail.
clean_up.
gibbs_params(5,10000,100000).
/* simple implementation of a topological sorting algorithm */
/* graph is as Node-[Parents] */
topsort([], []) :- !.
topsort(Graph0,Sorted) :-
add_parentless(Graph0, Sorted, IncludedI, Graph1, SortedRest),
sort(IncludedI, Included),
delete_parents(Graph1, Included, NoParents),
topsort(NoParents, SortedRest).
add_parentless([], Sorted, [], [], Sorted).
add_parentless([Node-[]|Graph0], [Node|Sorted], [Node|Included], Graph1, SortedRest) :- !,
add_parentless(Graph0, Sorted, Included, Graph1, SortedRest).
add_parentless([Node|Graph0], Sorted, Included, [Node|Graph1], SortedRest) :-
add_parentless(Graph0, Sorted, Included, Graph1, SortedRest).
delete_parents([], _, []).
delete_parents([Node-Parents|Graph1], Included, [Node-NewParents|NoParents]) :-
ord_subtract(Parents, Included, NewParents),
delete_parents(Graph1, Included, NoParents).
cvt2problist([], []).
cvt2problist([[[_|E]]|Est0], [Ps|Probs]) :-
sum_all(E,0,Sum),
do_probs(E,Sum,Ps),
cvt2problist(Est0, Probs) .
sum_all([],Sum,Sum).
sum_all([E|Es],S0,Sum) :-
SI is S0+E,
sum_all(Es,SI,Sum).
do_probs([],_,[]).
do_probs([E|Es],Sum,[P|Ps]) :-
P is E/Sum,
do_probs(Es,Sum,Ps).
show_sorted([], _) :- nl.
show_sorted([I|VarOrder], Graph) :-
arg(I,Graph,var(V,I,_,_,_,_,_,_,_)),
clpbn:get_atts(V,[key(K)]),
% format('~w ',[K]),
show_sorted(VarOrder, Graph).