Выбор семейства распределений в наивном байесе

In [1]:

    

%matplotlib inline

import numpy as np
from sklearn.datasets import load_digits, load_breast_cancer
from sklearn.model_selection import cross_val_score
from sklearn.naive_bayes import BernoulliNB, MultinomialNB, GaussianNB


    

In [2]:

    

#loading datasets
digits = load_digits()
X_dig = digits.data
y_dig = digits.target

breast_cancer = load_breast_cancer()
X_br_can = breast_cancer.data
y_br_can = breast_cancer.target


    

In [3]:

    

print(digits.DESCR)


    

    




Optical Recognition of Handwritten Digits Data Set
===================================================

Notes
-----
Data Set Characteristics:
    :Number of Instances: 5620
    :Number of Attributes: 64
    :Attribute Information: 8x8 image of integer pixels in the range 0..16.
    :Missing Attribute Values: None
    :Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)
    :Date: July; 1998

This is a copy of the test set of the UCI ML hand-written digits datasets
http://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits

The data set contains images of hand-written digits: 10 classes where
each class refers to a digit.

Preprocessing programs made available by NIST were used to extract
normalized bitmaps of handwritten digits from a preprinted form. From a
total of 43 people, 30 contributed to the training set and different 13
to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of
4x4 and the number of on pixels are counted in each block. This generates
an input matrix of 8x8 where each element is an integer in the range
0..16. This reduces dimensionality and gives invariance to small
distortions.

For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.
T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.
L. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,
1994.

References
----------
  - C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their
    Applications to Handwritten Digit Recognition, MSc Thesis, Institute of
    Graduate Studies in Science and Engineering, Bogazici University.
  - E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.
  - Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.
    Linear dimensionalityreduction using relevance weighted LDA. School of
    Electrical and Electronic Engineering Nanyang Technological University.
    2005.
  - Claudio Gentile. A New Approximate Maximal Margin Classification
    Algorithm. NIPS. 2000.

In [4]:

    

print(X_dig[42])


    

    




[  0.   0.   0.   0.  12.   5.   0.   0.   0.   0.   0.   2.  16.  12.   0.
   0.   0.   0.   1.  12.  16.  11.   0.   0.   0.   2.  12.  16.  16.  10.
   0.   0.   0.   6.  11.   5.  15.   6.   0.   0.   0.   0.   0.   1.  16.
   9.   0.   0.   0.   0.   0.   2.  16.  11.   0.   0.   0.   0.   0.   3.
  16.   8.   0.   0.]

In [5]:

    

print(breast_cancer.DESCR)


    

    




Breast Cancer Wisconsin (Diagnostic) Database
=============================================

Notes
-----
Data Set Characteristics:
    :Number of Instances: 569

    :Number of Attributes: 30 numeric, predictive attributes and the class

    :Attribute Information:
        - radius (mean of distances from center to points on the perimeter)
        - texture (standard deviation of gray-scale values)
        - perimeter
        - area
        - smoothness (local variation in radius lengths)
        - compactness (perimeter^2 / area - 1.0)
        - concavity (severity of concave portions of the contour)
        - concave points (number of concave portions of the contour)
        - symmetry 
        - fractal dimension ("coastline approximation" - 1)

        The mean, standard error, and "worst" or largest (mean of the three
        largest values) of these features were computed for each image,
        resulting in 30 features.  For instance, field 3 is Mean Radius, field
        13 is Radius SE, field 23 is Worst Radius.

        - class:
                - WDBC-Malignant
                - WDBC-Benign

    :Summary Statistics:

    ===================================== ====== ======
                                           Min    Max
    ===================================== ====== ======
    radius (mean):                        6.981  28.11
    texture (mean):                       9.71   39.28
    perimeter (mean):                     43.79  188.5
    area (mean):                          143.5  2501.0
    smoothness (mean):                    0.053  0.163
    compactness (mean):                   0.019  0.345
    concavity (mean):                     0.0    0.427
    concave points (mean):                0.0    0.201
    symmetry (mean):                      0.106  0.304
    fractal dimension (mean):             0.05   0.097
    radius (standard error):              0.112  2.873
    texture (standard error):             0.36   4.885
    perimeter (standard error):           0.757  21.98
    area (standard error):                6.802  542.2
    smoothness (standard error):          0.002  0.031
    compactness (standard error):         0.002  0.135
    concavity (standard error):           0.0    0.396
    concave points (standard error):      0.0    0.053
    symmetry (standard error):            0.008  0.079
    fractal dimension (standard error):   0.001  0.03
    radius (worst):                       7.93   36.04
    texture (worst):                      12.02  49.54
    perimeter (worst):                    50.41  251.2
    area (worst):                         185.2  4254.0
    smoothness (worst):                   0.071  0.223
    compactness (worst):                  0.027  1.058
    concavity (worst):                    0.0    1.252
    concave points (worst):               0.0    0.291
    symmetry (worst):                     0.156  0.664
    fractal dimension (worst):            0.055  0.208
    ===================================== ====== ======

    :Missing Attribute Values: None

    :Class Distribution: 212 - Malignant, 357 - Benign

    :Creator:  Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian

    :Donor: Nick Street

    :Date: November, 1995

This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.
https://goo.gl/U2Uwz2

Features are computed from a digitized image of a fine needle
aspirate (FNA) of a breast mass.  They describe
characteristics of the cell nuclei present in the image.

