Stochastic Gradient Descent (SGD) - Beginners' Guide

When delving into the field of machine learning, it's common to come across the term Stochastic Gradient Descent (SGD). SGD is a commonly used optimization algorithm in machine learning and deep learning. Its goal is to find the minimum value of a given cost function.

Gradient descent is a widely used optimization algorithm in machine learning, but there's a problem with using it alone. When using only gradient descent, the optimization process updates the parameters based on the average gradient of the entire training dataset. This means that for each iteration, the algorithm processes the entire dataset to calculate the gradient, which can be super time-consuming for large datasets.

Also, the optimization process can get stuck in local minima, which are regions of the cost function that aren't the global minimum, but still yield a low value. This leads to suboptimal model performance as the optimization process won't continue to search for a better solution.

SGD was introduced to overcome these problems. With SGD, the optimization process updates the parameters based on the gradient of individual training examples, leading to faster convergence and avoiding getting stuck in local minima. But, SGD can be more volatile and may require techniques like mini-batch processing or momentum to stabilize the optimization process.

The basic idea behind SGD is to update the model parameters with the gradient of the loss function with respect to each parameter, in a more efficient and faster way than traditional gradient descent. The main difference between SGD and traditional gradient descent is that in SGD, the update to the model parameters is done using only a single sample from the training dataset at a time, while in traditional gradient descent, the update is done using the average of the gradients of the loss function with respect to the parameters, calculated over the entire training dataset.

One big advantage of SGD is efficiency. Because the update is done using only a single sample, SGD can converge much faster, especially in large datasets. SGD can also handle noisy data better, leading to better generalization of the model.

Let's use an example to understand this better. Imagine we have a simple linear regression model with a single input feature and a single output. We have 100 data points and want to fit the model to the data using SGD. Initially, the model parameters like slope and constant are set to random values. In each iteration, we pick a single sample from the training data randomly, calculate the gradient using the chain rule from calculus, of the loss function with respect to the model parameters, and update the parameters using the calculated gradient and a small learning rate. We repeat this process multiple times until the model parameters converge to optimal values.

In Tensorflow, SGD can be used as an optimizer in deep learning models by using the SGD function from Keras library - tensorflow.keras.optimizer.SGD()

In this way, SGD updates the model parameters in a more random and efficient way, leading to faster convergence and better generalization of the model.

In short, SGD is a powerful optimization algorithm that can be used to quickly optimize models in machine learning. With its efficiency, robustness, and ability to handle large datasets, SGD is an important tool for any machine learning practitioner.