547 lines
15 KiB
Prolog
547 lines
15 KiB
Prolog
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%
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% each variable is represented by a node in a binary tree.
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% each node contains:
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% key,
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% current_value
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% Markov Blanket
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%
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:- module(clpbn_gibbs,
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[gibbs/3,
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check_if_gibbs_done/1,
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init_gibbs_solver/4,
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run_gibbs_solver/3]).
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:- use_module(library(rbtrees),
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[rb_new/1,
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rb_insert/4,
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rb_lookup/3]).
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:- use_module(library(lists),
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[member/2,
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append/3,
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delete/3,
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max_list/2,
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sum_list/2]).
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:- use_module(library(ordsets),
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[ord_subtract/3]).
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:- use_module(library('clpbn/matrix_cpt_utils'), [
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project_from_CPT/3,
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reorder_CPT/5,
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multiply_possibly_deterministic_factors/3,
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column_from_possibly_deterministic_CPT/3,
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normalise_possibly_deterministic_CPT/2,
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list_from_CPT/2]).
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:- use_module(library('clpbn/utils'), [
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check_for_hidden_vars/3]).
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:- use_module(library('clpbn/dists'), [
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get_possibly_deterministic_dist_matrix/5,
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get_dist_domain_size/2]).
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:- use_module(library('clpbn/topsort'), [
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topsort/2]).
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:- use_module(library('clpbn/display'), [
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clpbn_bind_vals/3]).
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:- use_module(library('clpbn/connected'),
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[
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influences/4
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]).
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:- dynamic gibbs_params/3.
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:- dynamic explicit/1.
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% arguments:
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%
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% list of output variables
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% list of attributed variables
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%
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gibbs(LVs,Vs0,AllDiffs) :-
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init_gibbs_solver(LVs, Vs0, AllDiffs, Vs),
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run_gibbs_solver(LVs, LPs, Vs),
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clpbn_bind_vals(LVs,LPs,AllDiffs),
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clean_up.
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init_gibbs_solver(GoalVs, Vs0, _, Vs) :-
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clean_up,
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term_variables(GoalVs, LVs),
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check_for_hidden_vars(Vs0, Vs0, Vs1),
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influences(Vs1, LVs, _, Vs2),
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sort(Vs2,Vs).
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run_gibbs_solver(LVs, LPs, Vs) :-
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initialise(Vs, Graph, LVs, OutputVars, VarOrder),
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process(VarOrder, Graph, OutputVars, Estimates),
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sum_up_all(Estimates, LPs),
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clean_up.
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initialise(LVs, Graph, GVs, OutputVars, VarOrder) :-
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init_keys(Keys0),
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gen_keys(LVs, 0, VLen, Keys0, Keys),
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functor(Graph,graph,VLen),
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graph_representation(LVs, Graph, 0, Keys, TGraph),
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compile_graph(Graph),
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topsort(TGraph, VarOrder),
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%writeln(TGraph:VarOrder),
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% show_sorted(VarOrder, Graph),
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add_all_output_vars(GVs, Keys, OutputVars).
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init_keys(Keys0) :-
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rb_new(Keys0).
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gen_keys([], I, I, Keys, Keys).
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gen_keys([V|Vs], I0, If, Keys0, Keys) :-
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clpbn:get_atts(V,[evidence(_)]), !,
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gen_keys(Vs, I0, If, Keys0, Keys).
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gen_keys([V|Vs], I0, If, Keys0, Keys) :-
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I is I0+1,
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rb_insert(Keys0,V,I,KeysI),
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gen_keys(Vs, I, If, KeysI, Keys).
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graph_representation([],_,_,_,[]).
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graph_representation([V|Vs], Graph, I0, Keys, TGraph) :-
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clpbn:get_atts(V,[evidence(_)]), !,
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clpbn:get_atts(V, [dist(Id,Parents)]),
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get_possibly_deterministic_dist_matrix(Id, Parents, _, Vals, Table),
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get_sizes(Parents, Szs),
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length(Vals,Sz),
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project_evidence_out([V|Parents],[V|Parents],Table,[Sz|Szs],Variables,NewTable),
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% all variables are parents
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propagate2parents(Variables, NewTable, Variables, Graph, Keys),
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graph_representation(Vs, Graph, I0, Keys, TGraph).
