-
Notifications
You must be signed in to change notification settings - Fork 7
/
demo.m
229 lines (223 loc) · 6.68 KB
/
demo.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
% Copyright (C) 2016 Arno Onken
%
% This file is part of the Mixed Vine Toolbox.
%
% The Mixed Vine Toolbox is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as published
% by the Free Software Foundation; either version 3 of the License, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
% Public License for more details.
%
% You should have received a copy of the GNU General Public License along
% with this program; if not, see <http://www.gnu.org/licenses/>.
%% Construct 4D mixed copula vine
disp('Constructing mixed copula vine...');
d = 4; % Dimension
vine.type = 'c-vine'; % Canonical vine type
% Set margins
vine.margins = cell(d,1);
% Standard normal margin
vine.margins{1}.dist = 'norm';
vine.margins{1}.theta = [0;1];
vine.margins{1}.iscont = true; % Continuous margin
% Gamma margin
vine.margins{2}.dist = 'gam';
vine.margins{2}.theta = [2;4];
vine.margins{2}.iscont = true; % Continuous margin
% Poisson margin
vine.margins{3}.dist = 'poiss';
vine.margins{3}.theta = 10;
vine.margins{3}.iscont = false; % Discrete margin
% Binomial margin
vine.margins{4}.dist = 'bino';
vine.margins{4}.theta = [20;0.4];
vine.margins{4}.iscont = false; % Discrete margin
% Set copula families
vine.families = cell(d);
vine.theta = cell(d);
% Gaussian copula family
vine.families{1,2} = 'gaussian';
vine.theta{1,2} = 0.5;
% Student copula family
vine.families{1,3} = 'student';
vine.theta{1,3} = [0.5;2];
% Clayton copula family
vine.families{1,4} = 'clayton';
vine.theta{1,4} = 5;
% Clayton copula family rotated 90° clockwise
vine.families{2,3} = 'claytonrot090';
vine.theta{2,3} = 5;
% Clayton copula family survival transformed
vine.families{2,4} = 'claytonrot180';
vine.theta{2,4} = 5;
% Independence
vine.families{3,4} = 'ind';
vine.theta{3,4} = [];
fprintf('\n');
%% Test probability density function
disp('Calculating probability density function on a grid...');
% Calculate probability density function on lattice
x1gv = linspace(-3,3,100);
x2gv = linspace(0.5,25,100);
x3gv = 0:20;
x4gv = 0:15;
[x1,x2,x3,x4] = ndgrid(x1gv,x2gv,x3gv,x4gv);
p = mixedvinepdf(vine,[x1(:),x2(:),x3(:),x4(:)]);
p = reshape(p,size(x1));
% Plot 2D margins
figure('Name','2D margins of mixed vine copula PDF','Position',[0,0,1600,1000]);
subplot(2,3,1);
margin12 = reshape(sum(sum(p,4),3),[length(x1gv),length(x2gv)]);
imagesc(x1gv,x2gv,margin12');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 1');
ylabel('Margin 2');
subplot(2,3,2);
margin13 = reshape(sum(sum(p,4),2),[length(x1gv),length(x3gv)]);
imagesc(x1gv,x3gv,margin13');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 1');
ylabel('Margin 3');
subplot(2,3,3);
margin14 = reshape(sum(sum(p,3),2),[length(x1gv),length(x4gv)]);
imagesc(x1gv,x4gv,margin14');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 1');
ylabel('Margin 4');
subplot(2,3,4);
margin23 = reshape(sum(sum(p,4),1),[length(x2gv),length(x3gv)]);
imagesc(x2gv,x3gv,margin23');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 2');
ylabel('Margin 3');
subplot(2,3,5);
margin24 = reshape(sum(sum(p,3),1),[length(x2gv),length(x4gv)]);
