In the field of machine learning, gradient descent is a widely used optimization technique that helps us find the optimal parameters for our models. While there are numerous libraries available to implement gradient descent, such as TensorFlow and PyTorch, understanding the underlying principles and building a gradient descent model in pure Python can greatly enhance our understanding of the technique. In this blog post, we will explore the process of creating gradient descent models using only the Python programming language.
Understanding Gradient Descent
Gradient descent is an iterative optimization algorithm that aims to minimize a given cost function by adjusting the model’s parameters in the direction of steepest descent. The algorithm starts with initial parameter values and repeatedly updates them based on the gradient of the cost function. This process continues until convergence, where the parameters reach the optimal values.
To create a gradient descent model in pure Python, we need to follow a few steps:
- Defining the Cost Function: The cost function measures the discrepancy between the predicted and actual values. It represents what we want to minimize during the optimization process. Depending on the problem at hand, the cost function can vary. For instance, in linear regression, the mean squared error (MSE) is commonly used.
- Initializing Model Parameters: We need to initialize the model’s parameters, such as weights and biases, with some initial values. These parameters will be updated during the gradient descent iterations.
- Computing the Gradient: The gradient of the cost function with respect to the parameters is calculated using numerical differentiation or analytical methods, depending on the complexity of the model. Numerical differentiation, such as the finite difference method, estimates the gradient by evaluating the cost function at slightly perturbed parameter values.
- Updating Model Parameters: Once we have computed the gradient, we update the model’s parameters using the learning rate, which determines the step size of each parameter update. The learning rate should be carefully chosen to avoid overshooting or slow convergence.
- Convergence: The model iteratively updates its parameters using the computed gradients until convergence. Convergence is typically defined by a stopping criterion, such as reaching a certain number of iterations or when the change in the cost function becomes negligible.
On the link below you can see Python code with examples of how to build such models.
