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I'm trying to implement "Stochastic gradient descent" in MATLAB. I followed the algorithm exactly but I'm getting a VERY VERY large w (coefficients) for the prediction/fitting function. Do I have a mistake in the algorithm?

The Algorithm :enter image description here

x = 0:0.1:2*pi      // X-axis

    n = size(x,2);      

    r = -0.2+(0.4).*rand(n,1);  //generating random noise to be added to the sin(x) function

    t=zeros(1,n);

    y=zeros(1,n);

    for i=1:n

        t(i)=sin(x(i))+r(i);          // adding the noise

        y(i)=sin(x(i));               // the function without noise

    end

    f = round(1+rand(20,1)*n);        //generating random indexes

    h = x(f);                         //choosing random x points

    k = t(f);                         //chossing random y points

    m=size(h,2);                     // length of the h vector

    scatter(h,k,'Red');              // drawing the training points (with noise)

    %scatter(x,t,2);

    hold on;

    plot(x,sin(x));                 // plotting the Sin function

    w = [0.3 1 0.5];                    // starting point of w

    a=0.05;                         // learning rate "alpha"

// ---------------- ALGORITHM ---------------------//

    for i=1:20

        v = [1 h(i) h(i).^2];                      // X vector

        e = ((w*v') - k(i)).*v;            // prediction - observation

        w = w - a*e;                       // updating w

    end

    hold on;

    l = 0:1:6;

    g = w(1)+w(2)*l+w(3)*(l.^2);

    plot(l,g,'Yellow');                      // drawing the prediction function

1 Answer

0 votes
by (96.2k points)

Typically, if we ended up with too large values, there is .overfitting. If you take too big learning rate, SGD is likely to diverge. The learning rate should converge to zero

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