How are parameters that minimize the loss function found in practice?1 pointGradient descentSimplex algorithmStochastic gradient descentFractal geometry

In practice, parameters that minimize the loss function are found using Gradient Descent or Stochastic Gradient Descent.

Here's a step-by-step explanation:

1. Initialize parameters: The first step in these methods is to initialize the parameters with some values. This could be random initialization where the parameters are assigned random values, or zero initialization where the parameters are set to zero.

2. Compute the cost: The next step is to compute the cost or loss function. This is a measure of how well the model is performing. The goal is to minimize this cost.

3. Compute the gradient: The gradient is a vector that points in the direction of the greatest increase of the function. It is computed using the derivatives of the cost function with respect to the parameters.

4. Update the parameters: The parameters are then updated in the opposite direction of the gradient. This is because we want to decrease the cost, so we move in the direction where the function decreases the fastest. The size of the step we take in the direction of the gradient is determined by the learning rate.

5. Repeat steps 2-4: These steps are repeated until the cost function converges to the minimum value. If the cost function is convex, this will be the global minimum, otherwise it could be a local minimum.

The difference between Gradient Descent and Stochastic Gradient Descent lies in the amount of data used to compute the gradient of the cost function. In Gradient Descent, the gradient