Bayessian-classification-Prediction-Risk/bayesianClassification.m at master · Jeffresh/Bayessian-classification-Prediction-Risk · GitHub

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%%  Generate data for two different classes using normal distribution
% different std and mean.
clc;
clear;
close all;

ma = 20;
sa = 3;

mb = 25;
sb = 2;

n = 5000;

%% Supposing same probability

randn('seed',0);

pa = 0.5;
pb = 0.5;

% Generate data set

[x,y] = generate_data(ma,sa,pa,mb,sb,pb,n);

% numer of elements of each class
indices1=find(y==1); indices2=find(y==2);

% gets mean and std of each lass
m1=mean(x(indices1)); m2=mean(x(indices2));
s1=std(x(indices1)); s2=std(x(indices2));

% gets prior probability of each class, P(W1), P(W2)
Pw1=length(indices1)/length(y);
Pw2=length(indices2)/length(y);

% gets conditional probability - likehood using Gaussian distribution
% P(X | W1) P(X | W2)

I = -40:0.01:40;
PXW1 = normpdf(I,m1,s1);
PXW2 = normpdf(I,m2,s2);

% Evalue using Maximum - Likelihood criteria
% p1 + p2 is not 1

example =  x(3);
p1= Pw1 * normpdf(example,m1,s1)
p2= Pw2 * normpdf(example,m2,s2)
[~,class] = max([p1,p2])

% Evalue using MAP criteria
%  the results are probabilities so p1 + p2 = 1

example =  x(3);
p1= Pw1 * normpdf(example,m1,s1);
p2= Pw2 * normpdf(example,m2,s2);
px = p1+p2;
p1 = p1/px
p2 = p2/px
[~,class] = max([p1,p2])

[x1,x2] = get_boundaries(m1,s1,m2,s2,Pw1,Pw2);

plot(I,Pw1*PXW1);hold on;
plot(x1*ones(1,10),linspace(0,0.15,10),'g');
plot(x2*ones(1,10),linspace(0,0.15,10),'g');
plot(I,Pw2*PXW2,'r');hold off;

%% Generate dataset with probs p(a) > p(b)

randn('seed',0);

pa = 0.7;
pb = 0.3;

% Generate data set
[x,y] = generate_data(ma,sa,pa,mb,sb,pb,n);

% numer of elements of each class
indices1=find(y==1); indices2=find(y==2);

% gets mean and std of each lass
m1=mean(x(indices1)); m2=mean(x(indices2));
s1=std(x(indices1)); s2=std(x(indices2));

% gets prior probability of each class, P(W1), P(W2)
Pw1=length(indices1)/length(y);
Pw2=length(indices2)/length(y);

I = -40:0.01:40;
[x1,x2] = get_boundaries(m1,s1,m2,s2,Pw1,Pw2);

I=x1-10:0.1:x2+10;
plot(I,Pw1*normpdf(I,m1,s1));hold on;
plot(x1*ones(1,10),linspace(0,0.15,10),'g');
plot(x2*ones(1,10),linspace(0,0.15,10),'g');
plot(I,Pw2*normpdf(I,m2,s2),'r');hold off;


%% Generate dataset with probs p(a) < p(b)

randn('seed',0);

pa = 0.3;
pb = 0.7;

% Generate data set
[x,y] = generate_data(ma,sa,pa,mb,sb,pb,n);

% numer of elements of each class
indices1=find(y==1); indices2=find(y==2);

% gets mean and std of each lass
m1=mean(x(indices1)); m2=mean(x(indices2));
s1=std(x(indices1)); s2=std(x(indices2));

% gets prior probability of each class, P(W1), P(W2)
Pw1=length(indices1)/length(y);
Pw2=length(indices2)/length(y);

I = -40:0.01:40;
[x1,x2] = get_boundaries(m1,s1,m2,s2,Pw1,Pw2);

I=x1-80:0.1:x2+80;
plot(I,Pw1*normpdf(I,m1,s1));hold on;
plot(x1*ones(1,10),linspace(0,0.15,10),'g');
plot(x2*ones(1,10),linspace(0,0.15,10),'g');
plot(I,Pw2*normpdf(I,m2,s2),'r');hold off;

%% Be carefull the boundaries are not symetrical for classifaction p(a) = x, p(b) = y and p(a) = y and p(b) = x

% in p(a) = 0.5 and p(b) = 0.5 the boundaries are:
x1 = 33.8638;
x2 = 22.5118;

% in p(a) = 0.7 and p(b) = 0.3 the boundaries are :

x1d = 33.3597;
x2d = 23.4963;

% % in p(a) = 0.3 and p(b) = 0.7 the boundaries are :

x1f = 35.1978;
x2f = 21.6353;

variation1 = sqrt((x1-x1d)^2+(x2-x2d)^2)
variation2 = sqrt((x1-x1f)^2+(x2-x2f)^2)

% The variation is not equal