comparison toolboxes/FullBNT-1.0.7/bnt/CPDs/@boolean_CPD/boolean_CPD.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function CPD = boolean_CPD(bnet, self, ftype, fname, pfail)
+% BOOLEAN_CPD Make a tabular CPD representing a (noisy) boolean function
+%
+% CPD = boolean_cpd(bnet, self, 'inline', f) uses the inline function f
+% to specify the CPT.
+% e.g., suppose X4 = X2 AND (NOT X3). Then we can write
+%    bnet.CPD{4} = boolean_CPD(bnet, 4, 'inline', inline('(x(1) & ~x(2)'));  
+% Note that x(1) refers pvals(1) = X2, and x(2) refers to pvals(2)=X3.
+%
+% CPD = boolean_cpd(bnet, self, 'named', f) assumes f is a function name.
+% f can be built-in to matlab, or a file.
+% e.g., If X4 = X2 AND X3, we can write
+%    bnet.CPD{4} = boolean_CPD(bnet, 4, 'named', 'and');
+% e.g., If X4 = X2 OR X3, we can write
+%    bnet.CPD{4} = boolean_CPD(bnet, 4, 'named', 'any');
+%
+% CPD = boolean_cpd(bnet, self, 'rnd') makes a random non-redundant bool fn.
+%
+% CPD = boolean_CPD(bnet, self, 'inline'/'named', f, pfail)
+% will put probability mass 1-pfail on f(parents), and put pfail on the other value.
+% This is useful for simulating noisy boolean functions.
+% If pfail is omitted, it is set to 0.
+% (Note that adding noise to a random (non-redundant) boolean function just creates a different
+% (potentially redundant) random boolean function.)
+%
+% Note: This cannot be used to simulate a noisy-OR gate.
+% Example: suppose C has parents A and B, and the
+% link of A->C fails with prob pA and the link B->C fails with pB.
+% Then the noisy-OR gate defines the following distribution
+%
+%  A  B  P(C=0)
+%  0  0  1.0
+%  1  0  pA
+%  0  1  pB
+%  1  1  pA * PB
+% 
+% By contrast, boolean_CPD(bnet, C, 'any', p) would define
+%
+%  A  B  P(C=0) 
+%  0  0  1-p    
+%  1  0  p      
+%  0  1  p
+%  1  1  p
+
+
+if nargin==0
+  % This occurs if we are trying to load an object from a file.
+  CPD = tabular_CPD(bnet, self);
+  return;
+elseif isa(bnet, 'boolean_CPD')
+  % This might occur if we are copying an object.
+  CPD = bnet;
+  return;
+end
+
+if nargin < 5, pfail = 0; end
+
+ps = parents(bnet.dag, self);
+ns = bnet.node_sizes;
+psizes = ns(ps);
+self_size = ns(self);
+
+psucc = 1-pfail;
+
+k = length(ps);
+switch ftype
+ case 'inline', f = eval_bool_fn(fname, k);
+ case 'named',  f = eval_bool_fn(fname, k);
+ case 'rnd',    f = mk_rnd_bool_fn(k);
+ otherwise,     error(['unknown function type ' ftype]);
+end
+
+CPT = zeros(prod(psizes), self_size);
+ndx = find(f==0);
+CPT(ndx, 1) = psucc;
+CPT(ndx, 2) = pfail;
+ndx = find(f==1);
+CPT(ndx, 2) = psucc;
+CPT(ndx, 1) = pfail;
+if k > 0
+  CPT = reshape(CPT, [psizes self_size]);  
+end
+
+clamp = 1;
+CPD = tabular_CPD(bnet, self, CPT, [], clamp);
+
+
+
+%%%%%%%%%%%%
+
+function f = eval_bool_fn(fname, n)
+% EVAL_BOOL_FN Evaluate a boolean function on all bit vectors of length n
+% f = eval_bool_fn(fname, n)
+%
+% e.g. f = eval_bool_fn(inline('x(1) & x(3)'), 3)
+% returns   0     0     0     0     0     1     0     1
+
+ns = 2*ones(1, n);
+f = zeros(1, 2^n);
+bits = ind2subv(ns, 1:2^n);
+for i=1:2^n
+  f(i) = feval(fname, bits(i,:)-1);
+end
+
+%%%%%%%%%%%%%%%
+
+function f = mk_rnd_bool_fn(n)
+% MK_RND_BOOL_FN Make a random bit vector of length n that encodes a non-redundant boolean function
+% f = mk_rnd_bool_fn(n)
+
+red = 1;
+while red
+  f = sample_discrete([0.5 0.5], 2^n, 1)-1;
+  red = redundant_bool_fn(f);
+end
+
+%%%%%%%%
+
+
+function red = redundant_bool_fn(f)
+% REDUNDANT_BOOL_FN Does a boolean function depend on all its input values?
+% r = redundant_bool_fn(f)
+%
+% f is a vector of length 2^n, representing the output for each bit vector.
+% An input is redundant if there is no assignment to the other bits
+% which changes the output e.g., input 1 is redundant if u(2:n) s.t.,
+% f([0 u(2:n)]) <> f([1 u(2:n)]). 
+% A function is redundant it it has any redundant inputs.
+
+n = log2(length(f));
+ns = 2*ones(1,n);
+red = 0;
+for i=1:n
+  ens = ns;
+  ens(i) = 1;
+  U = ind2subv(ens, 1:2^(n-1));
+  U(:,i) = 1;
+  f1 = f(subv2ind(ns, U));
+  U(:,i) = 2;
+  f2 = f(subv2ind(ns, U));
+  if isequal(f1, f2)
+    red = 1;
+    return;
+  end
+end
+
+
+%%%%%%%%%%
+
+function [b, iter] = rnd_truth_table(N)
+% RND_TRUTH_TABLE Construct the output of a random truth table s.t. each input is non-redundant
+% b = rnd_truth_table(N)
+%
+% N is the number of inputs. 
+% b is a random bit string of length N, representing the output of the truth table.
+% Non-redundant means that, for each input position k,
+% there are at least two bit patterns, u and v, that differ only in the k'th position,
+% s.t., f(u) ~= f(v), where f is the function represented by b.
+% We use rejection sampling to ensure non-redundancy.
+%
+% Example: b = [0 0 0 1  0 0 0 1] is indep of 3rd input (AND of inputs 1 and 2)
+
+bits = ind2subv(2*ones(1,N), 1:2^N)-1;
+redundant = 1;
+iter = 0;
+while redundant & (iter < 4)
+  iter = iter + 1;
+  b = sample_discrete([0.5 0.5], 1, 2^N)-1;
+  redundant = 0;
+  for i=1:N
+    on = find(bits(:,i)==1);
+    off = find(bits(:,i)==0);
+    if isequal(b(on), b(off))
+      redundant = 1;
+      break;
+    end
+  end
+end
+