356 lines
10 KiB
Prolog
356 lines
10 KiB
Prolog
%
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% The world famous EM algorithm, in a nutshell
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%
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:- module(clpbn_em, [em/5]).
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:- reexport(library(clpbn),
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[clpbn_flag/2,
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clpbn_flag/3
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]).
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:- use_module(library(clpbn),
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[clpbn_init_graph/1,
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clpbn_init_solver/4,
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clpbn_run_solver/3,
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clpbn_finalize_solver/1,
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pfl_init_solver/5,
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pfl_run_solver/3,
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conditional_probability/3,
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clpbn_flag/2
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]).
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:- use_module(library('clpbn/dists'),
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[get_dist_domain_size/2,
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empty_dist/2,
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dist_new_table/2,
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get_dist_key/2,
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randomise_all_dists/0,
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uniformise_all_dists/0
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]).
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:- use_module(library('clpbn/ground_factors'),
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[generate_network/5,
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f/3
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]).
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:- use_module(library('clpbn/utils'),
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[check_for_hidden_vars/3,
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sort_vars_by_key/3
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]).
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:- use_module(library('clpbn/learning/learn_utils'),
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[run_all/1,
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clpbn_vars/2,
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normalise_counts/2,
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compute_likelihood/3,
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soften_sample/2
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]).
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:- use_module(library(bhash),
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[b_hash_new/1,
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b_hash_lookup/3,
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b_hash_insert/4
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]).
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:- use_module(library(matrix),
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[matrix_add/3,
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matrix_to_list/2
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]).
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:- use_module(library(lists),
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[member/2]).
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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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]).
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:- use_module(library(maplist)).
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:- meta_predicate em(:,+,+,-,-), init_em(:,-).
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em(Items, MaxError, MaxIts, Tables, Likelihood) :-
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catch(init_em(Items, State),Error,handle_em(Error)),
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em_loop(0, 0.0, State, MaxError, MaxIts, Likelihood, Tables),
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clpbn_finalize_solver(State),
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assert(em_found(Tables, Likelihood)),
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fail.
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% get rid of new random variables the easy way :)
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em(_, _, _, Tables, Likelihood) :-
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retract(em_found(Tables, Likelihood)).
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handle_em(error(repeated_parents)) :- !,
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assert(em_found(_, -inf)),
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fail.
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handle_em(Error) :-
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throw(Error).
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% This gets you an initial configuration. If there is a lot of evidence
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% tables may be filled in close to optimal, otherwise they may be
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% close to uniform.
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% it also gets you a run for random variables
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% state collects all Info we need for the EM algorithm
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% it includes the list of variables without evidence,
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% the list of distributions for which we want to compute parameters,
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% and more detailed info on distributions, namely with a list of all instances for the distribution.
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init_em(Items, State) :-
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clpbn_flag(em_solver, Solver),
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% only used for PCGs
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clpbn_init_graph(Solver),
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% randomise_all_dists,
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% set initial values for distributions
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uniformise_all_dists,
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setup_em_network(Items, State).
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setup_em_network(Items, state(AllDists, AllDistInstances, MargKeys, SolverState)) :-
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clpbn:use_parfactors(on), !,
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% get all variables to marginalise
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run_examples(Items, Keys, Factors, EList),
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% get the EM CPT connections info from the factors
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generate_dists(Factors, EList, AllDists, AllDistInstances, MargKeys),
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% setup solver, if necessary
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pfl_init_solver(MargKeys, Keys, Factors, EList, SolverState).
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setup_em_network(Items, state(AllDists, AllDistInstances, MargVars, SolverState)) :-
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% create the ground network
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call_run_all(Items),
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% get all variables to marginalise
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attributes:all_attvars(AllVars0),
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% and order them
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sort_vars_by_key(AllVars0,AllVars,[]),
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% remove variables that do not have to do with this query.
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different_dists(AllVars, AllDists, AllDistInstances, MargVars),
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% setup solver by doing parameter independent work.
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clpbn_init_solver(MargVars, AllVars, _, SolverState).
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run_examples(user:Exs, Keys, Factors, EList) :-
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Exs = [_:_|_], !,
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findall(ex(EKs, EFs, EEs), run_example(Exs, EKs, EFs, EEs), VExs),
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foldl4(join_example, VExs, [], Keys, [], Factors, [], EList, 0, _).
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run_examples(Items, Keys, Factors, EList) :-
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run_ex(Items, Keys, Factors, EList).
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join_example( ex(EKs, EFs, EEs), Keys0, Keys, Factors0, Factors, EList0, EList, I0, I) :-
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I is I0+1,
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foldl(process_key(I0), EKs, Keys0, Keys),
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foldl(process_factor(I0), EFs, Factors0, Factors),
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foldl(process_ev(I0), EEs, EList0, EList).
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process_key(I0, K, Keys0, [I0:K|Keys0]).
