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Unformatted text preview: the fruit type of . Error rate
The true e rror rate '
defined as of a classifier having classification rule
and is defined as the probability that does not correctly classify any new data input, i.e., it is
are the known feature values and the true class of that input, respectively. The e mpirical e rror rate (or training e rror rate ) of a classifier having classification rule
inputs in the training set, i.e., it is defined as
and the true class of the is an indicator variable and is defined as the frequency at which . Here, and does not correctly classify the data are the known feature values training input, respectively. Bayes Clas s ifier
The principle of Bayes Classifier is to calculate the posterior probability of a given object from its prior probability via Bayes formula, and then place the object in the class
with the largest posterior probability
o lsiy Mathematically, for
value of w fn
e id sc ta
uh ht classes and given object
, we find
, we use Bayes f ormula where is referred to as the posterior probability, i mxmmoe altemmeso
f which maximizes as the prior probability, , and classify . into class . In order to calculate the as the likelihood, and as the evidence.
wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 4/74 10/09/2013 For the special case that
f ormula, we have Stat841 - Wiki Cour se Notes has only two classes, that is, . Consider the probability that . Given , By Bayes De finition:
The Bayes classification rule is 3 diffe re nt approache s to clas s ification:
1) Empirical Risk Minimization: Choose a set fo classifier
2) Regression: Find an estimate 3) Density Estimation: estimate and find that minimizes some estimate of of the function r and define and (less popular in high- dimension cases) Baye s Clas s ification Rule Optimality The ore m: The Bayes rule is optimal in true error rate, that is for any other classification rule
Intuitively speaking this theorem is saying we cannot do better than classifying
any other type. to when the probability of being of type for ,...
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This document was uploaded on 03/07/2014.
- Winter '13