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dc4e89805a
* Added doctest for sigmoid_function * Added doctest for sigmoid_function * Added doctest for sigmoid_function
103 lines
2.8 KiB
Python
103 lines
2.8 KiB
Python
#!/usr/bin/python
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# Logistic Regression from scratch
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# In[62]:
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# In[63]:
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# importing all the required libraries
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"""
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Implementing logistic regression for classification problem
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Helpful resources:
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Coursera ML course
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https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac
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"""
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import numpy as np
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from matplotlib import pyplot as plt
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from sklearn import datasets
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# get_ipython().run_line_magic('matplotlib', 'inline')
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# In[67]:
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# sigmoid function or logistic function is used as a hypothesis function in
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# classification problems
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def sigmoid_function(z):
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"""
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Also known as Logistic Function.
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1
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f(x) = -------
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1 + e⁻ˣ
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The sigmoid function approaches a value of 1 as its input 'x' becomes
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increasing positive. Opposite for negative values.
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Reference: https://en.wikipedia.org/wiki/Sigmoid_function
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@param z: input to the function
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@returns: returns value in the range 0 to 1
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"""
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return 1 / (1 + np.exp(-z))
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def cost_function(h, y):
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return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
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def log_likelihood(x, y, weights):
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scores = np.dot(x, weights)
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return np.sum(y * scores - np.log(1 + np.exp(scores)))
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# here alpha is the learning rate, X is the feature matrix,y is the target matrix
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def logistic_reg(alpha, x, y, max_iterations=70000):
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theta = np.zeros(x.shape[1])
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for iterations in range(max_iterations):
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z = np.dot(x, theta)
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h = sigmoid_function(z)
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gradient = np.dot(x.T, h - y) / y.size
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theta = theta - alpha * gradient # updating the weights
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z = np.dot(x, theta)
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h = sigmoid_function(z)
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j = cost_function(h, y)
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if iterations % 100 == 0:
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print(f"loss: {j} \t") # printing the loss after every 100 iterations
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return theta
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# In[68]:
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if __name__ == "__main__":
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iris = datasets.load_iris()
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x = iris.data[:, :2]
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y = (iris.target != 0) * 1
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alpha = 0.1
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theta = logistic_reg(alpha, x, y, max_iterations=70000)
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print("theta: ", theta) # printing the theta i.e our weights vector
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def predict_prob(x):
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return sigmoid_function(
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np.dot(x, theta)
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) # predicting the value of probability from the logistic regression algorithm
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plt.figure(figsize=(10, 6))
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plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color="b", label="0")
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plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color="r", label="1")
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(x1_min, x1_max) = (x[:, 0].min(), x[:, 0].max())
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(x2_min, x2_max) = (x[:, 1].min(), x[:, 1].max())
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(xx1, xx2) = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))
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grid = np.c_[xx1.ravel(), xx2.ravel()]
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probs = predict_prob(grid).reshape(xx1.shape)
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plt.contour(xx1, xx2, probs, [0.5], linewidths=1, colors="black")
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plt.legend()
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plt.show()
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