COMPUTER SCIENCE TRIPOS Part IB – 2021 – Paper 6
Artificial Intelligence (sbh11)
The standard linear regression model uses a hypothesis
h(x, w, b) = w
T x + b
to fit m examples ((x1, y1), . . . ,(xm, ym)) by minimizing the error
E(w, b) = Xm
i=1
(yi − h(xi
, w, b))2
.
(a) Derive a gradient descent algorithm for training the linear regression model
described. [5 marks]
(b) In the application of interest, you believe that it is desirable to train such that
the learned parameters have ||w|| ‘ 1. Suggest a modification to E(w, b) that
facilitates this, and derive the corresponding gradient descent training algorithm.
[5 marks]
(c) Describe the components of a general heuristic search problem. [4 marks]
(d) You are faced with a heuristic search problem, but the heuristics you have so far
developed are less effective than desired. Suggest two ways in which supervised
machine learning might be used to develop a better heuristic, mentioning if
necessary any corresponding disadvantages of using the approach. You may
assume that a collection of problems to be solved by the heuristic search is
available. [6 marks]