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function [bnet, Qnodes, Fnodes, Onode] = mk_hhmm(varargin)
% MK_HHMM Make a Hierarchical HMM
% function [bnet, Qnodes, Fnodes, Onode] = mk_hhmm(...)
%
% e.g. 3-layer hierarchical HMM where level 1 only connects to level 2
% and the parents of the observed node are levels 2 and 3.
% (This DBN is the same as Fig 10 in my tech report.)
%
% Q1 ----------> Q1
% | \ ^ |
% | v / |
% | F2 ------/ |
% | ^ ^ \ |
% | / | \ |
% | / | ||
% v | vv
% Q2----| --------> Q2
% /| \ | ^|
% / | v | / |
% | | F3 --------/ |
% | | ^ \ |
% | v / v v
% | Q3 -----------> Q3
% | |
% \ |
% v v
% O
%
%
% Optional arguments in name/value format [default value in brackets]
%
% Qsizes - sizes at each level [ none ]
% allQ - 1 means level i connects to all Q levels below, 0 means just to i+1 [0]
% transprob - transprob{d}(i,k,j) = P(Q(d,t)=j|Q(d,t-1)=i,Q(1:d-1,t)=k) ['leftright']
% startprob - startprob{d}(k,j) = P(Q(d,t)=j|Q(1:d-1,t)=k) ['leftstart']
% termprob - termprob{d}(k,j) = P(F(d,t)=2|Q(1:d-1,t)=k,Q(d,t)=j) for d>1 ['rightstop']
% selfprop - prob of a self transition (termprob default = 1-selfprop) [0.8]
% Osize - size of O node
% discrete_obs - 1 means O is tabular_CPD, 0 means gaussian_CPD [0]
% Oargs - cell array of args to pass to the O CPD [ {} ]
% Ops - Q parents of O [Qnodes(end)]
% F1 - 1 means level 1 can finish (restart), else there is no F1->Q1 arc [0]
% clamp1 - 1 means we clamp the params of the Q nodes in slice 1 (Qt1params) [1]
% Note: the Qt1params are startprob, which should be shared with other slices.
% However, in the current implementation, the Qt1params will only be estimated
% from the initial state of each sequence.
%
% For d=1, startprob{1}(1,j) is only used in the first slice and
% termprob{1} is ignored, since we assume the top level never resets.
% Also, transprob{1}(i,j) can be used instead of transprob{1}(i,1,j).
%
% leftstart means the model always starts in state 1.
% rightstop means the model can only finish in its last state (Qsize(d)).
% unif means each state is equally like to reach any other
% rnd means the transition/starting probs are random (drawn from rand)
%
% Q1:QD in slice 1 are of type tabular_CPD
% Q1:QD in slice 2 are of type hhmmQ_CPD.
% F(2:D-1) is of type hhmmF_CPD, FD is of type tabular_CPD.
args = varargin;
nargs = length(args);
% get sizes of nodes and topology
Qsizes = [];
Osize = [];
allQ = 0;
Ops = [];
F1 = 0;
for i=1:2:nargs
switch args{i},
case 'Qsizes', Qsizes = args{i+1};
case 'Osize', Osize = args{i+1};
case 'allQ', allQ = args{i+1};
case 'Ops', Ops = args{i+1};
case 'F1', F1 = args{i+1};
end
end
if isempty(Qsizes), error('must specify Qsizes'); end
if Osize==0, error('must specify Osize'); end
D = length(Qsizes);
Qnodes = 1:D;
if isempty(Ops), Ops = Qnodes(end); end
[intra, inter, Qnodes, Fnodes, Onode] = mk_hhmm_topo(D, allQ, Ops, F1);
ss = length(intra);
names = {};
if F1
Fnodes_ndx = Fnodes;
else
Fnodes_ndx = [-1 Fnodes]; % Fnodes(1) is a dummy index
end
% set default params
discrete_obs = 0;
Oargs = {};
startprob = cell(1,D);
startprob{1} = 'unif';
for d=2:D
startprob{d} = 'leftstart';
end
transprob = cell(1,D);
transprob{1} = 'unif';
for d=2:D
transprob{d} = 'leftright';
end
termprob = cell(1,D);
for d=2:D
termprob{d} = 'rightstop';
end
selfprob = 0.8;
clamp1 = 1;
for i=1:2:nargs
switch args{i},
case 'discrete_obs', discrete_obs = args{i+1};
case 'Oargs', Oargs = args{i+1};
case 'startprob', startprob = args{i+1};
case 'transprob', transprob = args{i+1};
case 'termprob', termprob = args{i+1};
case 'selfprob', selfprob = args{i+1};
