stat841: Difference between revisions
Jump to navigation
Jump to search
| Line 10: | Line 10: | ||
'''3. Error data'''<br /> | '''3. Error data'''<br /> | ||
Definition: | Definition:<br /> | ||
''True error rate'' of a classifier(h) is defined as the probability that the prediction of Y from X | ''True error rate'' of a classifier(h) is defined as the probability that the prediction of Y from X does not exactly equal to Y, namely, <math>\, L(h)=P(h(X) \neq Y)</math>.<br /> | ||
''Empirical error rate(training error rate)'' of a classifier(h) is . The mathematical defition is as below:<br /> | ''Empirical error rate(training error rate)'' of a classifier(h) is defined as the frequency of event that Y predicted from X does not equal to Y in totally n prediction. The mathematical defition is as below:<br /> | ||
<math>\, L_{h}= \frac{1}{n} \sum_{i=1}^{n} I(h(X_{i} \neq Y_{i}))</math>, where <math>\, I</math> | <math>\, L_{h}= \frac{1}{n} \sum_{i=1}^{n} I(h(X_{i} \neq Y_{i}))</math>, where <math>\,I</math> is an indicator that <math>\, I=</math>. | ||
'''4. Bayes Classifier'''<br /> | '''4. Bayes Classifier'''<br /> | ||
Revision as of 16:46, 30 September 2009
Scribe sign up
Course Note for Sept.30th (Classfication_by Liang Jiaxi)
1.
2. Classification
Classification is a function between two random varialbe
3. Error data
Definition:
True error rate of a classifier(h) is defined as the probability that the prediction of Y from X does not exactly equal to Y, namely, [math]\displaystyle{ \, L(h)=P(h(X) \neq Y) }[/math].
Empirical error rate(training error rate) of a classifier(h) is defined as the frequency of event that Y predicted from X does not equal to Y in totally n prediction. The mathematical defition is as below:
[math]\displaystyle{ \, L_{h}= \frac{1}{n} \sum_{i=1}^{n} I(h(X_{i} \neq Y_{i})) }[/math], where [math]\displaystyle{ \,I }[/math] is an indicator that [math]\displaystyle{ \, I= }[/math].
4. Bayes Classifier