Minimizing a loss function

In this exercise you'll implement linear regression "from scratch" using scipy.optimize.minimize.

We'll train a model on the Boston housing price data set, which is already loaded into the variables X and y. For simplicity, we won't include an intercept in our regression model.

Cet exercice fait partie du cours

Linear Classifiers in Python

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Instructions

Fill in the loss function for least squares linear regression.
Print out the coefficients from fitting sklearn's LinearRegression.

Exercice interactif pratique

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# The squared error, summed over training examples
def my_loss(w):
    s = 0
    for i in range(y.size):
        # Get the true and predicted target values for example 'i'
        y_i_true = y[i]
        y_i_pred = w@X[i]
        s = s + (____)**2
    return s

# Returns the w that makes my_loss(w) smallest
w_fit = minimize(my_loss, X[0]).x
print(w_fit)

# Compare with scikit-learn's LinearRegression coefficients
lr = LinearRegression(fit_intercept=False).fit(X,y)
print(____)

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