Mathematical Theorem and Credit Transaction Prediction Using Stochastic and Batch Gradient Descent

Welcome to this tutorial where we will explore how to apply Stochastic and Batch Gradient Descent (GD) for predicting credit transactions and understanding mathematical theorems. Whether you are a beginner in machine learning or looking to enhance your knowledge, this guide will walk you through the concepts and applications step by step.

Prerequisites

Before diving into the tutorial, it’s essential to have a basic understanding of the following concepts:

• Linear Algebra: Familiarity with vectors and matrices will help you understand the mathematical operations involved.
• Calculus: A basic grasp of derivatives is necessary since gradient descent relies on them.
• Python Programming: Basic knowledge of Python will be beneficial as we will use it for coding examples.
• Machine Learning Basics: Understanding the fundamentals of machine learning will provide context for our discussion.

Step-by-Step Guide

1. Understanding Gradient Descent

Gradient Descent is an optimization algorithm used to minimize a function by iteratively moving towards the steepest descent as defined by the negative of the gradient. In the context of machine learning, it helps in minimizing the cost function, which measures how well our model is performing.

2. Types of Gradient Descent

There are two primary types of Gradient Descent we will focus on:

• Batch Gradient Descent: This method computes the gradient of the cost function using the entire dataset. It is stable and provides a precise direction for the update but can be slow for large datasets.
• Stochastic Gradient Descent (SGD): In contrast, SGD updates the model parameters using only one training example at a time. This makes it faster and allows the model to start learning immediately, but it can introduce noise in the updates.

3. Implementing Gradient Descent in Python

Let’s implement both Batch and Stochastic Gradient Descent using Python. We will create a simple linear regression model to predict credit transactions.

Batch Gradient Descent Implementation

import numpy as np

# Sample data
X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
y = np.array([1, 2, 2, 3])

# Parameters
m = len(y)  # number of training examples
alpha = 0.01  # learning rate
iterations = 1000

# Initialize weights
theta = np.zeros(X.shape[1])

# Batch Gradient Descent
for _ in range(iterations):
    predictions = X.dot(theta)
    errors = predictions - y
    gradient = (1/m) * X.T.dot(errors)
    theta -= alpha * gradient

print(theta)  # Final weights

Stochastic Gradient Descent Implementation

import numpy as np

# Sample data
X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
y = np.array([1, 2, 2, 3])

# Parameters
alpha = 0.01  # learning rate
iterations = 1000

# Initialize weights
theta = np.zeros(X.shape[1])

# Stochastic Gradient Descent
for _ in range(iterations):
    for i in range(len(y)):
        prediction = X[i].dot(theta)
        error = prediction - y[i]
        gradient = X[i] * error
        theta -= alpha * gradient

print(theta)  # Final weights

Explanation of the Code

In both implementations, we start by initializing our parameters and weights. The main difference lies in how we compute the gradient:

• In Batch Gradient Descent, we calculate the gradient using the entire dataset, which gives us a stable update direction.
• In Stochastic Gradient Descent, we update our weights for each training example, which allows for faster convergence but can lead to fluctuations in the path taken towards the minimum.

Conclusion

In this tutorial, we explored the concepts of Stochastic and Batch Gradient Descent and implemented them in Python for predicting credit transactions. Understanding these techniques is crucial for anyone looking to delve into machine learning and data science.

For further reading and resources, check out the original post Prototyping Gradient Descent in Machine Learning”>here and explore more on this topic Towards Data Science”>here.