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graph_representation([V|Vs], Graph, I0, Keys, [I-IParents|TGraph]) :-
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I is I0+1,
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clpbn:get_atts(V, [dist(Id,Parents)]),
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get_possibly_deterministic_dist_matrix(Id, Parents, _, Vals, Table),
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get_sizes(Parents, Szs),
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length(Vals,Sz),
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project_evidence_out([V|Parents],[V|Parents],Table,[Sz|Szs],Variables,NewTable),
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Variables = [V|NewParents],
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sort_according_to_indices(NewParents,Keys,SortedNVs,SortedIndices),
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reorder_CPT(Variables,NewTable,[V|SortedNVs],NewTable2,_),
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add2graph(V, Vals, NewTable2, SortedIndices, Graph, Keys),
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propagate2parents(NewParents, NewTable, Variables, Graph,Keys),
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parent_indices(NewParents, Keys, IVariables0),
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sort(IVariables0, IParents),
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arg(I, Graph, var(_,_,_,_,_,_,_,NewTable2,SortedIndices)),
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graph_representation(Vs, Graph, I, Keys, TGraph).
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write_pars([]).
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write_pars([V|Parents]) :-
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clpbn:get_atts(V, [key(K),dist(I,_)]),write(K:I),nl,
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write_pars(Parents).
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get_sizes([], []).
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get_sizes([V|Parents], [Sz|Szs]) :-
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clpbn:get_atts(V, [dist(Id,_)]),
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get_dist_domain_size(Id, Sz),
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get_sizes(Parents, Szs).
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parent_indices([], _, []).
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parent_indices([V|Parents], Keys, [I|IParents]) :-
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rb_lookup(V, I, Keys),
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parent_indices(Parents, Keys, IParents).
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%
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% first, remove nodes that have evidence from tables.
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%
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project_evidence_out([],Deps,Table,_,Deps,Table).
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project_evidence_out([V|Parents],Deps,Table,Szs,NewDeps,NewTable) :-
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clpbn:get_atts(V,[evidence(_)]), !,
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project_from_CPT(V,tab(Table,Deps,Szs),tab(ITable,IDeps,ISzs)),
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project_evidence_out(Parents,IDeps,ITable,ISzs,NewDeps,NewTable).
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project_evidence_out([_Par|Parents],Deps,Table,Szs,NewDeps,NewTable) :-
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project_evidence_out(Parents,Deps,Table,Szs,NewDeps,NewTable).
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propagate2parents([], _, _, _, _).
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propagate2parents([V|NewParents], Table, Variables, Graph, Keys) :-
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delete(Variables,V,NVs),
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sort_according_to_indices(NVs,Keys,SortedNVs,SortedIndices),
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reorder_CPT(Variables,Table,[V|SortedNVs],NewTable,_),
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add2graph(V, _, NewTable, SortedIndices, Graph, Keys),
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propagate2parents(NewParents,Table, Variables, Graph, Keys).
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add2graph(V, Vals, Table, IParents, Graph, Keys) :-
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rb_lookup(V, Index, Keys),
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(var(Vals) -> true ; length(Vals,Sz)),
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arg(Index, Graph, var(V,Index,_,Vals,Sz,VarSlot,_,_,_)),
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member(tabular(Table,Index,IParents), VarSlot), !.
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sort_according_to_indices(NVs,Keys,SortedNVs,SortedIndices) :-
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vars2indices(NVs,Keys,ToSort),
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keysort(ToSort, Sorted),
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split_parents(Sorted, SortedNVs,SortedIndices).
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split_parents([], [], []).
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split_parents([I-V|Sorted], [V|SortedNVs],[I|SortedIndices]) :-
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split_parents(Sorted, SortedNVs, SortedIndices).
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vars2indices([],_,[]).
