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:

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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