comparison toolboxes/FullBNT-1.0.7/bnt/learning/learn_struct_pdag_pc.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [pdag, G] = learn_struct_pdag_pc(cond_indep, n, k, varargin)
+% LEARN_STRUCT_PDAG_PC Learn a partially oriented DAG (pattern) using the PC algorithm
+% P = learn_struct_pdag_pc(cond_indep, n, k, ...)
+%
+% n is the number of nodes.
+% k is an optional upper bound on the fan-in (default: n)
+% cond_indep is a boolean function that will be called as follows:
+%   feval(cond_indep, x, y, S, ...)
+% where x and y are nodes, and S is a set of nodes (positive integers),
+% and ... are any optional parameters passed to this function.
+%
+% The output P is an adjacency matrix, in which
+% P(i,j) = -1 if there is an i->j edge.
+% P(i,j) = P(j,i) = 1 if there is an undirected edge i <-> j
+%
+% The PC algorithm does structure learning assuming all variables are observed.
+% See Spirtes, Glymour and Scheines, "Causation, Prediction and Search", 1993, p117.
+% This algorithm may take O(n^k) time if there are n variables and k is the max fan-in,
+% but this is quicker than the Verma-Pearl IC algorithm, which is always O(n^n).
+
+  
+sep = cell(n,n);
+ord = 0;
+done = 0;
+G = ones(n,n);
+G=setdiag(G,0);
+while ~done
+  done = 1;
+  [X,Y] = find(G); 
+  for i=1:length(X)
+    x = X(i); y = Y(i);
+    %nbrs = mysetdiff(myunion(neighbors(G, x), neighbors(G,y)), [x y]);
+    nbrs = mysetdiff(neighbors(G, y), x);  % bug fix by Raanan Yehezkel <[e-mail]> 6/27/04
+    if length(nbrs) >= ord & G(x,y) ~= 0
+      done = 0;
+      %SS = subsets(nbrs, ord, ord); % all subsets of size ord
+      SS = subsets1(nbrs, ord);
+      for si=1:length(SS)
+	S = SS{si};
+	if feval(cond_indep, x, y, S, varargin{:})
+	  %if isempty(S)
+ 	  %  fprintf('%d indep of %d ', x, y);
+	  %else
+ 	  %  fprintf('%d indep of %d given ', x, y); fprintf('%d ', S);
+ 	  %end
+ 	  %fprintf('\n');
+	  
+	  % diagnostic
+	  %[CI, r] = cond_indep_fisher_z(x, y, S, varargin{:});
+	  %fprintf(': r = %6.4f\n', r);
+	  
+	  G(x,y) = 0;
+	  G(y,x) = 0;
+	  sep{x,y} = myunion(sep{x,y}, S);
+	  sep{y,x} = myunion(sep{y,x}, S);
+	  break; % no need to check any more subsets 
+	end
+      end
+    end 
+  end
+  ord = ord + 1;
+end
+
+
+% Create the minimal pattern,
+% i.e., the only directed edges are V structures.
+pdag = G;
+[X, Y] = find(G);
+% We want to generate all unique triples x,y,z
+% This code generates x,y,z and z,y,x.
+for i=1:length(X)
+  x = X(i);
+  y = Y(i);
+  Z = find(G(y,:));
+  Z = mysetdiff(Z, x);
+  for z=Z(:)'
+    if G(x,z)==0 & ~ismember(y, sep{x,z}) & ~ismember(y, sep{z,x})
+      %fprintf('%d -> %d <- %d\n', x, y, z);
+      pdag(x,y) = -1; pdag(y,x) = 0;
+      pdag(z,y) = -1; pdag(y,z) = 0;
+    end
+  end
+end
+
+% Convert the minimal pattern to a complete one,
+% i.e., every directed edge in P is compelled
+% (must be directed in all Markov equivalent models),
+% and every undirected edge in P is reversible.
+% We use the rules of Pearl (2000) p51 (derived in Meek (1995))
+
+old_pdag = zeros(n);
+iter = 0;
+while ~isequal(pdag, old_pdag)
+  iter = iter + 1;
+  old_pdag = pdag;
+  % rule 1
+  [A,B] = find(pdag==-1); % a -> b
+  for i=1:length(A)
+    a = A(i); b = B(i);
+    C = find(pdag(b,:)==1 & G(a,:)==0); % all nodes adj to b but not a
+    if ~isempty(C)
+      pdag(b,C) = -1; pdag(C,b) = 0;
+      %fprintf('rule 1: a=%d->b=%d and b=%d-c=%d implies %d->%d\n', a, b, b, C, b, C);
+    end
+  end
+  % rule 2
+  [A,B] = find(pdag==1); % unoriented a-b edge
+  for i=1:length(A)
+    a = A(i); b = B(i);
+    if any( (pdag(a,:)==-1) & (pdag(:,b)==-1)' );
+      pdag(a,b) = -1; pdag(b,a) = 0;
+      %fprintf('rule 2: %d -> %d\n', a, b);
+    end
+  end
+  % rule 3
+  [A,B] = find(pdag==1); % a-b
+  for i=1:length(A)
+    a = A(i); b = B(i);
+    C = find( (pdag(a,:)==1) & (pdag(:,b)==-1)' );
+    % C contains nodes c s.t. a-c->ba
+    G2 = setdiag(G(C, C), 1);
+    if any(G2(:)==0) % there are 2 different non adjacent elements of C
+      pdag(a,b) = -1; pdag(b,a) = 0;
+      %fprintf('rule 3: %d -> %d\n', a, b);
+    end
+  end
+end
+
+