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2011-06-26 23:13:43 +01:00
%%% -*- Mode: Prolog; -*-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
2012-01-11 14:44:59 +00:00
% $Date: 2011-11-28 14:41:26 +0100 (Mon, 28 Nov 2011) $
% $Revision: 6764 $
2011-06-26 23:13:43 +01:00
%
% This file is part of ProbLog
% http://dtai.cs.kuleuven.be/problog
%
% ProbLog was developed at Katholieke Universiteit Leuven
%
% Copyright 2009
% Angelika Kimmig, Vitor Santos Costa, Bernd Gutmann
%
% Main authors of this file:
% Bernd Gutmann
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Artistic License 2.0
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Discrete probability distributions for ProbLog
%
% this file contains predicates to emulate discrete distributions in ProbLog
%
% uniform(I,N,ID)
% emulates a uniform discrete distribution
% P(I) = 1/N for I in {1,2,...,N}
% If I is a variable, the predicate backtracks over all
% possible values for I
% ID has to be ground, it is an identifier which - if in the same proof -
% reused, will always return the same value
%
% binomial(K,N,P,ID)
% emulates a binomial distribution
% P(K) = (N over K) x P^K x (1-P)^(N-K) for K in {0,1,...,N}
% If K is a variable, the predicate backtracks over all
% possible values for K
% ID has to be ground, it is an identifier which - if in the same proof -
% reused, will always return the same value
%
% poisson(K,Lambda,ID)
% emulates a Poisson distribution
% P(K) = Lamda^K / K! x exp(-Lambda) for K in {0,1,2, ....}
% If K is a variable, the predicate backtracks over all
% possible values for K
% ID has to be ground, it is an identifier which - if in the same proof -
% reused, will always return the same value
%
%
% Author : Bernd Gutmann, bernd.gutmann@cs.kuleuven.be
% Version : January 14, 2009
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
:- module(discrete, [uniform/3,binomial/4,poisson/3]).
:- use_module('../problog').
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A distribution over 1,2, ..., N
% where P(I) := 1/N
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Prob::p_uniform(_I,_N,_ID,Prob).
uniform(I,N,ID) :-
integer(N),
N>0,
( var(I) ; integer(I), I>0, I=<N),
uniform(1,I,true,N,ID).
uniform(I,I,Old,N,ID) :-
I=<N,
FactProb is 1/(N-I+1),
call(Old),
p_uniform(I,N,ID,FactProb).
uniform(I,I2,Old,N,ID) :-
I<N,
FactProb is 1/(N-I+1),
NextI is I+1,
uniform(NextI,I2,(problog_not(p_uniform(I,N,ID,FactProb)),Old),N,ID).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Binomial Distribution
% K in { 0,1,2,3, ... }
% Lambda >= 0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Prob::p_binomial(_K,_N,_P,_ID,Prob).
binomial(K,N,P,ID) :-
number(P),
P >= 0,
P =< 1,
integer(N),
N>=0,
( var(K) ; integer(K),K>=0,K=<N),
binomial(0,K,N,P,true,0.0,ID).
binomial(K,KResult,N,P,Old,ProbAcc,ID) :-
% KResult is a number, make sure, not to go over it
% safes some time
(
number(KResult)
->
K=<KResult;
true
),
binomial_coefficient(N,K,BinomCoeff),
Prob is BinomCoeff * (P ** K) * ((1-P) ** (N-K)),
FactProb is Prob / (1-ProbAcc),
% this check stops the derivation, if the floating-point-based
% rounding errors get too big
FactProb > 0.0,
FactProb =< 1.0,
(
(
call(Old),
p_binomial(K,N,P,ID,FactProb),
KResult=K
); (
K<N,
NextK is K+1,
NextProbAcc is ProbAcc+Prob,
binomial(NextK,KResult,N,P,(problog_not(p_binomial(K,N,P,ID,FactProb)),Old),NextProbAcc,ID)
)
).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Poisson Distribution
% K in { 0,1,2,3, ... } or var(K)
% Lambda >= 0
% ID has to be ground
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
P :: p_poisson(_K,_Lambda,_ID,P).
poisson(K,Lambda,ID) :-
( var(K); integer(K),K>=0 ),
number(Lambda),
Lambda>=0,
ground(ID),
poisson(0,K,true,Lambda,0.0,ID).
poisson(K,K2,Old,Lambda,ProbAcc,ID) :-
% KResult is a number, make sure, not to go over it
% safes some time
(
integer(K2)
->
K=<K2;
true
),
power_over_factorial(K,Lambda,Part1),
% Prob is P(K) for a Poisson distribution with Lambda
Prob is Part1 * exp(-Lambda),
% now we have to determine the fact probability
% conditioned on the aggregated probabilities so far
FactProb is Prob/(1-ProbAcc),
% this check stops the derivation, if the floating-point-based
% rounding errors get too big
FactProb > 0.0,
FactProb =< 1.0,
(
(
call(Old),
p_poisson(K,Lambda,ID,FactProb),
K2=K
); (
NextK is K+1,
NextProbAcc is ProbAcc+Prob,
poisson(NextK,K2,(problog_not(p_poisson(K,Lambda,ID,FactProb)),Old),Lambda,NextProbAcc,ID)
)
).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculates (Lambda ** N) / N!
power_over_factorial(N,Lambda,Result) :-
integer(N),
N>=0,
power_over_factorial(N,Lambda,1.0,Result).
power_over_factorial(N,Lambda,Old,Result) :-
(
N>0
->
(
N2 is N-1,
New is Old * Lambda/N,
power_over_factorial(N2,Lambda,New,Result)
); Result=Old
).
% calculates (N \over K) = N!/(K! * (N-K)!)
binomial_coefficient(N,K,Result) :-
integer(K),
K >= 0,
binomial_coefficient(K,N,1,Result).
binomial_coefficient(I,N,Product,Result) :-
(
I=0
->
Result=Product;
(
I2 is I-1,
Product2 is Product * (N+1-I)/I,
binomial_coefficient(I2,N,Product2,Result)
)
).