Classification

In [90]:
import numpy
import urllib
import scipy.optimize
import random
from sklearn import svm # Library for SVM classification
from sklearn import linear_model # Logistic Regression (among other things)
import ast
In [91]:
def parseData(fname):
  for l in urllib.urlopen(fname):
    yield eval(l)
In [92]:
def parseDataFromFile(fname):
  for l in open(fname):
    yield eval(l)
In [ ]:
data1 = list(parseDataFromFile("C:/Users/Julian McAuley/Documents/class_files/book_descriptions_50000.json"))
In [93]:
data2 = list(parseDataFromFile("C:/Users/Julian McAuley/Documents/class_files/book_images_5000.json"))
In [ ]:
data = data1
In [ ]:
data[2]

Priors...

p(label)

In [ ]:
prior = ["Children's Books" in d['categories'] for d in data]
prior = sum(prior) / len(prior)
In [ ]:
prior
In [ ]:
prior_neg = 1 - prior
In [ ]:
prior_neg

p(wizard in description | Children's Book)

In [ ]:
p1 = ["wizard" in b['description'] for b in data
      if "Children's Books" in b['categories']]
p1 = sum(p1) / len(p1)
In [ ]:
p1
In [ ]:
p1_neg = ["wizard" in b['description'] for b in data
         if not ("Children's Books" in b['categories'])]
p1_neg = sum(p1_neg) / len(p1_neg)
In [ ]:
p1_neg

p(witch in description | Children's Book)

In [ ]:
p2 = ["witch" in b['description'] for b in data if "Children's Books" in b['categories']]
p2 = sum(p2) * 1.0 / len(p2)
In [ ]:
p2
In [ ]:
p2_neg = ["witch" in b['description'] for b in data if not "Children's Books" in b['categories']]
p2_neg = sum(p2_neg) * 1.0 / len(p2_neg)
In [ ]:
p2_neg
In [ ]:
score = prior * p1 * p2
score_neg = prior_neg * p1_neg * p2_neg
In [ ]:
score / score_neg
In [ ]:
p = ["Children's Books" in b['categories'] for b in data if
     'witch' in b['description'] and 'wizard' in b['description']]
p = sum(p) * 1.0 / len(p)
In [ ]:
p / (1 - p)

Classification - Judging a book by its cover

In [94]:
data = data2
In [95]:
data[0]
Out[95]:
{'asin/ID': '1573110639',
 'url': 'http://www.amazon.com/dp/1573110639',
 'description': 'one of the worlds great reference books newsweek',
 'categories': ['New',
  'Politics & Social Sciences',
  'Science & Math',
  'Education & Reference'],
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 3.4881999492645264,
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 4.341400146484375,
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 0.7858999967575073,
 3.214200019836426,
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 0.7221999764442444,
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 2.6951000690460205,
 0.0,
 0.0,
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 1.4142999649047852,
 2.0550999641418457,
 3.257999897003174,
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 0.049400001764297485,
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 0.5530999898910522,
 0.0,
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 0.08510000258684158,
 1.2936999797821045,
 3.5964999198913574,
 0.6341000199317932,
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 0.82669997215271,
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 0.5914999842643738,
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 0.0,
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 0.0,
 0.0,
 ...]
In [97]:
X = [b['image_feature'] for b in data]
y = ["Children's Books" in b['categories'] for b in data]
In [98]:
X_train = X[:len(X)//2]
y_train = y[:len(y)//2]

X_test = X[len(X)//2:]
y_test = y[len(y)//2:]
In [99]:
mod = linear_model.LogisticRegression(C=1.0)
mod.fit(X_train, y_train)

C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
Out[99]:
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
                   intercept_scaling=1, l1_ratio=None, max_iter=100,
                   multi_class='warn', n_jobs=None, penalty='l2',
                   random_state=None, solver='warn', tol=0.0001, verbose=0,
                   warm_start=False)
In [100]:
train_predictions = mod.predict(X_train)
test_predictions = mod.predict(X_test)
In [102]:
# accuracy
sum(test_predictions == y_test) / len(y_test)
Out[102]:
0.9456
In [103]:
y_false = numpy.array([False for b in y_test])
In [104]:
# accuracy when predicting "false" always
sum(y_false == y_test) / len(y_test)
Out[104]:
0.962

Diagnostics

Data from: https://archive.ics.uci.edu/ml/datasets/Polish+companies+bankruptcy+data

In [105]:
f = open("C:/users/Julian McAuley/Documents/class_files/bankruptcy.arff", 'r')
In [106]:
while not '@data' in f.readline():
    pass
In [107]:
dataset = []
for l in f:
    if '?' in l: # Missing entry
        continue
    l = l.split(',')
    values = [1] + [float(x) for x in l]
    values[-1] = values[-1] > 0 # Convert to bool
    dataset.append(values)
In [108]:
dataset[0]
Out[108]:
[1,
 0.088238,
 0.55472,
 0.01134,
 1.0205,
 -66.52,
 0.34204,
 0.10949,
 0.57752,
 1.0881,
 0.32036,
 0.10949,
 0.1976,
 0.096885,
 0.10949,
 1475.2,
 0.24742,
 1.8027,
 0.10949,
 0.077287,
 50.199,
 1.1574,
 0.13523,
 0.062287,
 0.41949,
 0.32036,
 0.20912,
 1.0387,
 0.026093,
 6.1267,
 0.37788,
 0.077287,
 155.33,
 2.3498,
 0.24377,
 0.13523,
 1.4493,
 571.37,
 0.32101,
 0.095457,
 0.12879,
 0.11189,
 0.095457,
 127.3,
 77.096,
 0.45289,
 0.66883,
 54.621,
 0.10746,
 0.075859,
 1.0193,
 0.55407,
 0.42557,
 0.73717,
 0.73866,
 15182.0,
 0.080955,
 0.27543,
 0.91905,
 0.002024,
 7.2711,
 4.7343,
 142.76,
 2.5568,
 3.2597,
 False]

Data setup

In [109]:
X = [d[:-1] for d in dataset]
y = [d[-1] for d in dataset]

Fit model

In [110]:
mod = linear_model.LogisticRegression(C=1.0)
mod.fit(X,y)

C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\svm\base.py:929: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  "the number of iterations.", ConvergenceWarning)
Out[110]:
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
                   intercept_scaling=1, l1_ratio=None, max_iter=100,
                   multi_class='warn', n_jobs=None, penalty='l2',
                   random_state=None, solver='warn', tol=0.0001, verbose=0,
                   warm_start=False)
In [111]:
pred = mod.predict(X)
In [112]:
sum(pred == y) / len(y)
Out[112]:
0.9663477400197954
In [113]:
sum(y)
Out[113]:
102
In [114]:
len(y)
Out[114]:
3031
In [116]:
1 - 102/3031
Out[116]:
0.9663477400197954
In [117]:
sum(pred)
Out[117]:
6

Balanced model

In [118]:
mod = linear_model.LogisticRegression(C=1.0, class_weight = 'balanced')
In [119]:
mod.fit(X,y)

C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\svm\base.py:929: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  "the number of iterations.", ConvergenceWarning)
Out[119]:
LogisticRegression(C=1.0, class_weight='balanced', dual=False,
                   fit_intercept=True, intercept_scaling=1, l1_ratio=None,
                   max_iter=100, multi_class='warn', n_jobs=None, penalty='l2',
                   random_state=None, solver='warn', tol=0.0001, verbose=0,
                   warm_start=False)
In [120]:
pred = mod.predict(X)
In [121]:
sum(pred == y) / len(y)
Out[121]:
0.7832398548333883
In [122]:
# How many positive predictions?
sum(pred)
Out[122]:
717

Train/validation/test splits

In [128]:
Xy = list(zip(X,y))
In [130]:
random.shuffle(Xy)
In [131]:
X = [d[0] for d in Xy]
y = [d[1] for d in Xy]
In [132]:
N = len(y)
In [133]:
Ntrain = 1000
Nvalid = 1000
Ntest = 1031
In [134]:
Xtrain = X[:Ntrain]
Xvalid = X[Ntrain:Ntrain+Nvalid]
Xtest = X[Ntrain+Nvalid:]
In [135]:
ytrain = y[:Ntrain]
yvalid = y[Ntrain:Ntrain+Nvalid]
ytest = y[Ntrain+Nvalid:]
In [136]:
mod.fit(Xtrain, ytrain)

