Gradient Descent Optimization Algorithm The Gradient Descent optimization algorithm is a widely used technique in machine learning for finding the optimal s...
Gradient Descent Optimization Algorithm
The Gradient Descent optimization algorithm is a widely used technique in machine learning for finding the optimal set of parameters that minimize a loss function.
Loss Function:
A loss function measures how far off a model's predictions are from the actual target values. Common loss functions include mean squared error (MSE) and mean absolute error (MAE).
Algorithm Steps:
Initialisation: Choose an initial set of parameter values.
Iteration:
For each iteration, compute the gradient of the loss function with respect to the parameters.
Update the parameters in the direction of the negative gradient.
Update the learning rate to control how large the step size will be.
Repeat until convergence (a minimum error or a specified number of iterations).
Gradient:
The gradient is a vector containing the partial derivatives of the loss function with respect to each parameter. The gradient points in the direction of the steepest descent of the loss function.
Regularisation:
To prevent overfitting, the algorithm can be regularised by adding a penalty term to the loss function, such as L1 or L2 norm. This penalises large parameter values, which can lead to a more sparse model that generalises better.
Convergence:
Gradient descent converges when the gradient becomes small or reaches a specified convergence criterion. The algorithm reaches convergence when the error function stops decreasing or the number of iterations is reached.
Benefits:
Adaptability to different loss functions.
Ability to handle high-dimensional data.
Relatively easy to implement.
Example:
Suppose we have a dataset with a target variable that is linearly related to a set of features. We can use gradient descent to find the optimal values of the slope and intercept of this linear relationship