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why is cost function(log term) not plugged in while calculating gradient descent(w,b) ?

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Hello @shouryaangrish
can you be little more clear in your question?

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TMosh
May 3, 2024, 7:45am
4
Gradient descent uses the gradients of the cost function. It doesn’t directly use the cost function itself - only the gradients.

The gradients are found from the equations for the partial derivative of the cost function.

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@shouryaangrish

I am sorry, I didn’t fully understand your question.

Still, Logistic regression does use gradient descent as its main optimization method to find the best model parameters. Log loss is our cost function that is used for logistic regression. As, it is related to maximum likelihood estimation, it works especially well for classification issues.

Also, to get the cost function as low as possible, gradient descent is used. We can find the direction and size of changes that need to be made to the model parameters to get the smallest mistake by looking at the gradient of the log loss function.

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Sorry i missed your replies,

Yeah i think i got it sorry for basic question,

so when cost function is calculated for logistic regression-

J[w,b]x = 1/m(1/2*Loss[w,b],y)

it is not put in as loss term for gradient descent for logistic regression which is calculated as below -

w = w - alpha*d/dw(J[w,b]x)

This J[w,b]x != J[w,b]x(^above)

Rather it just get’s the squared error cost function - 1/(2*m)sum(f[w,b]x - y)**2

instead of the Loss for logistic regression

-1/m*(y*sum[log(x)] + (1-y)*sum[log(1-x)])

so exactly my point cost function for logistic regression is -1/m*(y*sum[log(f[w,b]x)] + (1-y)*sum[log(1-f[w,b]x)])

whereas when we do the gradient we take it as (f[w,b]x - y)**2 basically the squared error cost function.

normal cost function and the gradient descent cost function are different

TMosh
May 8, 2024, 7:54am
9
You are correct in that the linear regression and logistic regression cost functions are different.

When you compute the partial derivatives (i.e. the gradients), they are also different.

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Yup and the cost function for logistic regression is different with the cost function for gradient descent when we compute partial derivatives