Mathematics of L1 norm

Let's gets start with "What we have to do?"

In such case of simple linear regression(OLS).b=y_mean-m*x_mean and m=∑(Xi-X_mean)(yi-y_mean)/∑(Xi-X_mean)²

^{In such as case of lasso we derive every things again but we don't derive b because in lasso we reduces m not b will same as well.}

1. Choose a loss function.In this case I choose L=𝜮(yi-p)²

2. Calculate dL/dm=∑(Xi-X_mean)(yi-y_mean)+λ/∑(Xi-X_mean)² to minimize loss

Then m=∑(Xi-X_mean)(yi-y_mean)+λ/∑(Xi-X_mean)²

And in this case you clearly see if we increase λ m decrease but it effects b also but not that much

And λ is hyperparameter in whole Regularization

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