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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(2,4,2);
pfin = 0.8;
termprob{2}(1,:,2) = [0 0 0 pfin]; % finish in state 4 (DU)
termprob{2}(1,:,1) = 1 - [0 0 0 pfin];
if topright
termprob{2}(2,:,2) = [0 0 0 pfin];
termprob{2}(2,:,1) = 1 - [0 0 0 pfin];
else
termprob{2}(2,:,2) = [0 0 pfin 0]; % finish in state 3 (RL)
termprob{2}(2,:,1) = 1 - [0 0 pfin 0];
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);
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