Following Qs

Part 1 Regression In non-linear, basis-function regression, our goal is to build a model for an input data set using a set of functions that have useful properties. In this problem, you will set up the formulation for a non-linear basis-function regression problem, up to the point where you have a target cost function with a known solution The basis functions you will use are of the form TF) where T is simply the maximum value our input x can take within the domain of our problem. This is a single-input, single-output regression problem a) [2 marks]-Outputs y are modeled as a function y f(x). Show the equation that des operations erms of a set of K basis functians without vector b) [2 marks] Show how to express the function in a) as an equation in terms of vector dot products V0 c) [3 marks]- Show without using vector operations the form of the target function E(w) that needs to be optimized to learn optimal weights This function should account for all input pairs in the d?taset and all basis functions d) 12 marks]- Show the formulation for E(w) in terms of matrix and vector operations.

Part 1 - Regression In non-linear. basis-function regression. our goal is to build a model for an input data set using a set of functions that have useful properties. In this problem. you will set up the formulation for a non-linear basis-function regression problem. up to the point where you have a target cost function with a known solution. The basis functions you will use are of the form: bsr} = sings!!!) where T ls simply the maximum value our Input x can take within the dorrIaln of our problem. This is a singleinput. singleoutput regression problem. a) [2 marks} - Outputs y are modeled as a function y=ffo. Show the a cation that de - I... - enns of a set of lg basis functidsymutm? M . q..i.eez>