Polynomial Regression issues such as memory issue due to parameter redundancy when performing polynomial multiplication for features

As you can see, when I convert X to a quadratic multiple regression with Polynomialfeatures, I run into memory problems due to the huge increase in the number of parameters. I run into such a problem when I only want a 2nd degree polynomial, or if I want more 2nd degree polynomials this will create a bigger problem. Is there no alternative solution for Polynomial Regression memory overflow? If so, what? What is the most logical thing to do when I want to do a polynomial regression, how should I optimize it?

Creating new polynomial features always increases the size of the data set. There is no avoiding that.

However, if you’re using a neural network, typically you do not need to create additional polynomial terms. This is because each hidden layer contains a non-linear activation function (relu, sigmoid, etc). This allows each layer to create new non-linear combinations of the input features.

Polynomial features are typically only used in linear or logistic regression.

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In the evaluating model found in the first week, it was mentioned which degree we would choose a polynomial function, so I tried to run Polynomial Regression and encountered such errors. What was the purpose of this lesson then?

Polynomial regression is a useful tool, but it’s only feasible to use on datasets that have a small number of features.

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