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vars2indices([V|Parents],Keys,[I-V|IParents]) :-
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rb_lookup(V, I, Keys),
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vars2indices(Parents,Keys,IParents).
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%
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% This is the really cool bit.
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%
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compile_graph(Graph) :-
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Graph =.. [_|VarsInfo],
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compile_vars(VarsInfo,Graph).
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compile_vars([],_).
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compile_vars([var(_,I,_,Vals,Sz,VarSlot,Parents,_,_)|VarsInfo],Graph)
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:-
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compile_var(I,Vals,Sz,VarSlot,Parents,Graph),
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compile_vars(VarsInfo,Graph).
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compile_var(I,Vals,Sz,VarSlot,Parents,Graph) :-
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fetch_all_parents(VarSlot,Graph,[],Parents,[],Sizes),
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mult_list(Sizes,1,TotSize),
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compile_var(TotSize,I,Vals,Sz,VarSlot,Parents,Sizes,Graph).
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fetch_all_parents([],_,Parents,Parents,Sizes,Sizes) :- !.
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fetch_all_parents([tabular(_,_,Ps)|CPTs],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
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merge_these_parents(Ps,Graph,Parents0,ParentsI,Sizes0,SizesI),
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fetch_all_parents(CPTs,Graph,ParentsI,ParentsF,SizesI,SizesF).
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merge_these_parents([],_,Parents,Parents,Sizes,Sizes).
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merge_these_parents([I|Ps],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
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member(I,Parents0), !,
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merge_these_parents(Ps,Graph,Parents0,ParentsF,Sizes0,SizesF).
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merge_these_parents([I|Ps],Graph,Parents0,ParentsF,Sizes0,SizesF) :-
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arg(I,Graph,var(_,I,_,Vals,_,_,_,_,_)),
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length(Vals, Sz),
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add_parent(Parents0,I,ParentsI,Sizes0,Sz,SizesI),
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merge_these_parents(Ps,Graph,ParentsI,ParentsF,SizesI,SizesF).
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add_parent([],I,[I],[],Sz,[Sz]).
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add_parent([P|Parents0],I,[I,P|Parents0],Sizes0,Sz,[Sz|Sizes0]) :-
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P > I, !.
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add_parent([P|Parents0],I,[P|ParentsI],[S|Sizes0],Sz,[S|SizesI]) :-
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add_parent(Parents0,I,ParentsI,Sizes0,Sz,SizesI).
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mult_list([],Mult,Mult).
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mult_list([Sz|Sizes],Mult0,Mult) :-
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MultI is Sz*Mult0,
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mult_list(Sizes,MultI,Mult).
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% compile node as set of facts, faster execution
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compile_var(TotSize,I,_Vals,Sz,CPTs,Parents,_Sizes,Graph) :-
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TotSize < 1024*64, TotSize > 0, !,
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multiply_all(I,Parents,CPTs,Sz,Graph).
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% do it dynamically
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compile_var(_,_,_,_,_,_,_,_).
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multiply_all(I,Parents,CPTs,Sz,Graph) :-
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markov_blanket_instance(Parents,Graph,Values),
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(
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multiply_all(CPTs,Graph,Probs)
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->
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store_mblanket(I,Values,Probs)
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;
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throw(error(domain_error(bayesian_domain),gibbs_cpt(I,Parents,Values,Sz)))
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),
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fail.
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multiply_all(I,_,_,_,_) :-
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assert(explicit(I)).
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% note: what matters is how this predicate instantiates the temp
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% slot in the graph!
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markov_blanket_instance([],_,[]).
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markov_blanket_instance([I|Parents],Graph,[Pos|Values]) :-
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arg(I,Graph,var(_,I,Pos,Vals,_,_,_,_,_)),
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fetch_val(Vals,0,Pos),
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markov_blanket_instance(Parents,Graph,Values).
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% backtrack through every value in domain
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%
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fetch_val([_|_],Pos,Pos).
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fetch_val([_|Vals],I0,Pos) :-
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I is I0+1,
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fetch_val(Vals,I,Pos).
