Mercurial > hg > camir-aes2014
comparison toolboxes/FullBNT-1.0.7/bnt/CPDs/@gaussian_CPD/Old/maximize_params.m @ 0:e9a9cd732c1e tip
first hg version after svn
author | wolffd |
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date | Tue, 10 Feb 2015 15:05:51 +0000 |
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-1:000000000000 | 0:e9a9cd732c1e |
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1 function CPD = maximize_params(CPD, temp) | |
2 % MAXIMIZE_PARAMS Set the params of a CPD to their ML values (Gaussian) | |
3 % CPD = maximize_params(CPD, temperature) | |
4 % | |
5 % Temperature is currently only used for entropic prior on Sigma | |
6 | |
7 % For details, see "Fitting a Conditional Gaussian Distribution", Kevin Murphy, tech. report, | |
8 % 1998, available at www.cs.berkeley.edu/~murphyk/papers.html | |
9 % Refering to table 2, we use equations 1/2 to estimate the covariance matrix in the untied/tied case, | |
10 % and equation 9 to estimate the weight matrix and mean. | |
11 % We do not implement spherical Gaussians - the code is already pretty complicated! | |
12 | |
13 if ~adjustable_CPD(CPD), return; end | |
14 | |
15 %assert(approxeq(CPD.nsamples, sum(CPD.Wsum))); | |
16 assert(~any(isnan(CPD.WXXsum))) | |
17 assert(~any(isnan(CPD.WXYsum))) | |
18 assert(~any(isnan(CPD.WYYsum))) | |
19 | |
20 [self_size cpsize dpsize] = size(CPD.weights); | |
21 | |
22 % Append 1s to the parents, and derive the corresponding cross products. | |
23 % This is used when estimate the means and weights simultaneosuly, | |
24 % and when estimatting Sigma. | |
25 % Let x2 = [x 1]' | |
26 XY = zeros(cpsize+1, self_size, dpsize); % XY(:,:,i) = sum_l w(l,i) x2(l) y(l)' | |
27 XX = zeros(cpsize+1, cpsize+1, dpsize); % XX(:,:,i) = sum_l w(l,i) x2(l) x2(l)' | |
28 YY = zeros(self_size, self_size, dpsize); % YY(:,:,i) = sum_l w(l,i) y(l) y(l)' | |
29 for i=1:dpsize | |
30 XY(:,:,i) = [CPD.WXYsum(:,:,i) % X*Y | |
31 CPD.WYsum(:,i)']; % 1*Y | |
32 % [x * [x' 1] = [xx' x | |
33 % 1] x' 1] | |
34 XX(:,:,i) = [CPD.WXXsum(:,:,i) CPD.WXsum(:,i); | |
35 CPD.WXsum(:,i)' CPD.Wsum(i)]; | |
36 YY(:,:,i) = CPD.WYYsum(:,:,i); | |
37 end | |
38 | |
39 w = CPD.Wsum(:); | |
40 % Set any zeros to one before dividing | |
41 % This is valid because w(i)=0 => WYsum(:,i)=0, etc | |
42 w = w + (w==0); | |
43 | |
44 if CPD.clamped_mean | |
45 % Estimating B2 and then setting the last column (the mean) to the clamped mean is *not* equivalent | |
46 % to estimating B and then adding the clamped_mean to the last column. | |
47 if ~CPD.clamped_weights | |
48 B = zeros(self_size, cpsize, dpsize); | |
49 for i=1:dpsize | |
50 if det(CPD.WXXsum(:,:,i))==0 | |
51 B(:,:,i) = 0; | |
52 else | |
53 % Eqn 9 in table 2 of TR | |
54 %B(:,:,i) = CPD.WXYsum(:,:,i)' * inv(CPD.WXXsum(:,:,i)); | |
55 B(:,:,i) = (CPD.WXXsum(:,:,i) \ CPD.WXYsum(:,:,i))'; | |
56 end | |
57 end | |
58 %CPD.weights = reshape(B, [self_size cpsize dpsize]); | |
59 CPD.weights = B; | |
