384 lines
11 KiB
Prolog
384 lines
11 KiB
Prolog
%
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% generate explicit CPTs
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%
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:- module(clpbn_aggregates,
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[check_for_agg_vars/2,
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cpt_average/6,
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cpt_average/7,
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cpt_max/6,
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cpt_min/6,
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avg_factors/5
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]).
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:- use_module(library(clpbn),
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[{}/1]).
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:- use_module(library(lists),
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[last/2,
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sumlist/2,
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sum_list/3,
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max_list/2,
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min_list/2,
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nth0/3
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]).
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:- use_module(library(matrix),
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[matrix_new/3,
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matrix_to_list/2,
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matrix_set/3
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]).
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:- use_module(library(clpbn/dists),
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[add_dist/6,
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get_dist_domain_size/2
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]).
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:- use_module(library(clpbn/matrix_cpt_utils),
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[normalise_CPT_on_lines/3]).
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:- use_module(library(pfl),
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[skolem/2,
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add_ground_factor/5
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]).
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:- use_module(library(bhash)).
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:- use_module(library(maplist)).
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check_for_agg_vars([], []).
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check_for_agg_vars([V|Vs0], [V|Vs1]) :-
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clpbn:get_atts(V, [key(K), dist(Id,Parents)]), !,
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simplify_dist(Id, V, K, Parents, Vs0, Vs00),
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check_for_agg_vars(Vs00, Vs1).
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check_for_agg_vars([V|Vs0], [V|Vs1]) :-
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check_for_agg_vars(Vs0, Vs1).
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% transform aggregate distribution into tree
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simplify_dist(avg(Domain), V, Key, Parents, Vs0, VsF) :- !,
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cpt_average([V|Parents], Key, Domain, NewDist, Vs0, VsF),
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NewDist = p(Dom, Tab, Ps),
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add_dist(Dom, tab, Tab, Ps, Key, Id),
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clpbn:put_atts(V, [dist(Id,Ps)]).
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simplify_dist(_, _, _, _, Vs0, Vs0).
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%
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avg_factors(Key, Parents, _Smoothing, NewParents, Id) :-
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% we keep ev as a list
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skolem(Key, Domain),
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avg_table(Parents, Parents, Domain, Key, 0, 1.0, NewParents, [], _ExtraSkolems, Id).
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% there are 4 cases:
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% no evidence on top node
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% evidence on top node compatible with values of parents
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% evidence on top node *entailed* by values of parents (so there is no real connection)
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% evidence incompatible with parents
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query_evidence(Key, EvHash, MAT0, MAT, NewParents0, NewParents, Vs, IVs, NewVs) :-
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b_hash_lookup(Key, Ev, EvHash), !,
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normalise_CPT_on_lines(MAT0, MAT1, L1),
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check_consistency(L1, Ev, MAT0, MAT1, L1, MAT, NewParents0, NewParents, Vs, IVs, NewVs).
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query_evidence(_, _, MAT, MAT, NewParents, NewParents, _, Vs, Vs).
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hash_ev(K=V, Es0, Es) :-
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b_hash_insert(Es0, K, V, Es).
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find_ev(Ev, Key, RemKeys, RemKeys, Ev0, EvF) :-
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b_hash_lookup(Key, V, Ev), !,
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EvF is Ev0+V.
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find_ev(_Evs, Key, RemKeys, [Key|RemKeys], Ev, Ev).
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% +Vars -> Keys without ev
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% +all keys
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% +domain to project to
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% +ouput key
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% +sum of evidence
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% +softness
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% +final CPT
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% - New Parents
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% + - list of new keys
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%
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avg_table(Vars, OVars, Domain, Key, TotEvidence, Softness, Vars, Vs, Vs, Id) :-
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length(Domain, SDomain),
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int_power(Vars, SDomain, 1, TabSize),
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TabSize =< 256,
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/* case gmp is not there !! */
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TabSize > 0, !,
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average_cpt(Vars, OVars, Domain, TotEvidence, Softness, CPT),
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matrix_to_list(CPT, Mat),
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add_ground_factor(bayes, Domain, [Key|OVars], Mat, Id).
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avg_table(Vars, OVars, Domain, Key, TotEvidence, Softness, [V1,V2], Vs, [V1,V2|NewVs], Id) :-
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length(Vars,L),
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LL1 is L//2,
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LL2 is L-LL1,
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list_split(LL1, Vars, L1, L2),
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Min = 0,
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length(Domain,Max1), Max is Max1-1,
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intermediate_table(LL1, sum(Min,Max), L1, V1, Key, 1.0, 0, I1, Vs, Vs1),
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intermediate_table(LL2, sum(Min,Max), L2, V2, Key, 1.0, I1, _, Vs1, NewVs),
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average_cpt([V1,V2], OVars, Domain, TotEvidence, Softness, CPT),
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matrix_to_list(CPT, Mat),
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add_ground_factor(bayes, Domain, [Key,V1,V2], Mat, Id).
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intermediate_table(1,_,[V],V, _, _, I, I, Vs, Vs) :- !.
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intermediate_table(2, Op, [V1,V2], V, Key, Softness, I0, If, Vs, Vs) :- !,
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If is I0+1,
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extra_key_factor(Op, 2, [V1,V2], V, Key, Softness, I0).
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intermediate_table(N, Op, L, V, Key, Softness, I0, If, Vs, [V1,V2|NewVs]) :-
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LL1 is N//2,
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LL2 is N-LL1,
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list_split(LL1, L, L1, L2),
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I1 is I0+1,
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intermediate_table(LL1, Op, L1, V1, Key, Softness, I1, I2, Vs, Vs1),
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intermediate_table(LL2, Op, L2, V2, Key, Softness, I2, If, Vs1, NewVs),
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extra_key_factor(Op, N, [V1,V2], V, Key, Softness, I0).
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extra_key_factor(sum(Min,Max), N, [V1,V2], V, Key, Softness, I) :-
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Lower is Min*N,
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Upper is Max*N,
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generate_list(Lower, Upper, Nbs),
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sum_cpt([V1,V2], Nbs, Softness, CPT),
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V = 'AVG'(I,Key),
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add_ground_factor(bayes, Nbs, [V,V1,V2], CPT, Id),
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assert(pfl:currently_defined(V)),
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assert(pfl:f(bayes, Id, [V,V1,V2])).
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cpt_average(AllVars, Key, Els0, Tab, Vs, NewVs) :-
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cpt_average(AllVars, Key, Els0, 1.0, Tab, Vs, NewVs).
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% support variables with evidence from domain. This should make everyone's life easier.
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cpt_average([Ev|Vars], Key, Els0, Softness, p(Els0, TAB, NewParents), Vs, NewVs) :-
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find_evidence(Vars, 0, TotEvidence, RVars),
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build_avg_table(RVars, Vars, Els0, Key, TotEvidence, Softness, MAT0, NewParents0, Vs, IVs),
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include_qevidence(Ev, MAT0, MAT, NewParents0, NewParents, Vs, IVs, NewVs),
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matrix_to_list(MAT, TAB).
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% find all fixed kids, this simplifies significantly the function.
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find_evidence([], TotEvidence, TotEvidence, []).
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find_evidence([V|Vars], TotEvidence0, TotEvidence, RVars) :-
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clpbn:get_atts(V,[evidence(Ev)]), !,
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TotEvidenceI is TotEvidence0+Ev,
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find_evidence(Vars, TotEvidenceI, TotEvidence, RVars).
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find_evidence([V|Vars], TotEvidence0, TotEvidence, [V|RVars]) :-
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find_evidence(Vars, TotEvidence0, TotEvidence, RVars).
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cpt_max([_|Vars], Key, Els0, CPT, Vs, NewVs) :-
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build_max_table(Vars, Els0, Els0, Key, 1.0, CPT, Vs, NewVs).
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cpt_min([_|Vars], Key, Els0, CPT, Vs, NewVs) :-
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build_min_table(Vars, Els0, Els0, Key, 1.0, CPT, Vs, NewVs).
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build_avg_table(Vars, OVars, Domain, _, TotEvidence, Softness, CPT, Vars, Vs, Vs) :-
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length(Domain, SDomain),
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int_power(Vars, SDomain, 1, TabSize),
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TabSize =< 256,
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/* case gmp is not there !! */
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TabSize > 0, !,
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average_cpt(Vars, OVars, Domain, TotEvidence, Softness, CPT).
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build_avg_table(Vars, OVars, Domain, Key, TotEvidence, Softness, CPT, [V1,V2], Vs, [V1,V2|NewVs]) :-
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length(Vars,L),
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LL1 is L//2,
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LL2 is L-LL1,
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list_split(LL1, Vars, L1, L2),
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Min = 0,
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length(Domain,Max1), Max is Max1-1,
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build_intermediate_table(LL1, sum(Min,Max), L1, V1, Key, 1.0, 0, I1, Vs, Vs1),
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build_intermediate_table(LL2, sum(Min,Max), L2, V2, Key, 1.0, I1, _, Vs1, NewVs),
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average_cpt([V1,V2], OVars, Domain, TotEvidence, Softness, CPT).
