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Gradient descent is a fundamental optimization algorithm used in training supervised machine learning models. It helps minimize the error function by iteratively adjusting model parameters. Understanding how to derive and apply this method is essential for effective model training.
Derivation of Gradient Descent
The core idea of gradient descent involves computing the gradient of the loss function with respect to model parameters. This gradient indicates the direction of steepest increase. To minimize the loss, parameters are updated in the opposite direction of the gradient.
Mathematically, the parameter update rule is expressed as:
θnew = θold – η ∇L(θ)
where θ represents the model parameters, η is the learning rate, and ∇L(θ) is the gradient of the loss function.
Applying Gradient Descent
To apply gradient descent, the following steps are typically followed:
- Initialize model parameters randomly or with specific values.
- Calculate the loss function based on current parameters and training data.
- Compute the gradient of the loss with respect to each parameter.
- Update the parameters using the gradient descent rule.
- Repeat the process until the loss converges or a set number of iterations is reached.
Choosing the Learning Rate
The learning rate η determines the size of each update step. A small learning rate may result in slow convergence, while a large one can cause overshooting the minimum. Selecting an appropriate learning rate is crucial for effective training.