Stochastic Gradient Descent In R

Gradient Descent is an iterative optimization process that searches for an objective function’s optimum value (Minimum/Maximum). It is one of the most used methods for changing a model’s parameters to reduce a cost function in machine learning projects. In this article, we will learn the concept of SGD and its implementation in the R Programming Language.

Introduction to Stochastic Gradient Descent

Stochastic Gradient Descent is an iterative optimization algorithm used to minimize a loss function by adjusting the parameters of a model. Unlike traditional Gradient Descent, which computes the gradient of the entire dataset, SGD updates the model parameters based on a single randomly chosen data point or a small subset of data points. This randomness introduces noise into the optimization process, but it allows SGD to converge more rapidly and handle large datasets more efficiently.

Key Features of SGD

GD is commonly used to update weights and biases during training. The algorithm calculates the gradient of the loss function concerning each parameter and adjusts them in the opposite direction of the gradient to minimize the loss.

• Frequent Updates: Parameters are updated more frequently, allowing faster iteration through the parameter space.
• Reduced Computation per Update: Each update requires less computation, making SGD suitable for large datasets.
• Potential for Faster Convergence: SGD can converge faster than batch gradient descent with appropriate hyperparameter tuning.

Setting Up and Running SGD in R

To implement SGD in R, we need to:

1. Set up the Environment and Libraries: Load necessary libraries and set up the environment.
2. Define the Model and the Loss Function: Specify the model architecture and choose an appropriate loss function.
3. Implement the SGD Algorithm: Develop the SGD algorithm to iteratively update model parameters based on sampled data points.
4. Visualize the Results: Plot the model's performance metrics to assess convergence and accuracy.

Implementing Stochastic Gradient Descent (SGD) in R

Implementing Stochastic Gradient Descent (SGD) in R involves a few steps: defining a model, choosing a loss function, and updating the model parameters iteratively based on randomly sampled data points. In this example, we will see a simple linear regression problem and demonstrate how to apply SGD to optimize the model parameters.

Step 1: Define the Model

We start by defining the linear model in R.

# Define the linear model: y = mx + c
linear_model <- function(x, m, c) {
  return(m * x + c)
}

Step 2: Choose the Loss Function

For linear regression, a common loss function is the Mean Squared Error (MSE), which measures the average squared difference between the predicted and actual values. We define the MSE function as follows: