855 B
855 B
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(20 points) \c{Derive the VC dimension of the following classifiers.}
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(20 points) \c{Let
P (x|C)
denote a Bernoulli density function for a class $C \in {C_1, C_2}$ andP (C)
denote the prior}a. \c{Given the priors
P (C_1)
andP (C_2)
, and the Bernoulli densities specified byp_1 \equiv p(x = 0|C_1)
andp_2 \equiv p(x = 0|C_2)
, derive the classification rules for classifying a samplex
intoC_1
andC_2
based on the posteriorsP (C_1|x)
andP (C_2|x)
. (Hint: give rules for classifyingx = 0
andx = 1
.)}For $x=0$, the posteriors $P(C_i | x)$ are given by $P(C_i | x = 0) = \frac{p(x = 0 | C_i) p(C_i)}{p(x = 0)}$. - $p(x = 0 | C_i)$ is given to us as $p_1$