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multiply_all([tabular(Table,_,Parents)|CPTs],Graph,Probs) :-
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fetch_parents(Parents, Graph, Vals),
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column_from_possibly_deterministic_CPT(Table,Vals,Probs0),
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multiply_more(CPTs,Graph,Probs0,Probs).
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fetch_parents([], _, []).
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fetch_parents([P|Parents], Graph, [Val|Vals]) :-
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arg(P,Graph,var(_,_,Val,_,_,_,_,_,_)),
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fetch_parents(Parents, Graph, Vals).
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multiply_more([],_,Probs0,LProbs) :-
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normalise_possibly_deterministic_CPT(Probs0, Probs),
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list_from_CPT(Probs, LProbs0),
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accumulate_up_list(LProbs0, 0.0, LProbs).
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multiply_more([tabular(Table,_,Parents)|CPTs],Graph,Probs0,Probs) :-
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fetch_parents(Parents, Graph, Vals),
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column_from_possibly_deterministic_CPT(Table, Vals, P0),
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multiply_possibly_deterministic_factors(Probs0, P0, ProbsI),
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multiply_more(CPTs,Graph,ProbsI,Probs).
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accumulate_up_list([], _, []).
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accumulate_up_list([P|LProbs], P0, [P1|L]) :-
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P1 is P0+P,
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accumulate_up_list(LProbs, P1, L).
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store_mblanket(I,Values,Probs) :-
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recordz(mblanket,m(I,Values,Probs),_).
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add_all_output_vars([], _, []).
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add_all_output_vars([Vs|LVs], Keys, [Is|OutputVars]) :-
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add_output_vars(Vs, Keys, Is),
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add_all_output_vars(LVs, Keys, OutputVars).
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add_output_vars([], _, []).
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add_output_vars([V|LVs], Keys, [I|OutputVars]) :-
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rb_lookup(V, I, Keys),
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add_output_vars(LVs, Keys, OutputVars).
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process(VarOrder, Graph, OutputVars, Estimates) :-
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gibbs_params(NChains,BurnIn,NSamples),
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functor(Graph,_,Len),
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init_chains(NChains,VarOrder,Len,Graph,Chains0),
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init_estimates(NChains,OutputVars,Graph,Est0),
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process_chains(BurnIn,VarOrder,BurnedIn,Chains0,Graph,Len,Est0,_),
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process_chains(NSamples,VarOrder,_,BurnedIn,Graph,Len,Est0,Estimates).
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%
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% I use an uniform distribution to generate the initial sample.
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%
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init_chains(0,_,_,_,[]) :- !.
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init_chains(I,VarOrder,Len,Graph,[Chain|Chains]) :-
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init_chain(VarOrder,Len,Graph,Chain),
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I1 is I-1,
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init_chains(I1,VarOrder,Len,Graph,Chains).
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init_chain(VarOrder,Len,Graph,Chain) :-
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functor(Chain,sample,Len),
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gen_sample(VarOrder,Graph,Chain).
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gen_sample([],_,_) :- !.
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gen_sample([I|Vs],Graph,Chain) :-
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arg(I,Graph,var(_,I,_,_,Sz,_,_,_,_)),
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Pos is integer(random*Sz),
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arg(I,Chain,Pos),
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gen_sample(Vs,Graph,Chain).
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init_estimates(0,_,_,[]) :- !.
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init_estimates(NChains,OutputVars,Graph,[Est|Est0]) :-
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NChainsI is NChains-1,
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init_estimate_all_outvs(OutputVars,Graph,Est),
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init_estimates(NChainsI,OutputVars,Graph,Est0).
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init_estimate_all_outvs([],_,[]).
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init_estimate_all_outvs([Vs|OutputVars],Graph,[E|Est]) :-
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init_estimate(Vs, Graph, E),
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init_estimate_all_outvs(OutputVars,Graph,Est).
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init_estimate([],_,[]).