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process_factor(I0, f(Type, Id, Keys), Keys0, [f(Type, Id, NKeys)|Keys0]) :-
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maplist(update_key(I0), Keys, NKeys).
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update_key(I0, K, I0:K).
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process_ev(I0, K=V, Es0, [(I0:K)=V|Es0]).
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run_example([_:Items|_], Keys, Factors, EList) :-
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run_ex(user:Items, Keys, Factors, EList).
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run_example([_|LItems], Keys, Factors, EList) :-
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run_example(LItems, Keys, Factors, EList).
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run_ex(Items, Keys, Factors, EList) :-
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% create the ground network
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call_run_all(Items),
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attributes:all_attvars(AllVars0),
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% and order them
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sort_vars_by_key(AllVars0,AllVars,[]),
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% no, we are in trouble because we don't know the network yet.
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% get the ground network
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generate_network(AllVars, _, Keys, Factors, EList).
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% loop for as long as you want.
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em_loop(Its, Likelihood0, State, MaxError, MaxIts, LikelihoodF, FTables) :-
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estimate(State, LPs),
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maximise(State, Tables, LPs, Likelihood),
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ltables(Tables, F0Tables),
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%writeln(iteration:Its:Likelihood:Its:Likelihood0:F0Tables),
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(
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(
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abs((Likelihood - Likelihood0)/Likelihood) < MaxError
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;
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Its == MaxIts
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)
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->
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ltables(Tables, FTables),
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LikelihoodF = Likelihood
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;
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Its1 is Its+1,
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em_loop(Its1, Likelihood, State, MaxError, MaxIts, LikelihoodF, FTables)
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).
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ltables([], []).
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ltables([Id-T|Tables], [Key-LTable|FTables]) :-
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matrix_to_list(T,LTable),
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get_dist_key(Id, Key),
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ltables(Tables, FTables).
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generate_dists(Factors, EList, AllDists, AllInfo, MargVars) :-
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b_hash_new(Ev0),
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foldl(elist_to_hash, EList, Ev0, Ev),
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maplist(process_factor(Ev), Factors, Dists0),
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sort(Dists0, Dists1),
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group(Dists1, AllDists, AllInfo, MargVars0, []),
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sort(MargVars0, MargVars).
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elist_to_hash(K=V, Ev0, Ev) :-
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b_hash_insert(Ev0, K, V, Ev).
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process_factor(Ev, f(bayes,Id,Ks), i(Id, Ks, Cases, NonEvs)) :-
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foldl( fetch_evidence(Ev), Ks, CompactCases, [], NonEvs),
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uncompact_cases(CompactCases, Cases).
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fetch_evidence(Ev, K, E, NonEvs, NonEvs) :-
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b_hash_lookup(K, E, Ev), !.
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fetch_evidence(_Ev, K, Ns, NonEvs, [K|NonEvs]) :-
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pfl:skolem(K,D),
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foldl(domain_to_number, D, Ns, 0, _).
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domain_to_number(_, I0, I0, I) :-
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I is I0+1.
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% collect the different dists we are going to learn next.
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different_dists(AllVars, AllDists, AllInfo, MargVars) :-
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all_dists(AllVars, AllVars, Dists0),
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sort(Dists0, Dists1),
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group(Dists1, AllDists, AllInfo, MargVars0, []),
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sort(MargVars0, MargVars).
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%
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% V -> to Id defining V. We get:
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% the random variables that are parents
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% the cases that can happen, eg if we have A <- B, C
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% A and B are boolean w/o evidence, and C is f, the cases could be
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% [0,0,1], [0,1,1], [1,0,0], [1,1,0],
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% Hiddens will be C
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%
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all_dists([], _, []).
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all_dists([V|AllVars], AllVars0, [i(Id, [V|Parents], Cases, Hiddens)|Dists]) :-
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% V is an instance of Id
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clpbn:get_atts(V, [dist(Id,Parents)]),
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sort([V|Parents], Sorted),
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length(Sorted, LengSorted),
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length(Parents, LengParents),
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(
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LengParents+1 =:= LengSorted
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->
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true
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;
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throw(error(repeated_parents))
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),
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generate_hidden_cases([V|Parents], CompactCases, Hiddens),
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uncompact_cases(CompactCases, Cases),
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all_dists(AllVars, AllVars0, Dists).
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generate_hidden_cases([], [], []).
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generate_hidden_cases([V|Parents], [P|Cases], Hiddens) :-
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clpbn:get_atts(V, [evidence(P)]), !,
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generate_hidden_cases(Parents, Cases, Hiddens).
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generate_hidden_cases([V|Parents], [Cases|MoreCases], [V|Hiddens]) :-
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clpbn:get_atts(V, [dist(Id,_)]),
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get_dist_domain_size(Id, Sz),
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gen_cases(0, Sz, Cases),
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generate_hidden_cases(Parents, MoreCases, Hiddens).
