Daniel@0: function [sampled_graphs, accept_ratio, num_edges] = learn_struct_mcmc(data, ns, varargin)
Daniel@0: % MY_LEARN_STRUCT_MCMC  Monte Carlo Markov Chain search over DAGs assuming fully observed data
Daniel@0: % [sampled_graphs, accept_ratio, num_edges] = learn_struct_mcmc(data, ns, ...)
Daniel@0: % 
Daniel@0: % data(i,m) is the value of node i in case m.
Daniel@0: % ns(i) is the number of discrete values node i can take on.
Daniel@0: %
Daniel@0: % sampled_graphs{m} is the m'th sampled graph.
Daniel@0: % accept_ratio(t) = acceptance ratio at iteration t
Daniel@0: % num_edges(t) = number of edges in model at iteration t
Daniel@0: %
Daniel@0: % The following optional arguments can be specified in the form of name/value pairs:
Daniel@0: % [default value in brackets]
Daniel@0: %
Daniel@0: % scoring_fn - 'bayesian' or 'bic' [ 'bayesian' ]
Daniel@0: %              Currently, only networks with all tabular nodes support Bayesian scoring.
Daniel@0: % type       - type{i} is the type of CPD to use for node i, where the type is a string
Daniel@0: %              of the form 'tabular', 'noisy_or', 'gaussian', etc. [ all cells contain 'tabular' ]
Daniel@0: % params     - params{i} contains optional arguments passed to the CPD constructor for node i,
Daniel@0: %              or [] if none.  [ all cells contain {'prior', 1}, meaning use uniform Dirichlet priors ]
Daniel@0: % discrete   - the list of discrete nodes [ 1:N ]
Daniel@0: % clamped    - clamped(i,m) = 1 if node i is clamped in case m [ zeros(N, ncases) ]
Daniel@0: % nsamples   - number of samples to draw from the chain after burn-in [ 100*N ]
Daniel@0: % burnin     - number of steps to take before drawing samples [ 5*N ]
Daniel@0: % init_dag   - starting point for the search [ zeros(N,N) ]
Daniel@0: %
Daniel@0: % e.g., samples = my_learn_struct_mcmc(data, ns, 'nsamples', 1000);
Daniel@0: %
Daniel@0: % Modified by Sonia Leach (SML) 2/4/02, 9/5/03
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: [n ncases] = size(data);
Daniel@0: 
Daniel@0: 
Daniel@0: % set default params
Daniel@0: type = cell(1,n);
Daniel@0: params = cell(1,n);
Daniel@0: for i=1:n
Daniel@0:  type{i} = 'tabular';
Daniel@0:  %params{i} = { 'prior', 1};
Daniel@0:  params{i} = { 'prior_type', 'dirichlet', 'dirichlet_weight', 1 };
Daniel@0: end
Daniel@0: scoring_fn = 'bayesian';
Daniel@0: discrete = 1:n;
Daniel@0: clamped = zeros(n, ncases);
Daniel@0: nsamples = 100*n;
Daniel@0: burnin = 5*n;
Daniel@0: dag = zeros(n);
Daniel@0: 
Daniel@0: args = varargin;
Daniel@0: nargs = length(args);
Daniel@0: for i=1:2:nargs
Daniel@0:  switch args{i},
Daniel@0:   case 'nsamples',   nsamples = args{i+1};
Daniel@0:   case 'burnin',     burnin = args{i+1};
Daniel@0:   case 'init_dag',   dag = args{i+1};
Daniel@0:   case 'scoring_fn', scoring_fn = args{i+1};
Daniel@0:   case 'type',       type = args{i+1}; 
Daniel@0:   case 'discrete',   discrete = args{i+1}; 
Daniel@0:   case 'clamped',    clamped = args{i+1}; 
Daniel@0:   case 'params',     if isempty(args{i+1}), params = cell(1,n); else params = args{i+1};  end
Daniel@0:  end
Daniel@0: end
Daniel@0: 
Daniel@0: % We implement the fast acyclicity check described by P. Giudici and R. Castelo,
Daniel@0: % "Improving MCMC model search for data mining", submitted to J. Machine Learning, 2001.
Daniel@0: 
Daniel@0: % SML: also keep descendant matrix C
Daniel@0: use_giudici = 1;
Daniel@0: if use_giudici
Daniel@0:  [nbrs, ops, nodes, A] = mk_nbrs_of_digraph(dag);
Daniel@0: else
Daniel@0:  [nbrs, ops, nodes] = mk_nbrs_of_dag(dag);
Daniel@0:  A = [];
Daniel@0: end
Daniel@0: 
Daniel@0: num_accepts = 1;
Daniel@0: num_rejects = 1;
Daniel@0: T = burnin + nsamples;
Daniel@0: accept_ratio = zeros(1, T);
Daniel@0: num_edges = zeros(1, T);
Daniel@0: sampled_graphs = cell(1, nsamples);
Daniel@0: %sampled_bitv = zeros(nsamples, n^2);
Daniel@0: 
Daniel@0: for t=1:T
Daniel@0:  [dag, nbrs, ops, nodes, A, accept] = take_step(dag, nbrs, ops, ...
