├── GussianKernal.m
├── README.md
├── SBLsinc.m
└── data.m


/GussianKernal.m:
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 1 | function GK = GussianKernal( r1, r2 )
 2 | 
 3 | ler1=size(r1,1);
 4 | ler2=size(r2,1);
 5 | GK=ones(ler1,ler2);
 6 | 
 7 | for j=2:ler2
 8 |     for i = 1:ler1 
 9 |     GK(i,j)=exp(-(r1(i)-r2(j))^2);
10 |     end
11 | end
12 |  
13 | end
14 | 


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/README.md:
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1 | # Sparse-Bayesian-Learning
2 | SBL matlab code
3 | 验证sinc函数，加入gussian白噪声
4 | 


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/SBLsinc.m:
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 1 | clc;
 2 | clear;
 3 | Ntrain = 200;     %训练集样本数
 4 | Ntest = 500;    %测试集样本数
 5 | [x,t] = data(Ntrain);  %生成训练数据集
 6 | f =  GussianKernal(x,x);  %生成高斯核函数
 7 | 
 8 | m=size(f,2);
 9 | alpha=rand(1,m);
10 | beta=rand();    %初始化学习参数
11 | 
12 | for ep = 1:3000
13 | A = diag(alpha);
14 | F = pinv(beta*f'*f+A);
15 | u = beta*F*f'*t;
16 | gamma = 1-alpha.*diag(F)';   %更新参数
17 | alpha_old=alpha;
18 | beta_old=beta;
19 | 
20 | index=abs(alpha)<1e3; 
21 | alpha(index)=gamma(index)./(u(index)'.^2);
22 | beta=(Ntrain-sum(gamma))/((t-f*u)'*(t-f*u));%将数值小于1000的列标去除，只更新此部分
23 | 
24 | err=max(abs(alpha(index)-alpha_old(index))./abs(alpha(index)))+abs(beta-beta_old)/abs(beta);
25 |     if err<0.1
26 |         break;
27 |     end %判断如果满足收敛条件，停止迭代
28 | end
29 | 
30 | tpre=f(:,index)*u(index);  %计算预测数据集
31 | 
32 | figure(1);
33 | plot(x,t,'r+');
34 | hold on;
35 | plot(x,tpre,'b*');
36 | hold on;
37 | plot(x(index(2:end)),t(index(2:end)),'ko'); %分别绘制原始数据、预测数据和相关向量
38 | 
39 | title('Testing Data1');
40 | xlabel('x');
41 | ylabel('t');
42 | legend('训练数据','预测数据','相关向量');%标注
43 | 
44 | [xte,tte]=data(Ntest);%生成500个测试数据集
45 | ftest =  GussianKernal(xte,x);%生成关联矩阵
46 | ttepre=ftest(:,index)*u(index);%预测
47 | figure(2)
48 | plot(xte,tte,'.');
49 | hold on;
50 | plot(xte,ttepre,'+');
51 | hold on;
52 | plot(x(index(2:end)),t(index(2:end)),'ko');%分别绘制原始数据、预测数据和关联向量（由200个数据给出）
53 | 
54 | title('Testing Data2');
55 | xlabel('x');
56 | ylabel('t');
57 | legend('训练数据','预测数据','相关向量');%标注
58 | 


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/data.m:
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1 | function [input, output ] = data( N )
2 | input=(rand(N,1)-0.5)*4;
3 | output=sin(input*5)+randn(N,1)/4; 
4 | end
5 | 


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