Write a program for Bayes classification algorithm using Matlab

Aim:- Write a program for Bayes classification algorithm.

Tools: -MATLAB

Theory: -

Bayesian reasoning is applied to decision making and inferential statistics that deals with probability inference. It is used the knowledge of prior events to predict future events.

The Bayes Theorem:             P(h/D)= P(D/h) P(h) / P(D) 

Where; P(h) : Prior probability of hypothesis h

P(D) : Prior probability of training data D

P(h/D) : Probability of h given D       

P(D/h) : Probability of D given h

Program:-

Example:- Consider the Following vector (likes shortbread, likes burger, eats porridge, watched england play football, nationality).

Now, Nationality is Scottish and England. For Scottish 1 and for England 0.        

X = [ 0 0 1 1 0 ;

1 0 1 0 0 ;

1 1 0 1 0 ;

1 1 0 0 0 ;

0 1 0 1 0 ;

0 0 1 0 0 ;

1 0 1 1 1 ;

1 1 0 1 1 ;

1 1 1 0 1 ;

1 1 1 0 1 ;

1 1 1 1 1 ;

1 0 1 0 1 ;

1 0 0 0 1 ];

Y = X(:,5);

X = X(:,1:4)';

pS = sum (Y)/size(Y,1);   

pE = sum(1 - Y)/size(Y,1); 

phiS = X * Y / sum(Y); 

phiE = X * (1-Y) / sum(1-Y) ;

x=[1 0 1 0]';

pxS = prod(phiS.^x.*(1-phiS).^(1-x));

pxE = prod(phiE.^x.*(1-phiE).^(1-x));

pxSF = (pxS * pS ) / (pxS + pxE)

pxEF = (pxE * pS ) / (pxS + pxE)