Prashant Kumar answered . 2024-04-18 00:37:58

% Weird data set:

 plot(input,target,'o')

 close all, clear all, clc

 N =30
 input  = [0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1]; 
 target = [ 1, zeros( 1,N-1)];

% The simplest model is the constant output model that outputs the mean of the target regardless of the input.

 y00   = (1/N)*ones(1,N); % 0.0333*ones(1,30)
 e00   = target-y00;     ; % [ 0.9667, -0.0333*ones(1,29)]
 MSE00 = mse(target-y00)       % 0.0322

% The next simplest is the linear model

 W0    =  target/[ ones(1,N) ; input ] % W0 = [ 0.0588 -0.0588 ]
 y0    =  W0 * [ ones(1,N) ; input ];  % y0 =  0.0588*(1-input)
 e0    =  target-y0;     ;             % [ 0.9412, -y0(2:end)]
 MSE0  =  mse(target-y0)               % 0.0314  Not much better than constant model
 R20   = 1 - MSE0/MSE00                %  0.0264   VERY BAD FIT

% Neural Model

 [ I N ] = size(input)                                 % [ 1 30 ]
 [ O N ] = size(target)                              % [ 1 30 ]
 Neq = N*O                                             % 30 =  No. of equations
% Nw = (I+1)*H+(H+1)*O = 1+3*H       % No. of unknown weights

% No overfitting Neq > Nw==> H <= Hub (upper bound)

 Hub  = -1+ceil( (Neq-O) / ( I+O+1) )  % 9
 Hmax = 9
 dH   = 1
 Hmin = 0  % Linear Model
 numH = length(Hmin:dH:Hmax) % 10

 Ntrials = 10
 rng(0)
 j=0

 for h=Hmin:dH:Hmax
    j=j+1
    if h==0
        net = patternnet([]);
        Nw = (I+1)*O
    else
        net = patternnet(h);
        Nw = (I+1)*h+(h+1)*O
    end

    for i=1:Ntrials
       net = configure(net, input,target);
       net.divideFcn = 'dividetrain';            % Default 'dividerand' is much worse
       [net tr y e ] = train(net,input,target);
       R2(i,j) = 1 - mse(e)/MSE00;
    end
 end
 R2 = R2   % 0.0264* ones(Ntrials,numH)     Same as Linear

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