Daniel@0:                     nodes, ns, data, clamped, A, ...
Daniel@0:                       scoring_fn, discrete, type, params);
Daniel@0:  num_edges(t) = sum(dag(:));
Daniel@0:  num_accepts = num_accepts + accept;
Daniel@0:  num_rejects = num_rejects + (1-accept);
Daniel@0:  accept_ratio(t) =  num_accepts/num_rejects;
Daniel@0:  if t > burnin
Daniel@0:    sampled_graphs{t-burnin} = dag;
Daniel@0:    %sampled_bitv(t-burnin, :) = dag(:)';
Daniel@0:  end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%%%
Daniel@0: 
Daniel@0: 
Daniel@0: function [new_dag, new_nbrs, new_ops, new_nodes, A,  accept] = ...
Daniel@0:    take_step(dag, nbrs, ops, nodes, ns, data, clamped, A,  ...
Daniel@0:      scoring_fn, discrete, type, params, prior_w)
Daniel@0: 
Daniel@0: 
Daniel@0: use_giudici = ~isempty(A);
Daniel@0: if use_giudici
Daniel@0:  [new_dag, op, i, j, new_A] =  pick_digraph_nbr(dag, nbrs, ops, nodes,A); % updates A
Daniel@0:  [new_nbrs, new_ops, new_nodes] =  mk_nbrs_of_digraph(new_dag, new_A);
Daniel@0: else
Daniel@0:  d = sample_discrete(normalise(ones(1, length(nbrs))));
Daniel@0:  new_dag = nbrs{d};
Daniel@0:  op = ops{d};
Daniel@0:  i = nodes(d, 1); j = nodes(d, 2);
Daniel@0:  [new_nbrs, new_ops, new_nodes] = mk_nbrs_of_dag(new_dag);
Daniel@0: end
Daniel@0: 
Daniel@0: bf =  bayes_factor(dag, new_dag, op, i, j, ns, data, clamped, scoring_fn, discrete, type, params);
Daniel@0: 
Daniel@0: %R = bf * (new_prior / prior) * (length(nbrs) / length(new_nbrs)); 
Daniel@0: R = bf * (length(nbrs) / length(new_nbrs)); 
Daniel@0: u = rand(1,1);
Daniel@0: if u > min(1,R) % reject the move
Daniel@0:  accept = 0;
Daniel@0:  new_dag = dag;
Daniel@0:  new_nbrs = nbrs;
Daniel@0:  new_ops = ops;
Daniel@0:  new_nodes = nodes;
Daniel@0: else
Daniel@0:  accept = 1;
Daniel@0:  if use_giudici
Daniel@0: A = new_A; % new_A already updated in pick_digraph_nbr
Daniel@0:  end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%%%
Daniel@0: 
Daniel@0: function bfactor = bayes_factor(old_dag, new_dag, op, i, j, ns, data, clamped, scoring_fn, discrete, type, params)
Daniel@0: 
Daniel@0: u = find(clamped(j,:)==0);
Daniel@0: LLnew = score_family(j, parents(new_dag, j), type{j}, scoring_fn, ns, discrete, data(:,u), params{j});
Daniel@0: LLold = score_family(j, parents(old_dag, j), type{j}, scoring_fn, ns, discrete, data(:,u), params{j});
Daniel@0: bf1 = exp(LLnew - LLold);
Daniel@0: 
Daniel@0: if strcmp(op, 'rev')  % must also multiply in the changes to i's family
Daniel@0:  u = find(clamped(i,:)==0);
Daniel@0:  LLnew = score_family(i, parents(new_dag, i), type{i}, scoring_fn, ns, discrete, data(:,u), params{i});
Daniel@0:  LLold = score_family(i, parents(old_dag, i), type{i}, scoring_fn, ns, discrete, data(:,u), params{i});
Daniel@0:  bf2 = exp(LLnew - LLold);
Daniel@0: else
Daniel@0:  bf2 = 1;
Daniel@0: end
Daniel@0: bfactor = bf1 * bf2;
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%% Giudici stuff follows %%%%%%%%%%
Daniel@0: 
Daniel@0: 
Daniel@0: % SML: This now updates A as it goes from digraph it choses
Daniel@0: function [new_dag, op, i, j, new_A] = pick_digraph_nbr(dag, digraph_nbrs, ops, nodes, A)
Daniel@0: 
Daniel@0: d = sample_discrete(normalise(ones(1, length(digraph_nbrs))));
Daniel@0: %d = myunidrnd(length(digraph_nbrs),1,1);
Daniel@0: i = nodes(d, 1); j = nodes(d, 2);
Daniel@0: new_dag = digraph_nbrs(:,:,d);
Daniel@0: op = ops{d};
Daniel@0: new_A = update_ancestor_matrix(A, op, i, j, new_dag); 
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%
Daniel@0: 
Daniel@0: 
Daniel@0: function A = update_ancestor_matrix(A,  op, i, j, dag)
Daniel@0: 