Separating plane described above was obtained using
Multisurface Method-Tree (MSM-T) [K. P. Bennett, "Decision Tree
Construction Via Linear Programming." Proceedings of the 4th
Midwest Artificial Intelligence and Cognitive Science Society,
pp. 97-101, 1992], a classification method which uses linear
programming to construct a decision tree.  Relevant features
were selected using an exhaustive search in the space of 1-4
features and 1-3 separating planes.

The actual linear program used to obtain the separating plane
in the 3-dimensional space is that described in:
[K. P. Bennett and O. L. Mangasarian: "Robust Linear
Programming Discrimination of Two Linearly Inseparable Sets",
Optimization Methods and Software 1, 1992, 23-34].

This database is also available through the UW CS ftp server:

ftp ftp.cs.wisc.edu
cd math-prog/cpo-dataset/machine-learn/WDBC/

References
----------
   - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction 
     for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on 
     Electronic Imaging: Science and Technology, volume 1905, pages 861-870,
     San Jose, CA, 1993.
   - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and 
     prognosis via linear programming. Operations Research, 43(4), pages 570-577, 
     July-August 1995.
   - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques
     to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) 
     163-171.

In [6]:

    

print(X_br_can[42])


    

    




[  1.90700000e+01   2.48100000e+01   1.28300000e+02   1.10400000e+03
   9.08100000e-02   2.19000000e-01   2.10700000e-01   9.96100000e-02
   2.31000000e-01   6.34300000e-02   9.81100000e-01   1.66600000e+00
   8.83000000e+00   1.04900000e+02   6.54800000e-03   1.00600000e-01
   9.72300000e-02   2.63800000e-02   5.33300000e-02   7.64600000e-03
   2.40900000e+01   3.31700000e+01   1.77400000e+02   1.65100000e+03
   1.24700000e-01   7.44400000e-01   7.24200000e-01   2.49300000e-01
   4.67000000e-01   1.03800000e-01]

In [7]:

    

#Initializing Naive Bayes classifiers
bnb = BernoulliNB()
mnb = MultinomialNB()
gnb = GaussianNB()


    

In [8]:

    

#Cross-validation of classifiers
score_bnb_dig = cross_val_score(bnb, X_dig, y_dig)
score_bnb_br_can = cross_val_score(bnb, X_br_can, y_br_can)

score_mnb_dig = cross_val_score(mnb, X_dig, y_dig)
score_mnb_br_can = cross_val_score(mnb, X_br_can, y_br_can)

score_gnb_dig = cross_val_score(gnb, X_dig, y_dig)
score_gnb_br_can = cross_val_score(gnb, X_br_can, y_br_can)


    

In [9]:

    

print('Digits dataset')
print('BernoulliNB mean cross_val_score: ' + str(score_bnb_dig.mean()))
print('MultinomialNB mean cross_val_score: ' + str(score_mnb_dig.mean()))
print('GaussianNB mean cross_val_score: ' + str(score_gnb_dig.mean()))


    

    




Digits dataset
BernoulliNB mean cross_val_score: 0.825823650778
MultinomialNB mean cross_val_score: 0.870877148974
GaussianNB mean cross_val_score: 0.818600380355

In [10]:

    

print('Breast cancer dataset')
print('BernoulliNB mean cross_val_score: ' + str(score_bnb_br_can.mean()))
print('MultinomialNB mean cross_val_score: ' + str(score_mnb_br_can.mean()))
print('GaussianNB mean cross_val_score: ' + str(score_gnb_br_can.mean()))


    

    




Breast cancer dataset
BernoulliNB mean cross_val_score: 0.627420402859
MultinomialNB mean cross_val_score: 0.894579040193
GaussianNB mean cross_val_score: 0.936749280609

In [15]:

    

with open('answer1.txt', 'w') as fout:
    fout.write(str(np.max([score_bnb_br_can.mean(), score_mnb_br_can.mean(), score_gnb_br_can.mean()])))


    

In [16]:

    

with open('answer2.txt', 'w') as fout:
    fout.write(str(np.max([score_bnb_dig.mean(), score_mnb_dig.mean(), score_gnb_dig.mean()])))


    

In [13]:

    

answer = '3' + ' ' + '4'
with open('answer3.txt', 'w') as fout:
    fout.write(answer)