Name: ———————-
Practice Exam
CS 591Q/791V - Pattern Recognition
Total Points: 60
Date: Posted on May 3, 2008
1. [15 points] Briefly describe each of the following terms in the context of pattern recognition with
an example.
(a) Bayes Risk.
(b) Bayesian Learning.
(c) Voronoi Tessellation.
2. [15 points] In many pattern classification problems one has the option either to assign the pattern
to one of cclasses, or to reject it as being unrecognizable. If the cost of rejecting is not too high,
it may be a desirable action.
Let
λ(αi|ωj) =
0if i=j, i, j = 1,2,...c
λrif i=c+ 1
λsotherwise,
where λris the loss incurred for choosing the (c+ 1)th action (i.e, rejection), and λsis the loss
incurred for making any substitution error. Show that the minimum risk decision rule is obtained
as follows:
If both the following conditions are satisfied:
•P(ωi|x)≥P(ωj|x),∀j,
•P(ωi|x)≥1−λr
λs,
then assign pattern xto class ωi,
else reject pattern x.
3. [15 points] MLE methods apply to estimates of prior probabilities as well. Consider a set of
labeled patterns in a “bag”. Each pattern can belong to one of cclasses, ω1, ω2,...ωc, whose
priors, P(ωi), are unknown. Now consider an experiment where patterns are successively (and
independently) drawn from the “bag” and their class noted. Let zik = 1 if the kth pattern drawn
from the bag belongs to class ωiand zik = 0 otherwise.
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