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init_estimate([V],Graph,[I|E0L]) :- !,
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arg(V,Graph,var(_,I,_,_,Sz,_,_,_,_)),
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gen_e0(Sz,E0L).
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init_estimate(Vs,Graph,me(Is,Mults,Es)) :-
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generate_est_mults(Vs, Is, Graph, Mults, Sz),
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gen_e0(Sz,Es).
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generate_est_mults([], [], _, [], 1).
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generate_est_mults([V|Vs], [I|Is], Graph, [M0|Mults], M) :-
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arg(V,Graph,var(_,I,_,_,Sz,_,_,_,_)),
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generate_est_mults(Vs, Is, Graph, Mults, M0),
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M is M0*Sz.
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gen_e0(0,[]) :- !.
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gen_e0(Sz,[0|E0L]) :-
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Sz1 is Sz-1,
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gen_e0(Sz1,E0L).
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process_chains(0,_,F,F,_,_,Est,Est) :- !.
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process_chains(ToDo,VarOrder,End,Start,Graph,Len,Est0,Estf) :-
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%format('ToDo = ~d~n',[ToDo]),
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process_chains(Start,VarOrder,Int,Graph,Len,Est0,Esti),
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% (ToDo mod 100 =:= 1 -> statistics,cvt2problist(Esti, Probs), Int =[S|_], format('did ~d: ~w~n ~w~n',[ToDo,Probs,S]) ; true),
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ToDo1 is ToDo-1,
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process_chains(ToDo1,VarOrder,End,Int,Graph,Len,Esti,Estf).
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process_chains([], _, [], _, _,[],[]).
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process_chains([Sample0|Samples0], VarOrder, [Sample|Samples], Graph, SampLen,[E0|E0s],[Ef|Efs]) :-
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functor(Sample,sample,SampLen),
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do_sample(VarOrder,Sample,Sample0,Graph),
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% format('Sample = ~w~n',[Sample]),
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update_estimates(E0,Sample,Ef),
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process_chains(Samples0, VarOrder, Samples, Graph, SampLen,E0s,Efs).
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do_sample([],_,_,_).
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do_sample([I|VarOrder],Sample,Sample0,Graph) :-
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do_var(I,Sample,Sample0,Graph),
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do_sample(VarOrder,Sample,Sample0,Graph).
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do_var(I,Sample,Sample0,Graph) :-
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( explicit(I) ->
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arg(I,Graph,var(_,_,_,_,_,_,Parents,_,_)),
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fetch_parents(Parents,I,Sample,Sample0,Args),
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recorded(mblanket,m(I,Args,Vals),_)
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;
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arg(I,Graph,var(_,_,_,_,_,CPTs,Parents,_,_)),
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fetch_parents(Parents,I,Sample,Sample0,Bindings),
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multiply_all_in_context(Parents,Bindings,CPTs,Graph,Vals)
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),
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X is random,
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pick_new_value(Vals,X,0,Val),
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arg(I,Sample,Val).
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multiply_all_in_context(Parents,Args,CPTs,Graph,Vals) :-
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set_pos(Parents,Args,Graph),
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multiply_all(CPTs,Graph,Vals),
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assert(mall(Vals)), fail.
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multiply_all_in_context(_,_,_,_,Vals) :-
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retract(mall(Vals)).
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set_pos([],[],_).
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set_pos([I|Is],[Pos|Args],Graph) :-
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arg(I,Graph,var(_,I,Pos,_,_,_,_,_,_)),
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set_pos(Is,Args,Graph).
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fetch_parents([],_,_,_,[]).
