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How gradient descent algorithm is used for minimizing the errors explain?
Gradient descent is an optimization algorithm that finds the optimal weights (a,b) that reduces prediction error. Step 2: Calculate the gradient i.e. change in SSE when the weights (a & b) are changed by a very small value from their original randomly initialized value.
What is the idea behind gradient descent?
Gradient descent is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent.
How does gradient descent affect the learning step?
Gradient descent is a first-order optimization algorithm, which means it doesn’t take into account the second derivatives of the cost function. However, the curvature of the function affects the size of each learning step.
What are the issues with gradient based optimization?
A common issue with gradient based optimization methods is being trapped in a local minimum far from the desired global minimum. With on-line learning the stochastic error surface is noisy which helps escaping such local minima. Batch learning, by averaging the gradients, removes noise and is more prone to being caught in local minima.
Is the number of iterations in gradient descent fixed?
The number of iterations can be fixed and given by the user. Or, if you have a precision in mind (~0.001). You can stop calculating once you reach this value of precision. We will explore both the approaches. We will implement a simple form of Gradient Descent using python.
Is the gradient descent algorithm guaranteed to converge?
We can use fixed learning rate during training without worrying about learning rate decay. It has straight trajectory towards the minimum and it is guaranteed to converge in theory to the global minimum if the loss function is convex and to a local minimum if the loss function is not convex. It has unbiased estimate of gradients.