Data Mining: Practical Machine Learning Tools and Techniques, Second Edition
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- Bu səhifədəki naviqasiya:
- Table 4.4 The numeric weather data with summary statistics.
- Bayesian models for document classification
- Table 4.5 Another new day.
set of numbers (the “one less than” is to do with the number of degrees of freedom in the sample, a statistical notion that we don’t want to get into here). The probability density function for a normal distribution with mean m and
standard deviation s is given by the rather formidable expression: But fear not! All this means is that if we are considering a yes outcome when
= 66, m = 73, and s = 6.2 into the formula. So the value of the probability density function is By the same token, the probability density of a yes outcome when humidity has value, say, of 90 is calculated in the same way: The probability density function for an event is very closely related to its prob- ability. However, it is not quite the same thing. If temperature is a continuous scale, the probability of the temperature being exactly 66—or exactly any other value, such as 63.14159262—is zero. The real meaning of the density function
say, between x - e/2 and x + e/2, is e f(x). What we have written above is correct
= ( ) = 90 0 0221 . . f temperature yes e = ( ) = ◊ = - ( ) ◊ 66 1 2 6 2 0 0340 66 73
2 6 2 2 2 p . . . .
e x ( ) = - ( ) 1 2 2 2 2 ps m s . 4 . 2
S TAT I S T I C A L M O D E L I N G 9 3
Table 4.4 The numeric weather data with summary statistics. Outlook
Temperature Humidity
Windy Play
yes no yes no yes no yes no yes no sunny
2 3 83 85 86 85 false 6 2 9 5 overcast 4 0 70 80 96 90 true 3 3 rainy 3 2 68 65 80 70 64 72 65 95 69 71 70 91 75 80 75 70 72 90 81 75 sunny 2/9 3/5
mean 73 74.6 mean 79.1
86.2 false
6/9 2/5
9/14 5/14
overcast 4/9
0/5 std. dev. 6.2
7.9 std. dev. 10.2
9.7 true
3/9 3/5
rainy 3/9
2/5 P088407-Ch004.qxd 4/30/05 11:13 AM Page 93 if temperature is measured to the nearest degree and humidity is measured to the nearest percentage point. You might think we ought to factor in the accu- racy figure e when using these probabilities, but that’s not necessary. The same e would appear in both the yes and no likelihoods that follow and cancel out when the probabilities were calculated. Using these probabilities for the new day in Table 4.5 yields which leads to probabilities These figures are very close to the probabilities calculated earlier for the new day in Table 4.3, because the temperature and humidity values of 66 and 90 yield similar probabilities to the cool and high values used before. The normal-distribution assumption makes it easy to extend the Naïve Bayes classifier to deal with numeric attributes. If the values of any numeric attributes are missing, the mean and standard deviation calculations are based only on the ones that are present.
One important domain for machine learning is document classification, in which each instance represents a document and the instance’s class is the doc- ument’s topic. Documents might be news items and the classes might be domes- tic news, overseas news, financial news, and sport. Documents are characterized by the words that appear in them, and one way to apply machine learning to document classification is to treat the presence or absence of each word as a Boolean attribute. Naïve Bayes is a popular technique for this application because it is very fast and quite accurate. However, this does not take into account the number of occurrences of each word, which is potentially useful information when determining the category Probability of no = +
0 000108 0 000036 0 000108 75 0 .
. . %.
Probability of yes = + = 0 000036
0 000036 0 000108 25 0
. . . . %, likelihood of likelihood of
= ¥ ¥ ¥ ¥ = = ¥ ¥ ¥ ¥ = 2 9 0 0340 0 0221 3 9 9 14 0 000036 3 5 0 0221 0 0381 3 5 5 14 0 000108 . . . , . . . ; 9 4 C H A P T E R 4 | A LG O R I T H M S : T H E BA S I C M E T H O D S Table 4.5 Another new day. Outlook
Temperature Humidity
Windy Play
sunny 66 90 true ? P088407-Ch004.qxd 4/30/05 11:13 AM Page 94 Yüklə 4,3 Mb. Dostları ilə paylaş:
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