Given the set of parameters of a logistic regression model, and a small set of data points, calculate the j^{th} partial derivative of the log-loss function for some j.
What kind of data points could be given here? The formula for the log-loss function I have is l(w,b)= 1/m ∑_(i=1)->m [ln(1+e^(-y_i(w∙x+b)))]
I get that I want to differentiate with respect to the weight w, but I'm just not sure what this type of problem could look like. Some advice would be helpful. Thanks.
You are given $(x_i, y_i), i=1, \ldots, m$ where $y_i$'s are either $1$ or $-1$.. These are the data points.
You are trying to build a linear prediction function and determining $w$ and $b$ which minimizes the loss is your desired task.