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build_max_table(Vars, Domain, Softness, p(Domain, CPT, Vars), Vs, Vs) :-
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length(Domain, SDomain),
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int_power(Vars, SDomain, 1, TabSize),
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TabSize =< 16,
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/* case gmp is not there !! */
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TabSize > 0, !,
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max_cpt(Vars, Domain, Softness, CPT).
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build_max_table(Vars, Domain, Softness, p(Domain, CPT, [V1,V2]), Vs, [V1,V2|NewVs]) :-
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length(Vars,L),
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LL1 is L//2,
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LL2 is L-LL1,
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list_split(LL1, Vars, L1, L2),
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build_intermediate_table(LL1, max(Domain,CPT), L1, V1, Key, 1.0, 0, I1, Vs, Vs1),
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build_intermediate_table(LL2, max(Domain,CPT), L2, V2, Key, 1.0, I1, _, Vs1, NewVs),
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max_cpt([V1,V2], Domain, Softness, CPT).
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build_min_table(Vars, Domain, Softness, p(Domain, CPT, Vars), Vs, Vs) :-
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length(Domain, SDomain),
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int_power(Vars, SDomain, 1, TabSize),
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TabSize =< 16,
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/* case gmp is not there !! */
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TabSize > 0, !,
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min_cpt(Vars, Domain, Softness, CPT).
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build_min_table(Vars, Domain, Softness, p(Domain, CPT, [V1,V2]), Vs, [V1,V2|NewVs]) :-
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length(Vars,L),
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LL1 is L//2,
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LL2 is L-LL1,
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list_split(LL1, Vars, L1, L2),
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build_intermediate_table(LL1, min(Domain,CPT), L1, V1, Key, 1.0, 0, I1, Vs, Vs1),
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build_intermediate_table(LL2, min(Domain,CPT), L2, V2, Key, 1.0, I1, _, Vs1, NewVs),
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min_cpt([V1,V2], Domain, Softness, CPT).
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int_power([], _, TabSize, TabSize).
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int_power([_|L], X, I0, TabSize) :-
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I is I0*X,
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int_power(L, X, I, TabSize).
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build_intermediate_table(1,_,[V],V, _, _, I, I, Vs, Vs) :- !.
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build_intermediate_table(2, Op, [V1,V2], V, Key, Softness, I0, If, Vs, Vs) :- !,
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If is I0+1,
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generate_tmp_random(Op, 2, [V1,V2], V, Key, Softness, I0).
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build_intermediate_table(N, Op, L, V, Key, Softness, I0, If, Vs, [V1,V2|NewVs]) :-
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LL1 is N//2,
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LL2 is N-LL1,
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list_split(LL1, L, L1, L2),
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I1 is I0+1,
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build_intermediate_table(LL1, Op, L1, V1, Key, Softness, I1, I2, Vs, Vs1),
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build_intermediate_table(LL2, Op, L2, V2, Key, Softness, I2, If, Vs1, NewVs),
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generate_tmp_random(Op, N, [V1,V2], V, Key, Softness, I0).
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% averages are transformed into sums.
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generate_tmp_random(sum(Min,Max), N, [V1,V2], V, Key, Softness, I) :-
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Lower is Min*N,
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Upper is Max*N,
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generate_list(Lower, Upper, Nbs),
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sum_cpt([V1,V2], Nbs, Softness, CPT),
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generate_var('AVG'(I,Key), Nbs, CPT, [V1,V2], V).
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% write(sum(Nbs, CPT, [V1,V2])),nl, % debugging
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generate_tmp_random(max(Domain,CPT), _, [V1,V2], V, Key, I) :-
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generate_var('MAX'(I,Key), Domain, CPT, [V1,V2], V).
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generate_tmp_random(min(Domain,CPT), _, [V1,V2], V, Key, I) :-
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generate_var('MIN'(I,Key), Domain, CPT, [V1,V2], V).
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generate_var(VKey, Domain, CPT, Parents, V) :-
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{ V = VKey with tab(Domain, CPT, Parents) }.
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generate_list(M, M, [M]) :- !.
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generate_list(I, M, [I|Nbs]) :-
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I1 is I+1,
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generate_list(I1, M, Nbs).
