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.

Deze oefening maakt deel uit van de cursus

Linear Classifiers in Python

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Oefeninstructies

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

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# 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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