examples with msws

examples/inference/kalman_filter.pl

@@ -61,7 +61,9 @@
 
 :- end_lpad.
 
-
+hist(Samples,NBins,Chart):-
+  mc_sample_arg(kf(1,_O1,Y),Samples,Y,L0),
+  histogram(L0,NBins,Chart).
 
 dens_lw(Samples,NBins,Chart):-
   mc_sample_arg(kf(1,_O1,Y),Samples,Y,L0),
@@ -76,6 +78,11 @@
 % plot the density of the state at time 1 in case of no observation (prior)
 % and in case of observing 2.5 by taking 1000 samples and dividing the domain
 % in 40 bins
+?- hist(1000,40,G).
+% plot the density of the state at time 1 in case of no observation
+% by taking 1000 samples and dividing the domain
+% in 40 bins
+
 
 */
 

examples/inference/kalman_filtermsw.pl

@@ -0,0 +1,85 @@
+/*
+One-dimensional  Kalman filter. Hidden Markov model with a real
+value as state and a real value as output. The next state is given by
+the current state plus Gaussian noise (mean 0 and variance 2 in this example)
+and the output is given by the current state plus Gaussian noise (mean
+0 and variance 1 in this example). 
+This example can be considered as modeling a random walk of a single continuous 
+state variable with noisy observations. 
+Given that at time 0 the value 2.5 was
+observed, what is the distribution of the state at time 1 (filtering problem)?
+The distribution of the state is plotted in the case of having (posterior) or 
+not having the observation (prior).
+Liklihood weighing is used to condition the distribution on evidence on
+a continuous random variable (evidence with probability 0).
+CLP(R) constraints allow both sampling and weighing samples with the same
+program.
+From
+Islam, Muhammad Asiful, C. R. Ramakrishnan, and I. V. Ramakrishnan. 
+"Inference in probabilistic logic programs with continuous random variables." 
+Theory and Practice of Logic Programming 12.4-5 (2012): 505-523.
+http://arxiv.org/pdf/1112.2681v3.pdf
+Russell, S. and Norvig, P. 2010. Arficial Intelligence: A Modern Approach. 
+Third Edition, Prentice Hall, Figure 15.10 page 587
+
+*/
+:- use_module(library(mcintyre)).
+:- use_module(library(clpr)).
+:- if(current_predicate(use_rendering/1)).
+:- use_rendering(c3).
+:- endif.
+:- mc.
+:- begin_lpad.
+
+kf(N,O, T) :-
+  msw(init,S),
+  kf_part(0, N, S,O,T).
+
+kf_part(I, N, S,[V|RO], T) :-
+  I < N, 
+  NextI is I+1,
+  trans(S,I,NextS),
+  emit(NextS,I,V),
+  kf_part(NextI, N, NextS,RO, T).
+
+kf_part(N, N, S, [],S).
+
+trans(S,_I,NextS) :-
+  {NextS =:= E + S},
+  msw(trans_err,E).
+
+emit(NextS,_I,V) :-
+  {NextS =:= V+X},
+  msw(obs_err,X).
+
+values(init,real).
+values(trans_err,real).
+values(obs_err,real).
+
+:- set_sw(init, norm(0,1)).
+:- set_sw(trans_err,norm(0,2)).
+:- set_sw(obs_err,norm(0,1)).
+
+% prior as in Russel and Norvig 2010, Fig 15.10
+% transition noise as in Russel and Norvig 2010, Fig 15.10
+% observation noise as in Russel and Norvig 2010, Fig 15.10
+
+:- end_lpad.
+
+
+
+hist(Samples,NBins,Chart):-
+  mc_sample_arg(kf(1,_O1,Y),Samples,Y,L0),
+  histogram(L0,NBins,Chart).
+% plot the density of the state at time 1 in case of no observation (prior)
+% and in case of observing 2.5.
+% Observation as in Russel and Norvig 2010, Fig 15.10
+
+/** <examples>
+?- dens(1000,40,G).
+% plot the density of the state at time 1 in case of no observation
+% by taking 1000 samples and dividing the domain
+% in 40 bins
+
+*/
+

examples/inference/widgetmsw.pl

@@ -0,0 +1,61 @@
+/*
+Factory producing widgets.
+Consider a factory with two machines a and b. Each machine produces a widget
+with a continuous feature. A widget is produced by machine a with probability
+0.7 and by machine b with probability b.
+If the widget is produced by machine a, the feature is distributed as a
+Gaussian with mean 2.0 and variance 1.0.
+If the widget is produced by machine b, the feature is distributed as a
+Gaussian with mean 3.0 and variance 1.0.
+The widget then is processed by a third machine that adds a random quantity to
+the feature distributed as a Gaussian with mean 0.5 and variance 1.5.
+What is the distribution of the feature?
+What is the distribution of the feature given that the widget was procuded
+by machine a?
+What is the distribution of the feature given that the third machine added a
+quantity greater than 0.2?
+What is the distribution of the feature given that the third machine added
+a quantity of 2.0?
+Adapted from
+Islam, Muhammad Asiful, C. R. Ramakrishnan, and I. V. Ramakrishnan. 
+"Inference in probabilistic logic programs with continuous random variables." 
+Theory and Practice of Logic Programming 12.4-5 (2012): 505-523.
+http://arxiv.org/pdf/1112.2681v3.pdf
+*/
+:- use_module(library(mcintyre)).
+:- use_module(library(clpr)).
+
+:- if(current_predicate(use_rendering/1)).
+:- use_rendering(c3).
+:- endif.
+:- mc.
+:- begin_lpad.
+widget(X) :- msw(m, M),
+msw(st(M), Z),
+msw(pt, Y),
+{X = Y + Z}.
+% Ranges of RVs
+values(m, [a,b]).
+values(st(_), real).
+values(pt, real).
+% PDFs and PMFs:
+:- set_sw(m, [0.3, 0.7]),
+set_sw(st(a), norm(2.0, 1.0)),
+set_sw(st(b), norm(3.0, 1.0)),
+set_sw(pt, norm(0.5, 0.1)).
+
+
+:- end_lpad.
+
+hist_uncond(Samples,NBins,Chart):-
+  mc_sample_arg(widget(X),Samples,X,L0),
+  histogram(L0,NBins,Chart).
+% What is the distribution of the feature?
+
+
+/** <examples>
+?- hist_uncond(10000,40,G).
+% What is the distribution of the feature?
+
+*/
+