imagesc(x2gv,x4gv,margin24');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 2');
ylabel('Margin 4');
subplot(2,3,6);
margin34 = reshape(sum(sum(p,2),1),[length(x3gv),length(x4gv)]);
imagesc(x3gv,x4gv,margin34');
colormap('hot');
set(gca,'YDir','normal');
xlabel('Margin 3');
ylabel('Margin 4');
fprintf('\n');
%% Test sampling
disp('Sampling from mixed copula vine...');
% Draw samples
cases = 1000;
x = mixedvinernd(vine,cases);
% Plot samples in 2D
figure('Name','Mixed vine copula samples in 2D','Position',[0,0,1600,1000]);
subplot(2,3,1);
scatter(x(:,1),x(:,2),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 2');
subplot(2,3,2);
scatter(x(:,1),x(:,3),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 3');
subplot(2,3,3);
scatter(x(:,1),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 4');
subplot(2,3,4);
scatter(x(:,2),x(:,3),20,[0 0 0],'filled');
xlabel('Margin 2');
ylabel('Margin 3');
subplot(2,3,5);
scatter(x(:,2),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 2');
ylabel('Margin 4');
subplot(2,3,6);
scatter(x(:,3),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 3');
ylabel('Margin 4');
% Plot samples in 3D
figure('Name','Mixed vine copula samples in 3D','Position',[0,0,1000,1000]);
subplot(2,2,1);
scatter3(x(:,1),x(:,2),x(:,3),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 2');
zlabel('Margin 3');
subplot(2,2,2);
scatter3(x(:,1),x(:,2),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 2');
zlabel('Margin 4');
subplot(2,2,3);
scatter3(x(:,1),x(:,3),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 1');
ylabel('Margin 3');
zlabel('Margin 4');
subplot(2,2,4);
scatter3(x(:,2),x(:,3),x(:,4),20,[0 0 0],'filled');
xlabel('Margin 2');
ylabel('Margin 3');
zlabel('Margin 4');
fprintf('\n');
%% Test vine fit
disp('Fitting parameters to samples...');
% Construct argument to specify which margins are continuous
iscont = false(d,1);
for i = 1:d
iscont(i) = vine.margins{i}.iscont;
end
vineest = mixedvinefit(x,vine.type,iscont);
% Compare ground-truth and estimated mixed vine
fprintf('\nGround-truth mixed vine:\n');
for i = 1:d
fprintf(' Margin %d: %s with parameters\t',i,vine.margins{i}.dist);
for j = 1:length(vine.margins{i}.theta)
fprintf('\t%.2f ',vine.margins{i}.theta(j));
end
fprintf('\n');
end
for i = 1:d
for j = (i+1):d
fprintf(' Copula (%d,%d): %s with parameters\t',i,j,vine.families{i,j});
for k = 1:length(vine.theta{i,j})
fprintf('\t%.2f ',vine.theta{i,j}(k));
end
fprintf('\n');
end
end
fprintf('\n');
disp('Estimated mixed vine:');
for i = 1:d
fprintf(' Margin %d: %s with parameters\t',i,vineest.margins{i}.dist);
for j = 1:length(vineest.margins{i}.theta)
fprintf('\t%.2f ',vineest.margins{i}.theta(j));
end
fprintf('\n');
end
for i = 1:d
for j = (i+1):d
fprintf(' Copula (%d,%d): %s with parameters\t',i,j,vineest.families{i,j});
for k = 1:length(vineest.theta{i,j})
fprintf('\t%.2f ',vineest.theta{i,j}(k));
end
fprintf('\n');
end
end
fprintf('\n');
%% Estimate entropy
disp('Estimating entropy of mixed copula vine...');
alpha = 0.05; % Significance level of estimate (95% confidence)
erreps = 1e-1; % Maximum standard error
[h,stderr] = mixedvineentropy(vine,alpha,erreps);
% Display results
disp([' Estimated entropy: ' num2str(h) ' bit']);
disp([' Standard error of estimate: ' num2str(stderr) ' bit']);
fprintf('\n');