Implementing logistic regression
This is very similar to the earlier exercise where you implemented linear regression "from scratch" using scipy.optimize.minimize. However, this time we'll minimize the logistic loss and compare with scikit-learn's LogisticRegression (we've set C to a large value to disable regularization; more on this in Chapter 3!).
The log_loss() function from the previous exercise is already defined in your environment, and the sklearn breast cancer prediction dataset (first 10 features, standardized) is loaded into the variables X and y.
This exercise is part of the course
Linear Classifiers in Python
Exercise instructions
- Input the number of training examples into
range(). - Fill in the loss function for logistic regression.
- Compare the coefficients to sklearn's
LogisticRegression.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# The logistic loss, summed over training examples
def my_loss(w):
s = 0
for i in range(____):
raw_model_output = w@X[i]
s = s + ____(raw_model_output * y[i])
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 LogisticRegression
lr = LogisticRegression(fit_intercept=False, C=1000000).fit(X,y)
print(lr.coef_)