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list_split(0, L, [], L) :- !.
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list_split(I, [H|L], [H|L1], L2) :-
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I1 is I-1,
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list_split(I1, L, L1, L2).
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%
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% if we have evidence, we need to check if we are always consistent, never consistent, or can be consistent
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%
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include_qevidence(V, MAT0, MAT, NewParents0, NewParents, Vs, IVs, NewVs) :-
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clpbn:get_atts(V,[evidence(Ev)]), !,
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normalise_CPT_on_lines(MAT0, MAT1, L1),
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check_consistency(L1, Ev, MAT0, MAT1, L1, MAT, NewParents0, NewParents, Vs, IVs, NewVs).
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include_qevidence(_, MAT, MAT, NewParents, NewParents, _, Vs, Vs).
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check_consistency(L1, Ev, MAT0, MAT1, L1, MAT, NewParents0, NewParents, Vs, IVs, NewVs) :-
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sumlist(L1, Tot),
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nth0(Ev, L1, Val),
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(
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Val == Tot
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->
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MAT1 = MAT,
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NewParents = [],
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Vs = NewVs
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;
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Val == 0.0 ->
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throw(error(domain_error(incompatible_evidence),evidence(Ev)))
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;
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MAT0 = MAT,
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NewParents = NewParents0,
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IVs = NewVs
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).
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%
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% generate actual table, instead of trusting the solver
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%
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average_cpt(Vs, OVars, Vals, Base, _, MCPT) :-
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get_ds_lengths(Vs,Lengs),
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length(OVars, N),
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length(Vals, SVals),
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matrix_new(floats,[SVals|Lengs],MCPT),
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fill_in_average(Lengs,N,Base,MCPT).
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get_ds_lengths([],[]).
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get_ds_lengths([V|Vs],[Sz|Lengs]) :-
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get_vdist_size(V, Sz),
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get_ds_lengths(Vs,Lengs).
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fill_in_average(Lengs, N, Base, MCPT) :-
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generate(Lengs, Case),
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average(Case, N, Base, Val),
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matrix_set(MCPT,[Val|Case],1.0),
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fail.
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fill_in_average(_,_,_,_).
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generate([], []).
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generate([N|Lengs], [C|Case]) :-
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from(0,N,C),
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generate(Lengs, Case).
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from(I,_,I).
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from(I1,M,J) :-
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I is I1+1,
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I < M,
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from(I,M,J).
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average(Case, N, Base, Val) :-
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sum_list(Case, Base, Tot),
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Val is integer(round(Tot/N)).
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sum_cpt(Vs,Vals,_,CPT) :-
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get_ds_lengths(Vs,Lengs),
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length(Vals,SVals),
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matrix_new(floats,[SVals|Lengs],MCPT),
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fill_in_sum(Lengs,MCPT),
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matrix_to_list(MCPT,CPT).
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fill_in_sum(Lengs,MCPT) :-
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generate(Lengs, Case),
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sumlist(Case, Val),
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matrix_set(MCPT,[Val|Case],1.0),
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fail.
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fill_in_sum(_,_).
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max_cpt(Vs,Vals,_,CPT) :-
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get_ds_lengths(Vs,Lengs),
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length(Vals,SVals),
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matrix_new(floats,[SVals|Lengs],MCPT),
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fill_in_max(Lengs,MCPT),
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matrix_to_list(MCPT,CPT).
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fill_in_max(Lengs,MCPT) :-
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generate(Lengs, Case),
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max_list(Case, Val),
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matrix_set(MCPT,[Val|Case],1.0),
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fail.
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fill_in_max(_,_).
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min_cpt(Vs,Vals,_,CPT) :-
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get_ds_lengths(Vs,Lengs),
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length(Vals,SVals),
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matrix_new(floats,[SVals|Lengs],MCPT),
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fill_in_max(Lengs,MCPT),
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matrix_to_list(MCPT,CPT).
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fill_in_min(Lengs,MCPT) :-
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generate(Lengs, Case),
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max_list(Case, Val),
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matrix_set(MCPT,[Val|Case],1.0),
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fail.
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fill_in_min(_,_).
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get_vdist_size(V, Sz) :-
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var(V), !,
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clpbn:get_atts(V, [dist(Dist,_)]),
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get_dist_domain_size(Dist, Sz).
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get_vdist_size(V, Sz) :-
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skolem(V, Dom),
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length(Dom, Sz).
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