
In this post, you will learn about the following:
- How to represent the probability that an event will take place with the asssociated features (attributes / independent features)
- Sigmoid function python code
Table of Contents
Probability as Sigmoid Function
The below is the Logit Function code representing association between the probability that an event will occur and independent features.
$$Logit Function = \log(\frac{P}{(1-P)}) = {w_0} + {w_1}{x_1} + {w_2}{x_2} + …. + {w_n}{x_n}$$
$$Logit Function = \log(\frac{P}{(1-P)}) = W^TX$$
$$P = \frac{1}{1 + e^-W^TX}$$
The above equation can be called as sigmoid function.
Python Code for Sigmoid Function
import numpy as np import matplotlib.pyplot as plt # Sigmoid function # def sigmoid(z): return 1 / (1 + np.exp(-z)) # Creating sample Z points # z = np.arange(-5, 5, 0.1) # Invoking Sigmoid function on all Z points # phi_z = sigmoid(z) # Plotting the Sigmoid function # plt.plot(z, phi_z) plt.axvline(0.0, color='k') plt.xlabel('z') plt.ylabel('$\phi(z)$') plt.yticks([0.0, 0.5, 1.0]) ax = plt.gca() ax.yaxis.grid(True) plt.tight_layout() plt.show()
Executing the above code would result in the following plot:

Fig 1: Logistic Regression – Sigmoid Function Plot
Pay attention to some of the following in above plot:
- gca() function: Get the current axes on the current figure
- axvline() function: Draw the vertical line at the given value of X
- yticks() function: Get or set the current tick locations of the y-axis
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