Gradient Descent is a popular optimization algorithm used in machine learning. It is used to minimize a function by iteratively adjusting the parameters of a model. Here's a brief overview of the Gradient Descent algorithm.

1. Introduction to Gradient Descent

Gradient Descent is an optimization algorithm that finds the minimum of a function. It works by approximating the function locally with a tangent plane and then moving in the direction of steepest descent.

2. How Gradient Descent Works

  • Compute the Gradient: The gradient of a function is a vector that points in the direction of the steepest increase of the function.
  • Update Parameters: Using the gradient, we update the parameters of the model in the direction of steepest descent.
  • Iterate: Repeat the above steps until a desired level of accuracy is achieved.

3. Types of Gradient Descent

  • Stochastic Gradient Descent (SGD): Updates the parameters using a single data point at each iteration.
  • Mini-batch Gradient Descent: Updates the parameters using a small batch of data points at each iteration.

4. Example

Let's consider a simple linear regression model with a cost function:

$$
J(\theta) = \frac{1}{2m} \sum_{i=1}^{m} (h_\theta(x^{(i)}) - y^{(i)})^2
$$

where $h_\theta(x) = \theta_0x_0 + \theta_1x_1 + ... + \theta_nx_n$

To minimize $J(\theta)$ using Gradient Descent, we update the parameters $\theta$ as follows:

$$
\theta_j := \theta_j - \alpha \frac{\partial J(\theta)}{\partial \theta_j}
$$

where $\alpha$ is the learning rate.

5. Further Reading

For more information on Gradient Descent and its applications, you can read the following tutorials:

6. Image

Here's a visual representation of Gradient Descent:

Gradient Descent