Gradient descent

See also: Machine learning terms

Introduction

Gradient descent is a popular optimization algorithm in machine learning. It works by finding the minimum cost function, which can be adjusted to minimize errors between predicted output and actual output from a model. Gradient descent utilizes weights and biases as input parameters to achieve this minimal error margin.

How Gradient Descent Works

Gradient descent works by iteratively altering the parameters of a model in order to obtain steepest descent of the cost function, which measures how well it's performing. The goal of gradient descent is to find parameters that minimize this cost function.

The algorithm begins with an initial set of parameters and iteratively updates them until it reaches a minimum point in the cost function. At each iteration, a gradient of the cost function is computed with respect to those same parameters; this gradient is represented as a vector pointing in the direction of steepest increase in cost function. To minimize this cost function, parameters are updated in direct opposition to that direction.

The update rule for parameters is determined by a learning rate, which controls the step size of each iteration. A small learning rate may lead to slow convergence while an excessively high one could cause overshooting at the minimum point.

Types of Gradient Descent

Gradient descent can be divided into three types: batch gradient descent, stochastic gradient descent, and mini-batch gradient descent.

Batch Gradient Descent

Batch gradient descent updates the parameters after computing the gradient of a cost function over all training datasets. Although it can be computationally expensive for large datasets, it can converge to the global minimum in terms of this cost function.

Stochastic Gradient Descent

Stochastic gradient descent updates the parameters after computing the gradient of a cost function for one training example. It is less computationally expensive than batch gradient descent, though it may converge to a local minimum in the cost function.

Mini-Batch Gradient Descent

Mini-batch gradient descent is a method for updating parameters after computing the gradient of a cost function for a small set of training examples. It offers an alternative to batch gradient descent and stochastic gradient descent, being less computationally intensive than batch gradient descent and capable of convergeng to either global minimums or local minima in the cost function.

Regularization

Gradient descent can also be enhanced with regularization techniques, which reduce overfitting and enhance generalization of the model. Regularization techniques like L1 or L2 regularization add a penalty term to the cost function that penalizes large parameter values; this encourages models to use smaller parameter values while helping prevent overfitting.

Explain Like I'm 5 (ELI5)

Gradient descent is a technique for teaching your computer program how to learn by itself. It works like a treasure hunt where the program tries to find the treasure and uses that as its model for making accurate predictions. It starts by making an educated guess as to where it might be and looks for clues that can guide it closer. Gradient descent keeps moving in the direction of these clues until it finds the treasure - this treasure being the best way of making accurate predictions, while clues represent errors made while trying to predict something else.

Explain Like I'm 5 (ELI5)

Gradient descent is like finding the fastest route down a steep mountain. Imagine yourself perched atop this immense peak, eager to reach its base as quickly as possible.

To expedite your descent down the mountain, take steps in the direction that will bring you down fastest. You can tell which way to go by looking at the slope beneath your feet; if one direction is steeper than another, that is likely where you should head.

Take a step in that direction, then look again at the slope. Repeat this process until you reach the bottom.

Machine learning utilizes gradient descent to determine the best values for certain parameters that influence predictions. We examine how changing these parameters affects how accurately our predictions match actual outcomes, and use gradient descent to find these values that will give our forecasts maximum precision.