comparison toolboxes/FullBNT-1.0.7/bnt/inference/static/@belprop_mrf2_inf_engine/bp_mrf2.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [new_bel, niter, new_msg, edge_id, nstates] = bp_mrf2_general(adj_mat, pot, local_evidence, varargin)
+% BP_MRF2_GENERAL Belief propagation on an MRF with pairwise potentials
+% function [bel, niter] = bp_mrf2_general(adj_mat, pot, local_evidence, varargin)
+%
+% Input:
+% adj_mat(i,j) = 1 iff there is an edge between nodes i and j
+% pot(ki,kj,i,j) or pot{i,j}(ki,kj) = potential on edge between nodes i,j
+%   If the potentials on all edges are the same,
+%   you can just pass in 1 array, pot(ki,kj)
+% local_evidence(state, node) or local_evidence{i}(k) = Pr(observation at node i | Xi=k)
+%
+% Use cell arrays if the hidden nodes do not all have the same number of values.
+%
+% Output:
+% bel(k,i) or bel{i}(k) = P(Xi=k|evidence)
+% niter contains the number of iterations used 
+%
+% [ ... ] = bp_mrf2(..., 'param1',val1, 'param2',val2, ...)
+% allows you to specify optional parameters as name/value pairs.
+% Parameters names are below [default value in brackets]
+%
+% max_iter - max. num. iterations [ 5*nnodes]
+% momentum - weight assigned to old message in convex combination
+%            (useful for damping oscillations) - currently ignored i[0]
+% tol      - tolerance used to assess convergence [1e-3]
+% maximize - 1 means use max-product, 0 means use sum-product [0]
+% verbose - 1 means print error at every iteration [0]
+%
+% fn - name of function to call at end of every iteration [ [] ]
+% fnargs - we call feval(fn, bel, iter, fnargs{:}) [ [] ]
+
+nnodes = length(adj_mat);
+
+[max_iter, momentum, tol, maximize, verbose, fn, fnargs] = ...
+    process_options(varargin, 'max_iter', 5*nnodes, 'momentum', 0, ...
+		    'tol', 1e-3, 'maximize', 0, 'verbose', 0, ...
+		    'fn', [], 'fnargs', []);
+
+if iscell(local_evidence)
+  use_cell = 1;
+else
+  use_cell = 0;
+  [nstates nnodes] = size(local_evidence);
+end
+
+if iscell(pot)
+  tied_pot = 0;
+else
+  tied_pot = (ndims(pot)==2);
+end
+
+
+% give each edge a unique number
+ndx = find(adj_mat);
+nedges = length(ndx);
+edge_id = zeros(1, nnodes*nnodes);
+edge_id(ndx) = 1:nedges; 
+edge_id = reshape(edge_id, nnodes, nnodes);
+
+% initialise messages
+if use_cell
+  prod_of_msgs = cell(1, nnodes);
+  old_bel = cell(1, nnodes);
+  nstates = zeros(1, nnodes);
+  old_msg = cell(1, nedges);
+  for i=1:nnodes
+    nstates(i) = length(local_evidence{i});
+    prod_of_msgs{i} = local_evidence{i};
+    old_bel{i} = local_evidence{i};
+  end
+  for i=1:nnodes
+    nbrs = find(adj_mat(:,i));
+    for j=nbrs(:)'
+      old_msg{edge_id(i,j)} = normalise(ones(nstates(j),1));
+    end
+  end
+else
+  prod_of_msgs = local_evidence;
+  old_bel = local_evidence;
+  %old_msg = zeros(nstates, nnodes, nnodes); 
+  old_msg = zeros(nstates, nedges); 
+  m = normalise(ones(nstates,1));
+  for i=1:nnodes
+    nbrs = find(adj_mat(:,i));
+    for j=nbrs(:)'
+      old_msg(:, edge_id(i,j)) = m;
+      %old_msg(:,i,j) = m;
