comparison toolboxes/FullBNT-1.0.7/bnt/examples/dynamic/HHMM/Square/mk_square_hhmm.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function bnet = mk_square_hhmm(discrete_obs, true_params, topright)
+
+% Make a 3 level  HHMM described by the following grammar
+%
+% Square -> CLK | CCK % clockwise or counterclockwise
+% CLK -> LR UD RL DU start on top left (1 2 3 4)
+% CCK -> RL UD LR DU  if start at top right (3 2 1 4)
+% CCK -> UD LR DU RL if start at top left (2 1 4 3)
+%
+% LR = left-right, UD = up-down, RL = right-left, DU = down-up
+% LR, UD, RL, DU are sub HMMs.
+%
+% For discrete observations, the subHMMs are 2-state left-right.
+% LR emits L then l, etc.
+%
+% For cts observations, the subHMMs are 1 state.
+% LR emits a vector in the -> direction, with a little noise.
+% Since there is no constraint that we remain in the LR state as long as the RL state,
+% the sides of the square might have different lengths,
+% so the result is not really a square!
+%
+% If true_params = 0, we use random parameters at the top 2 levels
+% (ready for learning). At the bottom level, we use noisy versions
+% of the "true" observations.
+%
+% If topright=1, counter-clockwise starts at top right, not top left
+% This example was inspired by Ivanov and Bobick.
+
+if nargin < 3, topright = 1; end
+
+if 1 % discrete_obs
+  Qsizes = [2 4 2];
+else
+  Qsizes = [2 4 1];
+end
+
+D = 3;
+Qnodes = 1:D;
+startprob = cell(1,D);
+transprob = cell(1,D);
+termprob = cell(1,D);
+
+% LEVEL 1
+
+startprob{1} = 'unif';
+transprob{1} = 'unif';
+
+% LEVEL 2
+
+if true_params
+  startprob{2} = zeros(2, 4);
+  startprob{2}(1, :) = [1 0 0 0];
+  if topright
+    startprob{2}(2, :) = [0 0 1 0];
+  else
+    startprob{2}(2, :) = [0 1 0 0];
+  end
+  
+  transprob{2} = zeros(4, 2, 4);
+  
+  transprob{2}(:,1,:) = [0 1 0 0
+		    0 0 1 0
+		    0 0 0 1
+		    0 0 0 1]; % 4->e
+  if topright
+    transprob{2}(:,2,:) = [0 0 0 1
+		    1 0 0 0
+		    0 1 0 0
+		    0 0 0 1]; % 4->e
+  else
+    transprob{2}(:,2,:) = [0 0 0 1
+		    1 0 0 0
+		    0 0 1 0 % 3->e
+		    0 0 1 0];
+  end
+  
+  %termprob{2} = 'rightstop';
+  termprob{2} = zeros(2,4);
+  pfin = 0.8;
+  termprob{2}(1,:) = [0 0 0 pfin]; % finish in state 4 (DU)
+  if topright
+    termprob{2}(2,:) = [0 0 0 pfin];
+  else
+    termprob{2}(2,:) = [0 0 pfin 0];  % finish in state 3 (RL)
+  end
+else
+  % In the unsupervised case, it is essential that we break symmetry
+  % in the initial param estimates.
+  %startprob{2} = 'unif';
+  %transprob{2} = 'unif';
+  %termprob{2} = 'unif';
+  startprob{2} = 'rnd';
+  transprob{2} = 'rnd';
+  termprob{2} = 'rnd';
+end
+
+% LEVEL 3
+
+if 1 |  true_params
+  startprob{3} = 'leftstart';
+  transprob{3}  = 'leftright';
+  termprob{3} = 'rightstop';
+else
+  % If we want to be able to run a base-level model backwards...
+  startprob{3} = 'rnd';
+  transprob{3}  = 'rnd';
+  termprob{3} = 'rnd';
+end
+ 
+
+% OBS LEVEl
+
+if discrete_obs
+  % Initialise observations of lowest level primitives in a way which we can interpret
+  chars = ['L', 'l', 'U', 'u', 'R', 'r', 'D', 'd'];
+  L=find(chars=='L'); l=find(chars=='l');
+  U=find(chars=='U'); u=find(chars=='u');
+  R=find(chars=='R'); r=find(chars=='r');
+  D=find(chars=='D'); d=find(chars=='d');
+  Osize = length(chars);
+  
+  if true_params
+    p = 1; % makes each state fully observed
+  else
+    p = 0.9;
+  end
+  
+  obsprob = (1-p)*ones([4 2 Osize]);
+  %       Q2 Q3 O
+  obsprob(1, 1, L) =  p;
+  obsprob(1, 2, l) =  p;
+  obsprob(2, 1, U) =  p;
+  obsprob(2, 2, u) =  p;
+  obsprob(3, 1, R) =  p;
+  obsprob(3, 2, r) =  p;
+  obsprob(4, 1, D) =  p;
+  obsprob(4, 2, d) =  p;
+  obsprob = mk_stochastic(obsprob);
+  Oargs = {'CPT', obsprob};
+else
+  % Initialise means of lowest level primitives in a way which we can interpret
+  % These means are little vectors in the east, south, west, north directions.
+  % (left-right=east, up-down=south, right-left=west, down-up=north)
+  Osize = 2;
+  mu = zeros(2, Qsizes(2), Qsizes(3));
+  scale = 3;
+  if true_params
+    noise = 0;
+  else
+    noise = 0.5*scale;
+  end
+  for q3=1:Qsizes(3)
+    mu(:, 1, q3) = scale*[1;0] + noise*rand(2,1);
+  end
+  for q3=1:Qsizes(3)
+    mu(:, 2, q3) = scale*[0;-1] + noise*rand(2,1);
+  end
+  for q3=1:Qsizes(3)
+    mu(:, 3, q3) = scale*[-1;0] + noise*rand(2,1);
+  end
+  for q3=1:Qsizes(3)
+    mu(:, 4, q3) = scale*[0;1] + noise*rand(2,1);
+  end
+  Sigma = repmat(reshape(scale*eye(2), [2 2 1 1 ]), [1 1 Qsizes(2) Qsizes(3)]);
+  Oargs = {'mean', mu, 'cov', Sigma, 'cov_type', 'diag'};
+end
+
+if discrete_obs
+  selfprob = 0.5;
+else
+  selfprob = 0.95;
+  % If less than this, it won't look like a square
+  % because it doesn't spend enough time in each state
+  % Unfortunately, the variance on durations (lengths of each side)
+  % is very large
+end
+bnet = mk_hhmm('Qsizes', Qsizes, 'Osize', Osize', 'discrete_obs', discrete_obs, ...
+	       'Oargs', Oargs, 'Ops', Qnodes(2:3), 'selfprob', selfprob, ...
+	       'startprob', startprob, 'transprob', transprob, 'termprob', termprob);
+