bayesian.m

%to calculate the expected price change dp_j based on a given x, where
%x is the vector of current empirical prices, ending in our current price
%
%equation:
%dpj = (sum over i=1 to n(y_i * exp(c(x,x_i))))/(sum over i=1 to n(exp(c(x,x_i)))
%n=20 for our given set of patterns
%x_i is a given pattern
%y_i is the price change for the kmeans pattern
%c is a constant chosen for best fit
%defined in the paper
function dpj = bayesian(x, S)
    %based on the length of x, we choose S_j
    dpj = 0;
    c = -1/4; %TODO choose a better c, should it be negative or not??
    %compare x with the it in S using our similarity measure
    %and return the conditional expectation, which is dp
    num = 0.0;
    den = 0.0;
    % iterate through all kmeanspatterns 
    for i = 1:20
        cutS = S(i,1:length(x));
        distance = exp(c*(norm(x-cutS,2)^2));
        num = num + S(i,length(x)+1)*distance;
        den = den + distance;    
    end
    
    if den~=0
        dpj = num/den;
    end

    end