C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\linear_model\logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)
C:\Users\Julian McAuley\Anaconda3\lib\site-packages\sklearn\svm\base.py:929: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  "the number of iterations.", ConvergenceWarning)
Out[136]:
LogisticRegression(C=1.0, class_weight='balanced', dual=False,
                   fit_intercept=True, intercept_scaling=1, l1_ratio=None,
                   max_iter=100, multi_class='warn', n_jobs=None, penalty='l2',
                   random_state=None, solver='warn', tol=0.0001, verbose=0,
                   warm_start=False)

TP, TN, FP, FN, Accuracy, BER

In [137]:
pred = mod.predict(Xtest)
In [138]:
correct = pred == ytest
In [139]:
TP_ = numpy.logical_and(pred, ytest)
FP_ = numpy.logical_and(pred, numpy.logical_not(ytest))
TN_ = numpy.logical_and(numpy.logical_not(pred), numpy.logical_not(ytest))
FN_ = numpy.logical_and(numpy.logical_not(pred), ytest)
In [140]:
TP = sum(TP_)
FP = sum(FP_)
TN = sum(TN_)
FN = sum(FN_)
In [141]:
# accuracy
(TP + TN) / (TP + FP + TN + FN)
Out[141]:
0.8225024248302619
In [142]:
sum(correct) / len(correct)
Out[142]:
0.8225024248302619
In [143]:
# BER
1 - 0.5*(TP / (TP + FN) + TN / (TN + FP))
Out[143]:
0.34074209024108826

Ranking

In [144]:
scores = mod.decision_function(Xtest)
In [145]:
scores
Out[145]:
array([-0.77318466, -0.6581161 , -0.74149623, ..., -1.49607527,
       -0.9291817 , -2.65867657])
In [146]:
scoreslabels = list(zip(scores, ytest))
In [147]:
scoreslabels.sort(reverse=True)
In [149]:
scoreslabels
Out[149]:
[(20.439690291835287, False),
 (10.536847009816965, False),
 (9.712626998807286, False),
 (9.350710846782384, False),
 (7.842395225958438, True),
 (6.590474486739286, False),
 (6.588524732892533, True),
 (6.563726773813434, True),
 (5.548059989828498, False),
 (5.086841630348562, True),
 (4.944642526610214, False),
 (4.812316405708574, False),
 (4.794276730123465, False),
 (4.682747379455137, False),
 (4.447623205890571, False),
 (4.270804186374323, False),
 (4.250184212734646, False),
 (3.653335776879337, False),
 (3.4889521877721066, False),
 (3.46355933019042, False),
 (3.436463001668359, False),
 (3.4198634136702504, False),
 (3.414794145540118, False),
 (3.3293044674274617, False),
 (2.8361222975502187, False),
 (2.7104095419137417, False),
 (2.6999387473570358, False),
 (2.6954739311264393, False),
 (2.6059531284300865, False),
 (2.5506396164399265, False),
 (2.497613947591135, False),
 (2.434104441480049, False),
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 (2.1749874671742964, True),
 (2.1429001000034615, False),
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 (-1.904217679533705, False),
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 (-2.2265657796323852, False),
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 (-2.2301365956762447, False),
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 (-2.255136661841937, False),
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 (-2.479822798316745, False),
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 (-3.59665967115345, True),
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 (-4.548708688590777, False),
 (-4.651349281464104, False),
 (-4.68621279116234, False),
 (-4.740483073132025, False),
 ...]
In [150]:
sortedlabels = [x[1] for x in scoreslabels]
In [151]:
sortedlabels
Out[151]:
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 ...]
In [157]:
# precision
retrieved = sum(pred)
relevant = sum(ytest)
intersection = sum([y and p for y,p in zip(ytest,pred)])
In [158]:
intersection / retrieved
Out[158]:
0.08791208791208792
In [159]:
# recall
intersection / relevant
Out[159]:
0.48484848484848486
In [160]:
# precision at 10
sum(sortedlabels[:10]) / 10
Out[160]:
0.4