Daniel@0: switch op
Daniel@0: case 'add',
Daniel@0:  A = do_addition(A,  op, i, j, dag);
Daniel@0: case 'del', 
Daniel@0:  A = do_removal(A,  op, i, j, dag);
Daniel@0: case 'rev', 
Daniel@0:  A = do_removal(A,  op, i, j, dag);
Daniel@0:  A = do_addition(A,  op, j, i, dag);
Daniel@0: end
Daniel@0: 
Daniel@0:  
Daniel@0: %%%%%%%%%%%%
Daniel@0: 
Daniel@0: function A = do_addition(A, op, i, j, dag)
Daniel@0: 
Daniel@0: A(j,i) = 1; % i is an ancestor of j
Daniel@0: anci = find(A(i,:));
Daniel@0: if ~isempty(anci)
Daniel@0:  A(j,anci) = 1; % all of i's ancestors are added to Anc(j)
Daniel@0: end
Daniel@0: ancj = find(A(j,:));
Daniel@0: descj = find(A(:,j)); 
Daniel@0: if ~isempty(ancj)
Daniel@0:  for k=descj(:)'
Daniel@0:    A(k,ancj) = 1; % all of j's ancestors are added to each descendant of j
Daniel@0:  end
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%
Daniel@0: function A = do_removal(A, op, i, j, dag)
Daniel@0: 
Daniel@0: % find all the descendants of j, and put them in topological order
Daniel@0: 
Daniel@0: % SML: originally Kevin had the next line commented and the %* lines
Daniel@0: % being used but I think this is equivalent and much less expensive
Daniel@0: % I assume he put it there for debugging and never changed it back...?
Daniel@0: descj = find(A(:,j));
Daniel@0: %*  R = reachability_graph(dag);
Daniel@0: %*  descj = find(R(j,:));
Daniel@0: 
Daniel@0: order = topological_sort(dag);
Daniel@0: 
Daniel@0: % SML: originally Kevin used the %* line but this was extracting the
Daniel@0: % wrong things to sort
Daniel@0: %* descj_topnum = order(descj);
Daniel@0: [junk, perm] = sort(order); %SML:node i is perm(i)-TH in order
Daniel@0: descj_topnum = perm(descj); %SML:descj(i) is descj_topnum(i)-th in order
Daniel@0: 
Daniel@0: % SML: now re-sort descj by rank in descj_topnum
Daniel@0: [junk, perm] = sort(descj_topnum);
Daniel@0: descj = descj(perm);
Daniel@0: 
Daniel@0: % Update j and all its descendants
Daniel@0: A = update_row(A, j, dag);
Daniel@0: for k = descj(:)'
Daniel@0:    A = update_row(A, k, dag);
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%
Daniel@0: 
Daniel@0: function A = old_do_removal(A, op, i, j, dag)
Daniel@0: 
Daniel@0: % find all the descendants of j, and put them in topological order
Daniel@0: % SML: originally Kevin had the next line commented and the %* lines
Daniel@0: % being used but I think this is equivalent and much less expensive
Daniel@0: % I assume he put it there for debugging and never changed it back...?
Daniel@0: descj = find(A(:,j)); 
Daniel@0: %*  R = reachability_graph(dag);
Daniel@0: %*  descj = find(R(j,:)); 
Daniel@0: 
Daniel@0: order = topological_sort(dag);
Daniel@0: descj_topnum = order(descj);
Daniel@0: [junk, perm] = sort(descj_topnum);
Daniel@0: descj = descj(perm);
Daniel@0: % Update j and all its descendants
Daniel@0: A = update_row(A, j, dag);
Daniel@0: for k = descj(:)'
Daniel@0:  A = update_row(A, k, dag);
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%
Daniel@0: 
Daniel@0: function A = update_row(A, j, dag)
Daniel@0: 
Daniel@0: % We compute row j of A
Daniel@0: A(j, :) = 0;
Daniel@0: ps = parents(dag, j);
Daniel@0: if ~isempty(ps)
Daniel@0:  A(j, ps) = 1;
Daniel@0: end
Daniel@0: for k=ps(:)'
Daniel@0:  anck = find(A(k,:));
Daniel@0:  if ~isempty(anck)
Daniel@0:    A(j, anck) = 1;
Daniel@0:  end
Daniel@0: end
Daniel@0:  
Daniel@0: %%%%%%%%
Daniel@0: 
Daniel@0: function A = init_ancestor_matrix(dag)
Daniel@0: 
Daniel@0: order = topological_sort(dag);
Daniel@0: A = zeros(length(dag));
Daniel@0: for j=order(:)'
Daniel@0:  A = update_row(A, j, dag);
Daniel@0: end