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fetch_parents([P|Parents],I,Sample,Sample0,[VP|Args]) :-
|
|
arg(P,Sample,VP),
|
|
nonvar(VP), !,
|
|
fetch_parents(Parents,I,Sample,Sample0,Args).
|
|
fetch_parents([P|Parents],I,Sample,Sample0,[VP|Args]) :-
|
|
arg(P,Sample0,VP),
|
|
fetch_parents(Parents,I,Sample,Sample0,Args).
|
|
|
|
pick_new_value([V|Vals],X,I0,Val) :-
|
|
( X < V ->
|
|
Val = I0
|
|
;
|
|
I is I0+1,
|
|
pick_new_value(Vals,X,I,Val)
|
|
).
|
|
|
|
update_estimates([],_,[]).
|
|
update_estimates([Est|E0],Sample,[NEst|Ef]) :-
|
|
update_estimate(Est,Sample,NEst),
|
|
update_estimates(E0,Sample,Ef).
|
|
|
|
update_estimate([I|E],Sample,[I|NE]) :-
|
|
arg(I,Sample,V),
|
|
update_estimate_for_var(V,E,NE).
|
|
update_estimate(me(Is,Mult,E),Sample,me(Is,Mult,NE)) :-
|
|
get_estimate_pos(Is, Sample, Mult, 0, V),
|
|
update_estimate_for_var(V,E,NE).
|
|
|
|
get_estimate_pos([], _, [], V, V).
|
|
get_estimate_pos([I|Is], Sample, [M|Mult], V0, V) :-
|
|
arg(I,Sample,VV),
|
|
VI is VV*M+V0,
|
|
get_estimate_pos(Is, Sample, Mult, VI, V).
|
|
|
|
update_estimate_for_var(V0,[X|T],[X1|NT]) :-
|
|
( V0 == 0 ->
|
|
X1 is X+1,
|
|
NT = T
|
|
;
|
|
V1 is V0-1,
|
|
X1 = X,
|
|
update_estimate_for_var(V1,T,NT)
|
|
).
|
|
|
|
|
|
check_if_gibbs_done(Var) :-
|
|
get_atts(Var, [dist(_)]), !.
|
|
|
|
clean_up :-
|
|
eraseall(mblanket),
|
|
fail.
|
|
clean_up :-
|
|
retractall(explicit(_)),
|
|
fail.
|
|
clean_up.
|
|
|
|
gibbs_params(5,1000,10000).
|
|
|
|
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).
|
|
|
|
sum_up_all([[]|_], []).
|
|
sum_up_all([[C|MoreC]|Chains], [Dist|Dists]) :-
|
|
extract_sums(Chains, CurrentChains, LeftChains),
|
|
sum_up([C|CurrentChains], Dist),
|
|
sum_up_all([MoreC|LeftChains], Dists).
|
|
|
|
extract_sums([], [], []).
|
|
extract_sums([[C|Chains]|MoreChains], [C|CurrentChains], [Chains|LeftChains]) :-
|
|
extract_sums(MoreChains, CurrentChains, LeftChains).
|
|
|
|
sum_up([[_|Counts]|Chains], Dist) :-
|
|
add_up(Counts,Chains, Add),
|
|
normalise(Add, Dist).
|
|
sum_up([me(_,_,Counts)|Chains], Dist) :-
|
|
add_up_mes(Counts,Chains, Add),
|
|
normalise(Add, Dist).
|
|
|
|
add_up(Counts,[],Counts).
|
|
add_up(Counts,[[_|Cs]|Chains], Add) :-
|
|
sum_lists(Counts, Cs, NCounts),
|
|
add_up(NCounts, Chains, Add).
|
|
|
|
add_up_mes(Counts,[],Counts).
|
|
add_up_mes(Counts,[me(_,_,Cs)|Chains], Add) :-
|
|
sum_lists(Counts, Cs, NCounts),
|
|
add_up_mes(NCounts, Chains, Add).
|
|
|
|
sum_lists([],[],[]).
|
|
sum_lists([Count|Counts], [C|Cs], [NC|NCounts]) :-
|
|
NC is Count+C,
|
|
sum_lists(Counts, Cs, NCounts).
|
|
|
|
normalise(Add, Dist) :-
|
|
sum_list(Add, Sum),
|
|
divide_list(Add, Sum, Dist).
|
|
|
|
divide_list([], _, []).
|
|
divide_list([C|Add], Sum, [P|Dist]) :-
|
|
P is C/Sum,
|
|
divide_list(Add, Sum, Dist).
|
|
|
|
|
|
|