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gen_cases(Sz, Sz, []) :- !.
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gen_cases(I, Sz, [I|Cases]) :-
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I1 is I+1,
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gen_cases(I1, Sz, Cases).
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uncompact_cases(CompactCases, Cases) :-
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findall(Case, is_case(CompactCases, Case), Cases).
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is_case([], []).
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is_case([A|CompactCases], [A|Case]) :-
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integer(A), !,
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is_case(CompactCases, Case).
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is_case([L|CompactCases], [C|Case]) :-
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member(C, L),
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is_case(CompactCases, Case).
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group([], [], []) --> [].
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group([i(Id,Ps,Cs,[])|Dists1], [Id|Ids], [Id-[i(Id,Ps,Cs,[])|Extra]|AllInfo]) --> !,
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same_id(Dists1, Id, Extra, Rest),
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group(Rest, Ids, AllInfo).
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group([i(Id,Ps,Cs,Hs)|Dists1], [Id|Ids], [Id-[i(Id,Ps,Cs,Hs)|Extra]|AllInfo]) -->
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[Hs],
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same_id(Dists1, Id, Extra, Rest),
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group(Rest, Ids, AllInfo).
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same_id([i(Id,Vs,Cases,[])|Dists1], Id, [i(Id, Vs, Cases, [])|Extra], Rest) --> !,
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same_id(Dists1, Id, Extra, Rest).
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same_id([i(Id,Vs,Cases,Hs)|Dists1], Id, [i(Id, Vs, Cases, Hs)|Extra], Rest) --> !,
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[Hs],
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same_id(Dists1, Id, Extra, Rest).
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same_id(Dists, _, [], Dists) --> [].
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compact_mvars([], []).
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compact_mvars([X1,X2|MargVars], CMVars) :- X1 == X2, !,
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compact_mvars([X2|MargVars], CMVars).
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compact_mvars([X|MargVars], [X|CMVars]) :- !,
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compact_mvars(MargVars, CMVars).
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estimate(state(_, _, Margs, SolverState), LPs) :-
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clpbn:use_parfactors(on), !,
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pfl_run_solver(Margs, LPs, SolverState).
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estimate(state(_, _, Margs, SolverState), LPs) :-
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clpbn_run_solver(Margs, LPs, SolverState).
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maximise(state(_,DistInstances,MargVars,_), Tables, LPs, Likelihood) :-
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rb_new(MDistTable0),
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foldl(create_mdist_table, MargVars, LPs, MDistTable0, MDistTable),
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compute_parameters(DistInstances, Tables, MDistTable, 0.0, Likelihood, LPs:MargVars).
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create_mdist_table(Vs, Ps, MDistTable0, MDistTable) :-
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rb_insert(MDistTable0, Vs, Ps, MDistTable).
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compute_parameters([], [], _, Lik, Lik, _).
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compute_parameters([Id-Samples|Dists], [Id-NewTable|Tables], MDistTable, Lik0, Lik, LPs:MargVars) :-
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empty_dist(Id, Table0),
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add_samples(Samples, Table0, MDistTable),
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%matrix_to_list(Table0,Mat), lists:sumlist(Mat, Sum), format(user_error, 'FINAL ~d ~w ~w~n', [Id,Sum,Mat]),
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soften_sample(Table0, SoftenedTable),
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% matrix:matrix_sum(Table0,TotM),
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normalise_counts(SoftenedTable, NewTable),
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compute_likelihood(Table0, NewTable, DeltaLik),
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dist_new_table(Id, NewTable),
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NewLik is Lik0+DeltaLik,
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compute_parameters(Dists, Tables, MDistTable, NewLik, Lik, LPs:MargVars).
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add_samples([], _, _).
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add_samples([i(_,_,[Case],[])|Samples], Table, MDistTable) :- !,
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matrix_add(Table,Case,1.0),
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add_samples(Samples, Table, MDistTable).
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add_samples([i(_,_,Cases,Hiddens)|Samples], Table, MDistTable) :-
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rb_lookup(Hiddens, Ps, MDistTable),
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run_sample(Cases, Ps, Table),
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%matrix_to_list(Table,M), format(user_error, '~w ~w~n', [Cases,Ps]),
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add_samples(Samples, Table, MDistTable).
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run_sample([], [], _).
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run_sample([C|Cases], [P|Ps], Table) :-
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matrix_add(Table, C, P),
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run_sample(Cases, Ps, Table).
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call_run_all(Mod:Items) :-
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clpbn_flag(em_solver, pcg), !,
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backtrack_run_all(Items, Mod).
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call_run_all(Mod:Items) :-
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run_all(Mod:Items).
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backtrack_run_all([Item|_], Mod) :-
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call(Mod:Item),
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fail.
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backtrack_run_all([_|Items], Mod) :-
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backtrack_run_all(Items, Mod).
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backtrack_run_all([], _).
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