+    end
+  end
+end
+
+
+converged = 0;
+iter = 1;
+
+while ~converged & (iter <= max_iter)
+  
+  % each node sends a msg to each of its neighbors
+  for i=1:nnodes
+    nbrs = find(adj_mat(i,:));
+    for j=nbrs(:)'
+      if tied_pot
+	pot_ij = pot;
+      else
+	if iscell(pot)
+	  pot_ij = pot{i,j};
+	else
+	  pot_ij = pot(:,:,i,j);
+	end
+      end
+      pot_ij = pot_ij'; % now pot_ij(xj, xi) 
+      % so pot_ij * msg(xi) = sum_xi pot(xj,xi) msg(xi) = f(xj)
+
+      if 1
+	% Compute temp = product of all incoming msgs except from j
+	% by dividing out old msg from j from the product of all msgs sent to i
+	if use_cell
+	  temp = prod_of_msgs{i};
+	  m = old_msg{edge_id(j,i)};
+	else
+	  temp = prod_of_msgs(:,i);
+	  m = old_msg(:, edge_id(j,i));
+	end
+	if any(m==0)
+	  fprintf('iter=%d, send from i=%d to j=%d\n', iter, i, j);
+	  keyboard
+	end
+	m = m + (m==0); % valid since m(k)=0 => temp(k)=0, so can replace 0's with anything
+	temp = temp ./ m;
+	temp_div = temp;
+      end
+      
+      if 1
+	% Compute temp = product of all incoming msgs except from j in obvious way
+	if use_cell
+	  %temp = ones(nstates(i),1);
+	  temp = local_evidence{i};
+	  for k=nbrs(:)'
+	    if k==j, continue, end;
+	    temp = temp .* old_msg{edge_id(k,i)};
+	  end
+	else
+	  %temp = ones(nstates,1);
+	  temp = local_evidence(:,i);
+	  for k=nbrs(:)'
+	    if k==j, continue, end;
+	    temp = temp .* old_msg(:, edge_id(k,i));
+	  end
+	end
+      end
+      %assert(approxeq(temp, temp_div))
+      assert(approxeq(normalise(pot_ij * temp), normalise(pot_ij * temp_div)))
+	
+      if maximize
+	newm = max_mult(pot_ij, temp); % bottleneck
+      else
+	newm = pot_ij * temp;
+      end
+      newm = normalise(newm);
+      if use_cell
+	new_msg{edge_id(i,j)} = newm;
+      else
+	new_msg(:, edge_id(i,j)) = newm;
+      end
+    end % for j 
+  end % for i
+  old_prod_of_msgs = prod_of_msgs;
+  
+  % each node multiplies all its incoming msgs and computes its local belief
+  if use_cell
+    for i=1:nnodes
+      nbrs = find(adj_mat(:,i));
+      prod_of_msgs{i} = local_evidence{i};
+      for j=nbrs(:)'
+	prod_of_msgs{i} = prod_of_msgs{i} .* new_msg{edge_id(j,i)};
+      end
+      new_bel{i} = normalise(prod_of_msgs{i});
+    end
+    err = abs(cat(1,new_bel{:}) - cat(1, old_bel{:}));
+  else
+    for i=1:nnodes
+      nbrs = find(adj_mat(:,i));
+      prod_of_msgs(:,i) = local_evidence(:,i);
+      for j=nbrs(:)'
+	prod_of_msgs(:,i) = prod_of_msgs(:,i) .* new_msg(:,edge_id(j,i));
+      end
+      new_bel(:,i) = normalise(prod_of_msgs(:,i));
+    end
+    err = abs(new_bel(:) - old_bel(:));
+  end
+  converged = all(err < tol);
+  if verbose, fprintf('error at iter %d = %f\n', iter, sum(err)); end
+  if ~isempty(fn)
+    if isempty(fnargs)
+      feval(fn, new_bel);
+    else
+      feval(fn, new_bel, iter, fnargs{:});
+    end
+  end
+  
+  iter = iter + 1;
+  old_msg = new_msg;
+  old_bel = new_bel;
+end % while
+
+niter = iter-1;
+
+fprintf('converged in %d iterations\n', niter);
+