Contents
How are parameter estimates used in gradient descent?
We make an hypothesis about the parameters values, assigning values to $ heta_0$ and $ heta_1$, and then evaluate how good our hypothesis is, by computing the cost function. Then, we optimize the parameters values iteratively. This optimization is what the gradient descent algorithm does.
How to use gradient checking in a model?
Consider a 1D linear function J ( θ) = θ x. The model contains only a single real-valued parameter θ, and takes x as input. You will implement code to compute J (.) and its derivative ∂ J ∂ θ. You will then use gradient checking to make sure your derivative computation for J is correct.
How is gradient checking used in backpropagation?
Your CEO says, “Give me a proof that your backpropagation is actually working!” To give this reassurance, you are going to use “gradient checking”. Let’s do it! Backpropagation computes the gradients ∂ J ∂ θ, where θ denotes the parameters of the model. J is computed using forward propagation and your loss function.
When do you use the term gradient in a function?
The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to move) that The term “gradient” is typically used for functions with several inputs and a single output (a scalar field).
Do you use gradient descent or Monte Carlo for regression?
However, there are very valid reasons to learn both gradient descent and Monte Carlo methods. First of all, problems are typically not this simple. For most non-linear regression problems, there is no closed form solution. Also, the closed form solution scales very poorly when we have much more data, especially in terms of parameters.
What does convergence mean for a gradient descent?
Convergence means that the gradient descent is sufficiently close to a stationary point, i.e. a local or global minimum. For linear regression, the cost function will always be convex, which means we will always reach a global minimum and won’t get stuck in local minimum.