forked from burakbayramli/books
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathbayes_lin_regr_demo.m
131 lines (105 loc) · 3.27 KB
/
bayes_lin_regr_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
function bayes_lin_regr_demo()
% Demonstrate bayesian linear regression
% Based on code written by Frank Hutter
seed = 0;
randn('state', seed);
rand('state', seed);
useRBF = 0;
doSave = 0;
longRange = 0;
trainStep = 0.1;
%trainStep = 0.5;
doStandardize = 1
if doStandardize
figNum=1;
else
figNum=3;
end
if longRange
xTrainRaw = [-9:trainStep:-8, 3:trainStep:3.5]'+0;
xTestRaw = [-10:0.1:10]'+0;
else
xTrainRaw = [-1:trainStep:-0.5,3:trainStep:3.5]'+0;
xTestRaw = [-2:0.1:4.5]'+0;
end
yTrain = feval(@fun, xTrainRaw) + randn(size(xTrainRaw,1),1)*10;
yTestOpt = feval(@fun, xTestRaw);
if doStandardize
% We must standardize before doing an RBF expansion.
% For polynomial basis, we can standardize before or afterwords.
[xTrain, muTrain, sigmaTrain] = standardizeCols(xTrainRaw);
[xTest] = standardizeCols(xTestRaw, muTrain, sigmaTrain);
else
xTrain = xTrainRaw;
xTest = xTestRaw;
end
if useRBF
lo = min( min(xTrain), min(xTest) );
hi = min( max(xTrain), max(xTest) );
RBFcenters = linspace(lo, hi, 5)'
%RBFcenters = linspace(-5, 5, 5)';
xTrain = rbfBasis(xTrain, RBFcenters);
xTest = rbfBasis(xTest, RBFcenters);
else
xTrain = polyBasis(xTrain, 2);
xTest = polyBasis(xTest, 2);
end
%xTrain = [ones(size(xTrain,1), 1) xTrain];
%xTest = [ones(size(xTest,1), 1) xTest];
[N,p] = size(xTrain);
beta = 0.02; % observation precision
alpha = 1e-4; % prior precision
% We do not want to regularize the first component of the feature vector
% so we set the precision to 0
prior_precision = alpha*eye(p);
prior_prior(1,1) = 0;
Sigma_w = pinv(prior_precision + beta*xTrain'*xTrain);
mu_w = beta * Sigma_w * xTrain' * yTrain % ridge regression
[yPred, yPred_var] = bayes_fwd(mu_w, Sigma_w, beta, xTest);
[yPredTrain, yPredTrain_var] = bayes_fwd(mu_w, Sigma_w, beta, xTrain);
% Plot predictive distribution
figure(figNum); clf
hold off
subplot(111)
errorbar(xTestRaw(:,1), yPred, sqrt(yPred_var), 'kx-');
hold on
plot(xTestRaw(:,1),yTestOpt,'bx-');
h = errorbar(xTrainRaw(:,1), yPredTrain, sqrt(yPredTrain_var), 'gx');
h = plot(xTrainRaw(:,1), yTrain, 'ro');
set(h, 'linewidth', 3)
grid on
if doSave
fname = sprintf('bayes_lin_regr_demo_frank_rbf%d.eps', useRBF);
folder = 'C:\kmurphy\Teaching\stat406-spring06\Book\figures';
print(gcf, '-depsc', fullfile(folder, fname));
fname = sprintf('bayes_lin_regr_demo_frank_rbf%d.jpg', useRBF);
folder = 'C:\kmurphy\Teaching\stat406-spring06\Book\figures';
print(gcf, '-djpeg', fullfile(folder, fname));
end
% Plot samples from the posterior
figure(figNum+1); clf
plot(xTestRaw(:,1),yTestOpt,'bx-'); hold on
nsamples = 10;
for s=1:nsamples
w = mvnrnd(mu_w, Sigma_w, 1);
Y_mean = xTest * w(:);
plot(xTestRaw(:,1), Y_mean, 'kx-');
end
if doSave
fname = sprintf('bayes_lin_regr_demo_frank_samples_rbf%d.eps', useRBF);
folder = 'C:\kmurphy\Teaching\stat406-spring06\Book\figures';
print(gcf, '-depsc', fullfile(folder, fname));
fname = sprintf('bayes_lin_regr_demo_frank_samples_rbf%d.jpg', useRBF);
folder = 'C:\kmurphy\Teaching\stat406-spring06\Book\figures';
print(gcf, '-djpeg', fullfile(folder, fname));
end
%%%%%%%%
function f = fun(x) %target function
f = 10 + x + x.^4;
%f = x.^4;
%%%%%%%%
function [Y_mean, Y_var] = bayes_fwd(mu_w, Sigma_w, beta, X)
Y_mean = X * mu_w;
for i=1:size(X,1)
Y_var(i,1) = 1/beta + X(i,:) * Sigma_w * X(i,:)';
end