60 end | |
61 elseif CPD.clamped_weights % KPM 1/25/02 | |
62 if ~CPD.clamped_mean % ML estimate is just sample mean of the residuals | |
63 for i=1:dpsize | |
64 CPD.mean(:,i) = (CPD.WYsum(:,i) - CPD.weights(:,:,i) * CPD.WXsum(:,i)) / w(i); | |
65 end | |
66 end | |
67 else % nothing is clamped, so estimate mean and weights simultaneously | |
68 B2 = zeros(self_size, cpsize+1, dpsize); | |
69 for i=1:dpsize | |
70 if det(XX(:,:,i))==0 % fix by U. Sondhauss 6/27/99 | |
71 B2(:,:,i)=0; | |
72 else | |
73 % Eqn 9 in table 2 of TR | |
74 %B2(:,:,i) = XY(:,:,i)' * inv(XX(:,:,i)); | |
75 B2(:,:,i) = (XX(:,:,i) \ XY(:,:,i))'; | |
76 end | |
77 CPD.mean(:,i) = B2(:,cpsize+1,i); | |
78 CPD.weights(:,:,i) = B2(:,1:cpsize,i); | |
79 end | |
80 end | |
81 | |
82 % Let B2 = [W mu] | |
83 if cpsize>0 | |
84 B2(:,1:cpsize,:) = reshape(CPD.weights, [self_size cpsize dpsize]); | |
85 end | |
86 B2(:,cpsize+1,:) = reshape(CPD.mean, [self_size dpsize]); | |
87 | |
88 % To avoid singular covariance matrices, | |
89 % we use the regularization method suggested in "A Quasi-Bayesian approach to estimating | |
90 % parameters for mixtures of normal distributions", Hamilton 91. | |
91 % If the ML estimate is Sigma = M/N, the MAP estimate is (M+gamma*I) / (N+gamma), | |
92 % where gamma >=0 is a smoothing parameter (equivalent sample size of I prior) | |
93 | |
94 gamma = CPD.cov_prior_weight; | |
95 | |
96 if ~CPD.clamped_cov | |
97 if CPD.cov_prior_entropic % eqn 12 of Brand AI/Stat 99 | |
98 Z = 1-temp; | |
99 % When temp > 1, Z is negative, so we are dividing by a smaller | |
100 % number, ie. increasing the variance. | |
101 else | |
102 Z = 0; | |
103 end | |
104 if CPD.tied_cov | |
105 S = zeros(self_size, self_size); | |
106 % Eqn 2 from table 2 in TR | |
107 for i=1:dpsize | |
108 S = S + (YY(:,:,i) - B2(:,:,i)*XY(:,:,i)); | |
109 end | |
110 %denom = max(1, CPD.nsamples + gamma + Z); | |
111 denom = CPD.nsamples + gamma + Z; | |
112 S = (S + gamma*eye(self_size)) / denom; | |
113 if strcmp(CPD.cov_type, 'diag') | |
114 S = diag(diag(S)); | |
115 end | |
116 CPD.cov = repmat(S, [1 1 dpsize]); | |
117 else | |
118 for i=1:dpsize | |
119 % Eqn 1 from table 2 in TR | |
120 S = YY(:,:,i) - B2(:,:,i)*XY(:,:,i); | |
121 %denom = max(1, w(i) + gamma + Z); % gives wrong answers on mhmm1 | |
122 denom = w(i) + gamma + Z; | |
123 S = (S + gamma*eye(self_size)) / denom; | |
124 CPD.cov(:,:,i) = S; | |
125 end | |
126 if strcmp(CPD.cov_type, 'diag') | |
127 for i=1:dpsize | |
128 CPD.cov(:,:,i) = diag(diag(CPD.cov(:,:,i))); | |
129 end | |
130 end | |
131 end | |
132 end | |
133 | |
134 | |
135 check_covars = 0; | |
136 min_covar = 1e-5; | |
137 if check_covars % prevent collapsing to a point | |
138 for i=1:dpsize | |
139 if min(svd(CPD.cov(:,:,i))) < min_covar | |
140 disp(['resetting singular covariance for node ' num2str(CPD.self)]); | |
141 CPD.cov(:,:,i) = CPD.init_cov(:,:,i); | |
142 end | |
143 end | |
144 end | |
145 | |
146 | |
147 |