gradient descent: consider the code example discussed in class. the prediction function is 1 +ws and the loss function is y(w, i) t where t represents the vector of observed targets, and x represents the vector of observed features. (a) derive the gradient and hessian of l(wx), with respect to w b) implement them and re-run the example, playing around with the step size and starting values do you see how much work it took to get get newton's method to converge to something sensible? (c) modify the code to give you stochastic gradient descent. try this with different mini-batch sizes and starting values, to get a feel for how it works- particularly the stability of the algorithm with respect to these hyper-parameters.

there is no correct list among the choices you've provided.

the list might look something like this:

-- baby human

-- piccolo

-- flute

-- soprano singer

-- trumpet

-- tenor singer

-- trombone

-- baritone singer

-- baritone horn

-- bass singer

-- tuba

since i had to make up the list myself, i made it easy on myself, and i didn't try to shuffle the string instruments and woodwinds into it too.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.