weka.classifiers.bayes.NaiveBayesSimple

weka.classifiers.bayes.NaiveBayesSimple 為簡單貝氏機率學習器的簡化版，
記錄各類別事前機率，及給定類別下各屬性值出現之條件機率，
再依案例，累乘得到給定屬性值下各類別出現之事後機率，取機率高者為預測類別，
可提供案例集不錯表現值供標竿比較之用。

NaiveBayesSimple 學習分類時，同樣為每個類別統計其類別事前機率(prior probability)、給定類別下各屬性值出現之條件機率。
遇數值屬性時，一律假設母體為常態分布，統計其平均值、標準差，供條件機率之推估。
預測分類時，依新案例，累乘得到給定屬性值下各類別出現之事後機率(posterior probability)，取機率高者為預測類別。

參數說明:

出處: R. Duda and P. Hart (1973). Pattern Classification and Scene Analysis. Wiley, New York.

>java -cp simpleEducationalLearningSchemes.jar;weka.jar;. 
   weka.classifiers.bayes.NaiveBayesSimple -t data\weather.numeric.arff


Naive Bayes (simple)

Class yes: P(C) = 0.625

Attribute outlook
sunny   overcast        rainy
0.25            0.41666667      0.33333333

Attribute temperature
Mean: 73        Standard Deviation: 6.164414

Attribute humidity
Mean: 79.11111111       Standard Deviation: 10.21572861

Attribute windy
TRUE    FALSE
0.36363636      0.63636364



Class no: P(C) = 0.375

Attribute outlook
sunny   overcast        rainy
0.5             0.125           0.375

Attribute temperature
Mean: 74.6      Standard Deviation: 7.8930349

Attribute humidity
Mean: 86.2      Standard Deviation: 9.7313925

Attribute windy
TRUE    FALSE
0.57142857      0.42857143


Time taken to build model: 0.77 seconds
Time taken to test model on training data: 0 seconds

=== Error on training data ===

Correctly Classified Instances          13               92.8571 %
Incorrectly Classified Instances         1                7.1429 %
Kappa statistic                          0.8372
Mean absolute error                      0.3003
Root mean squared error                  0.3431
Relative absolute error                 64.6705 %
Root relative squared error             71.5605 %
Total Number of Instances               14


=== Detailed Accuracy By Class ===

                 TP Rate  FP Rate  Precision  Recall   F-Measure  MCC      ROC Area  PRC Area  Class
                 1.000    0.200    0.900      1.000    0.947      0.849    0.933     0.963     yes
                 0.800    0.000    1.000      0.800    0.889      0.849    0.933     0.925     no
Weighted Avg.    0.929    0.129    0.936      0.929    0.926      0.849    0.933     0.949


=== Confusion Matrix ===

 a b   <-- classified as
 9 0 | a = yes
 1 4 | b = no



=== Stratified cross-validation ===

Correctly Classified Instances           8               57.1429 %
Incorrectly Classified Instances         6               42.8571 %
Kappa statistic                         -0.0244
Mean absolute error                      0.4699
Root mean squared error                  0.5376
Relative absolute error                 98.6856 %
Root relative squared error            108.9683 %
Total Number of Instances               14


=== Detailed Accuracy By Class ===

                 TP Rate  FP Rate  Precision  Recall   F-Measure  MCC      ROC Area  PRC Area  Class
                 0.778    0.800    0.636      0.778    0.700      -0.026   0.444     0.636     yes
                 0.200    0.222    0.333      0.200    0.250      -0.026   0.444     0.398     no
Weighted Avg.    0.571    0.594    0.528      0.571    0.539      -0.026   0.444     0.551


=== Confusion Matrix ===

 a b   <-- classified as
 7 2 | a = yes
 4 1 | b = no


如下 weather.numeric.arff 案例集的14個案例利用2個文字屬性及2個數字屬性，預測文字屬性。

outlook
temperature
humidity
windy
play
sunny
85
85
FALSE
no
sunny
80
90
TRUE
no
rainy
65
70
TRUE
no
sunny
72
95
FALSE
no
rainy
71
91
TRUE
no
overcast
83
86
FALSE
yes
rainy
70
96
FALSE
yes
rainy
68
80
FALSE
yes
overcast
64
65
TRUE
yes
sunny
69
70
FALSE
yes
rainy
75
80
FALSE
yes
sunny
75
70
TRUE
yes
overcast
72
90
TRUE
yes
overcast
81
75
FALSE
yes

參考:
1.weka.classifiers.bayes.NaiveBayesSimple
   code | doc
2.從Weka 3.7.2版之後，NaiveBayesSimple 類別
  從 weka.jar 主套件改歸到 simpleEducationalLearningSchemes.jar 選擇性套件內，
  可利用Tools/Package Manager/Search: simpleEducationalSchemes/Install進行安裝。
  在Windows下，下載套件存放位置在 C:\Users\用戶名\wekafiles\packages\ 資料夾內。
  simpleEducationalSchemes 包含IB1,Prism,Id3,NaiveBayesSimple四個簡單分類器