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yap-6.3/packages/prism/exs/pdcg.psm
2011-11-10 12:24:47 +00:00

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%%%%
%%%% Probabilistic DCG --- pdcg.psm
%%%%
%%%% Copyright (C) 2004,2006,2008
%%%% Sato Laboratory, Dept. of Computer Science,
%%%% Tokyo Institute of Technology
%% PCFGs (probabilistic contex free grammars) are a stochastic extension
%% of CFG grammar such that in a (leftmost) derivation, each production
%% rule is selected probabilistically and applied. Look at the following
%% sample PCFG in which S is a start symbol and {a,b} are terminals.
%%
%% Rule 1: S -> SS (0.4)
%% Rule 2: S -> a (0.5)
%% Rule 3: S -> b (0.1)
%%
%% When S is expanded, three rules, Rule 1, 2 and 3 are applicable.
%% To determine a rule to apply, probabilistic selection is made in
%% such a way that Rule 1 is selected with probability 0.4, Rule 2
%% with probability 0.5 and Rule 3 with probability 0.1, respectively.
%% The probability of a derivation tree is defined to be the product
%% of probabilities associated with rules used in the derivation,
%% and that of a sentence is defined to be the sum of proabibities of
%% derivations for the sentence.
%%
%% When modeling PCFGs, we follow DCG (definite clause grammar)
%% formalism. So we write down a top-down parser using difference
%% list which represents the rest of the sentence to parse. Note that
%% the grammar is left-recursive, and hence running the program below
%% without a tabling mechanism goes into an infinite loop.
%%-------------------------------------
%% Quick start : learning experiment with the sample grammar
%%
%% ?- prism(pdcg),go. % Learn parameters of the PCFG above from
%% % randomly generated 100 samples
%%
%% ?- prob(pdcg([a,b,b])).
%% ?- prob(pdcg([a,b,b]),P).
%% ?- probf(pdcg([a,b,b])).
%% ?- probf(pdcg([a,b,b]),E),print_graph(E).
%% ?- sample(pdcg(X)).
%%
%% ?- viterbi(pdcg([a,b,b]),P). % P is the prob. of the most likely
%% ?- viterbif(pdcg([a,b,b]),P,E). % explanation E for pdcg([a,b,b])
%% ?- viterbif(pdcg([a,b,b]),P,E),print_graph(E).
go:- pdcg_learn(100).
max_str_len(20). % Maximum string length is 20.
%%------------------------------------
%% Declarations:
values('S',[['S','S'],a,b],[0.4,0.5,0.1]).
% We use a msw of the form msw('S',V) such
% that V is one of { ['S','S'], a, b },
% and when msw('S',V) is executed, the prob.
% of V=['S','S'] is 0.4, that of V=a is 0.5
% and that of V=b is 0.1.
%%------------------------------------
%% Modeling part:
start_symbol('S'). % Start symbol is S
pdcg(L):-
start_symbol(I),
pdcg2(I,L-[]).
% I is a category to expand.
pdcg2(I,L0-L2):- % L0-L2 is a list for I to span.
msw(I,RHS), % Choose a rule I -> RHS probabilistically.
( RHS == ['S','S'],
pdcg2('S',L0-L1),
pdcg2('S',L1-L2)
; RHS == a,
L0 = [RHS | L2]
; RHS == b,
L0 = [RHS | L2] ).
%%------------------------------------
%% Utility part:
pdcg_learn(N):-
max_str_len(MaxStrL),
get_samples_c(N,pdcg(X),(length(X,Y),Y =< MaxStrL),Goals,[Ns,_]),
format("#sentences= ~d~n",[Ns]),
unfix_sw('S'), % Make parameters of msw('S',.) changable
learn(Goals). % Conduct ML estimation by graphical EM learning