Theta computed from Gradient Descent in Linear Regression with one model produces NaN

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Saurav Shrestha 2020-8-6

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https://ww2.mathworks.cn/matlabcentral/answers/576298-theta-computed-from-gradient-descent-in-linear-regression-with-one-model-produces-nan

编辑： Safoura Tanbakouei 2022-1-12

I am running a simple linear regression model with one variable, trying to compute the unit cost of a unit based on the sizes available.The theta value produced from gradient descent function is NaN so I cannot plot the linear regression line. Could someone please help me fix this problem?

data = load('data.txt');
X = data(:,1);
y = data (:, 2);
plotData(X,y);
m = length(X);
X = [ones(m,1), data(:,1)];
theta = zeros(2,1);
J = computeCost(X,y,theta);
fprintf('The cost function J = \n%f \n', J); %need revision
iterations = 1500;
alpha = 0.1;
theta = gradientDescent(X, y, theta, alpha, iterations);
fprintf('Theta computed from gradient descent:\n%f, \n%f', theta(1), theta(2));

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Saurav Shrestha 2020-8-6

Here is my gradientDescent function

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y);
J_history = zeros(num_iters, 1);
for iter = 1 : num_iters
    
    prediction = X * theta;
    error = (prediction - y);
    theta = theta - ((alpha/m) * ((error)'*X)');
       
    J_history (iter) = computeCost(X, y, theta);
end
end

Safoura Tanbakouei 2022-1-12

编辑：Safoura Tanbakouei 2022-1-12

Untitled.jpg

@Saurav Shrestha I am doing the same exercise. I do not receive an error but the theta computed from the Gradient Descent is 0 and the plot I get is this figure attached.

This is my code:

temp0 = theta(1,1) - (alpha/m)*sum((X*theta-y));
    temp1 = theta(2,1) - (alpha/m)*sum((X*theta-y).*X(:,2));
    theta(1,1) = temp0;
    theta(2,1) = temp1;

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Answer 1

Raunak Gupta 2020-8-14

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Hi,

From the gradientDescent function mentioned in the comments I can see that theta is starting from zero column vector. So, for the very first iteration the prediction vector will also be zero. This makes a big change to the theta value in next iteration. Also, I don’t think the update equation of theta is written such that it will converge. So, I would suggest changing the starting values of theta vector and revisiting the updating equation of theta in gradient descent. I don’t think that computeCost is affecting the theta value.