case 'clamp1', clamp1 = args{i+1};
end
end
ns = zeros(1,ss);
ns(Qnodes) = Qsizes;
ns(Onode) = Osize;
ns(Fnodes) = 2;
dnodes = [Qnodes Fnodes];
if discrete_obs
dnodes = [dnodes Onode];
end
onodes = [Onode];
bnet = mk_dbn(intra, inter, ns, 'observed', onodes, 'discrete', dnodes, 'names', names);
eclass = bnet.equiv_class;
for d=1:D
if d==1
Qps = [];
elseif allQ
Qps = Qnodes(1:d-1);
else
Qps = Qnodes(d-1);
end
Qpsz = prod(ns(Qps));
Qsz = ns(Qnodes(d));
if isstr(startprob{d})
switch startprob{d}
case 'unif', startprob{d} = mk_stochastic(ones(Qpsz, Qsz));
case 'rnd', startprob{d} = mk_stochastic(rand(Qpsz, Qsz));
case 'leftstart', startprob{d} = zeros(Qpsz, Qsz); startprob{d}(:,1) = 1;
end
end
if isstr(transprob{d})
switch transprob{d}
case 'unif', transprob{d} = mk_stochastic(ones(Qsz, Qpsz, Qsz));
case 'rnd', transprob{d} = mk_stochastic(rand(Qsz, Qpsz, Qsz));
case 'leftright',
LR = mk_leftright_transmat(Qsz, selfprob);
temp = repmat(reshape(LR, [1 Qsz Qsz]), [Qpsz 1 1]); % transprob(k,i,j)
transprob{d} = permute(temp, [2 1 3]); % now transprob(i,k,j)
end
end
if isstr(termprob{d})
switch termprob{d}
case 'unif', termprob{d} = mk_stochastic(ones(Qpsz, Qsz, 2));
case 'rnd', termprob{d} = mk_stochastic(rand(Qpsz, Qsz, 2));
case 'rightstop',
%termprob(k,i,t) Might terminate if i=Qsz; will not terminate if i<Qsz
stopprob = 1-selfprob;
termprob{d} = zeros(Qpsz, Qsz, 2);
termprob{d}(:,Qsz,2) = stopprob;
termprob{d}(:,Qsz,1) = 1-stopprob;
termprob{d}(:,1:(Qsz-1),1) = 1;
otherwise, error(['unrecognized termprob ' termprob{d}])
end
elseif d>1 % passed in termprob{d}(k,j)
temp = termprob{d};
termprob{d} = zeros(Qpsz, Qsz, 2);
termprob{d}(:,:,2) = temp;
termprob{d}(:,:,1) = ones(Qpsz,Qsz) - temp;
end
end
% SLICE 1
for d=1:D
bnet.CPD{eclass(Qnodes(d),1)} = tabular_CPD(bnet, Qnodes(d), 'CPT', startprob{d}, 'adjustable', clamp1);
end
if F1
d = 1;
bnet.CPD{eclass(Fnodes_ndx(d),1)} = hhmmF_CPD(bnet, Fnodes_ndx(d), Qnodes(d), Fnodes_ndx(d+1), ...
'termprob', termprob{d});
end
for d=2:D-1
if allQ
Qps = Qnodes(1:d-1);
else
Qps = Qnodes(d-1);
end
bnet.CPD{eclass(Fnodes_ndx(d),1)} = hhmmF_CPD(bnet, Fnodes_ndx(d), Qnodes(d), Fnodes_ndx(d+1), ...
'Qps', Qps, 'termprob', termprob{d});
end
bnet.CPD{eclass(Fnodes_ndx(D),1)} = tabular_CPD(bnet, Fnodes_ndx(D), 'CPT', termprob{D});
if discrete_obs
bnet.CPD{eclass(Onode,1)} = tabular_CPD(bnet, Onode, Oargs{:});
else
bnet.CPD{eclass(Onode,1)} = gaussian_CPD(bnet, Onode, Oargs{:});
end
% SLICE 2
%for d=1:D
% bnet.CPD{eclass(Qnodes(d),2)} = hhmmQ_CPD(bnet, Qnodes(d)+ss, Qnodes, d, D, ...
% 'startprob', startprob{d}, 'transprob', transprob{d}, ...
% 'allQ', allQ);
%end
d = 1;
if F1
bnet.CPD{eclass(Qnodes(d),2)} = hhmmQ_CPD(bnet, Qnodes(d)+ss, 'Fself', Fnodes_ndx(d), ...
'Fbelow', Fnodes_ndx(d+1), ...
'startprob', startprob{d}, 'transprob', transprob{d});
else
bnet.CPD{eclass(Qnodes(d),2)} = hhmmQ_CPD(bnet, Qnodes(d)+ss, ...
'Fbelow', Fnodes_ndx(d+1), ...
'startprob', startprob{d}, 'transprob', transprob{d});
end
for d=2:D-1
if allQ
Qps = Qnodes(1:d-1);
else
Qps = Qnodes(d-1);
end
Qps = Qps + ss; % since all in slice 2
bnet.CPD{eclass(Qnodes(d),2)} = hhmmQ_CPD(bnet, Qnodes(d)+ss, 'Fself', Fnodes_ndx(d), ...
'Fbelow', Fnodes_ndx(d+1), 'Qps', Qps, ...
'startprob', startprob{d}, 'transprob', transprob{d});
end
d = D;
if allQ
Qps = Qnodes(1:d-1);
else
Qps = Qnodes(d-1);
end
Qps = Qps + ss; % since all in slice 2
bnet.CPD{eclass(Qnodes(d),2)} = hhmmQ_CPD(bnet, Qnodes(d)+ss, 'Fself', Fnodes_ndx(d), ...
'Qps', Qps, ...
'startprob', startprob{d}, 'transprob', transprob{d});
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