Added doctest, docstring and typehint for sigmoid_function & cost_function (#10828)

* Added doctest for sigmoid_function & cost_function

* Update logistic_regression.py

* Update logistic_regression.py

* Minor formatting changes in doctests

* Apply suggestions from code review

* Made requested changes in logistic_regression.py

* Apply suggestions from code review

---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
This commit is contained in:
Suyash Dongre 2023-10-26 13:25:56 +05:30 committed by GitHub
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@ -27,7 +27,7 @@ from sklearn import datasets
# classification problems
def sigmoid_function(z):
def sigmoid_function(z: float | np.ndarray) -> float | np.ndarray:
"""
Also known as Logistic Function.
@ -42,11 +42,63 @@ def sigmoid_function(z):
@param z: input to the function
@returns: returns value in the range 0 to 1
Examples:
>>> sigmoid_function(4)
0.9820137900379085
>>> sigmoid_function(np.array([-3, 3]))
array([0.04742587, 0.95257413])
>>> sigmoid_function(np.array([-3, 3, 1]))
array([0.04742587, 0.95257413, 0.73105858])
>>> sigmoid_function(np.array([-0.01, -2, -1.9]))
array([0.49750002, 0.11920292, 0.13010847])
>>> sigmoid_function(np.array([-1.3, 5.3, 12]))
array([0.21416502, 0.9950332 , 0.99999386])
>>> sigmoid_function(np.array([0.01, 0.02, 4.1]))
array([0.50249998, 0.50499983, 0.9836975 ])
>>> sigmoid_function(np.array([0.8]))
array([0.68997448])
"""
return 1 / (1 + np.exp(-z))
def cost_function(h, y):
def cost_function(h: np.ndarray, y: np.ndarray) -> float:
"""
Cost function quantifies the error between predicted and expected values.
The cost function used in Logistic Regression is called Log Loss
or Cross Entropy Function.
J(θ) = (1/m) * Σ [ -y * log((x)) - (1 - y) * log(1 - (x)) ]
Where:
- J(θ) is the cost that we want to minimize during training
- m is the number of training examples
- Σ represents the summation over all training examples
- y is the actual binary label (0 or 1) for a given example
- (x) is the predicted probability that x belongs to the positive class
@param h: the output of sigmoid function. It is the estimated probability
that the input example 'x' belongs to the positive class
@param y: the actual binary label associated with input example 'x'
Examples:
>>> estimations = sigmoid_function(np.array([0.3, -4.3, 8.1]))
>>> cost_function(h=estimations,y=np.array([1, 0, 1]))
0.18937868932131605
>>> estimations = sigmoid_function(np.array([4, 3, 1]))
>>> cost_function(h=estimations,y=np.array([1, 0, 0]))
1.459999655669926
>>> estimations = sigmoid_function(np.array([4, -3, -1]))
>>> cost_function(h=estimations,y=np.array([1,0,0]))
0.1266663223365915
>>> estimations = sigmoid_function(0)
>>> cost_function(h=estimations,y=np.array([1]))
0.6931471805599453
References:
- https://en.wikipedia.org/wiki/Logistic_regression
"""
return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
@ -75,6 +127,10 @@ def logistic_reg(alpha, x, y, max_iterations=70000):
# In[68]:
if __name__ == "__main__":
import doctest
doctest.testmod()
iris = datasets.load_iris()
x = iris.data[:, :2]
y = (iris.target != 0) * 1