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yap-6.3/packages/prism/exs/dcoin.psm

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2011-11-10 12:24:47 +00:00
%%%%
%%%% Double coin tossing --- dcoin.psm
%%%%
%%%% Copyright (C) 2004,2006,2008
%%%% Sato Laboratory, Dept. of Computer Science,
%%%% Tokyo Institute of Technology
%% A sequential mixture of two Bernoulli trials processes.
%% We have two coins, coin(1) and coin(2).
%% Start with coin(1), we keep flipping a coin and observe the outcome.
%% We change coins according to the rule in the process.
%% If the outcome is "head", the next coin to flip is coin(2).
%% If the outcome is "tail", the next coin to flip is coin(1).
%% The learning task is to estimate parameters for coin(1) and coin(2),
%% observing a sequence of outcomes.
%% As there is no hidden variable in this model, EM learning is just
%% ML estimation from complete data.
%%-------------------------------------
%% Quick start : sample session
%%
%% (1) load this program
%% ?- prism(dcoin).
%%
%% (2) sampling and probability computations
%% ?- sample(dcoin(10,X)),prob(dcoin(10,X)).
%% ?- sample(dcoin(10,X)),probf(dcoin(10,X)).
%%
%% (3) EM learning
%% ?- go.
go:- dcoin_learn(500).
%%------------------------------------
%% Declarations:
values(coin(1),[head,tail],[0.5,0.5]).
% Declare msw(coin(1),V) s.t. V = head or
% V = tail, where P(msw(coin(1),head)) = 0.5
% and P(msw(coin(1),tail)) = 0.5.
values(coin(2),[head,tail],[0.7,0.3]).
% Declare msw(coin(2),V) s.t. V = head or
% V = tail, where P(msw(coin(2),head)) = 0.7
% and P(msw(coin(2),tail)) = 0.3.
%%------------------------------------
%% Modeling part:
dcoin(N,Rs) :- % Rs is a list with length N of outcomes
dcoin(N,coin(1),Rs). % from two Bernoulli trials processes.
dcoin(N,Coin,[R|Rs]) :-
N > 0,
msw(Coin,R),
( R == head, NextCoin = coin(2)
; R == tail, NextCoin = coin(1) ),
N1 is N-1,
dcoin(N1,NextCoin,Rs).
dcoin(0,_,[]).
%%------------------------------------
%% Utility part:
dcoin_learn(N) :-
set_params, % Set parameters.
sample(dcoin(N,Rs)), % Get a sample Rs of size N.
Goals = [dcoin(N,Rs)], % Estimate the parameters from Rs.
learn(Goals).
set_params :-
set_sw(coin(1),[0.5,0.5]),
set_sw(coin(2),[0.7,0.3]).