Session 26/6/2017 - machine learning

Links: notebook, html, PDF, python, slides, slides(2), GitHub

Découverte des trois problèmes de machine learning exposé dans l’article Machine Learning - session 6.

from jyquickhelper import add_notebook_menu
add_notebook_menu()

Problème 1 : comparaison random forest, linéaire

C’est un problème de régression. On cherche à comparer une random forest avec un modèle linéaire.

Données

import pandas
df = pandas.read_csv("data/housing.data", delim_whitespace=True, header=None)
df.head()
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296.0 15.3 396.90 4.98 24.0
1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242.0 17.8 396.90 9.14 21.6
2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242.0 17.8 392.83 4.03 34.7
3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222.0 18.7 394.63 2.94 33.4
4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222.0 18.7 396.90 5.33 36.2
cols = "CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT MEDV".split()
df.columns = cols
df.head()
CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT MEDV
0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296.0 15.3 396.90 4.98 24.0
1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242.0 17.8 396.90 9.14 21.6
2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242.0 17.8 392.83 4.03 34.7
3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222.0 18.7 394.63 2.94 33.4
4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222.0 18.7 396.90 5.33 36.2
X = df.drop("MEDV", axis=1)
y = df["MEDV"]
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33)

Random Forest

from sklearn.ensemble import RandomForestRegressor
clr = RandomForestRegressor()
clr.fit(X, y)
RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,
                      max_features='auto', max_leaf_nodes=None,
                      min_impurity_decrease=0.0, min_impurity_split=None,
                      min_samples_leaf=1, min_samples_split=2,
                      min_weight_fraction_leaf=0.0, n_estimators=100,
                      n_jobs=None, oob_score=False, random_state=None,
                      verbose=0, warm_start=False)
importances = clr.feature_importances_
importances
array([0.04377988, 0.00098713, 0.00669368, 0.00092023, 0.02074126,
       0.4076033 , 0.01283279, 0.06458251, 0.0036521 , 0.01366027,
       0.01576497, 0.01209152, 0.39669034])

On s’inspire de l’exemple Feature importances with forests of trees.

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
plt.figure(figsize=(12,4))
indices = np.argsort(importances)[::-1]
std = np.std([tree.feature_importances_ for tree in clr.estimators_],
             axis=0)
plt.title("Feature importances")
plt.bar(range(X.shape[1]), importances[indices],
        color="r", yerr=std[indices], align="center")
xlabels = list(df.columns[:-1])
xlabels = [xlabels[i] for i in indices]
plt.xticks(range(X.shape[1]), xlabels)
plt.xlim([-1, X.shape[1]])
plt.show()
../_images/2017_session6_12_0.png
from sklearn.metrics import r2_score
r2_score(y_train, clr.predict(X_train))
0.979236135448983
r2_score(y_test, clr.predict(X_test))
0.9843720628811461

Modèle linéaire

import statsmodels.api as sm
model = sm.OLS(y_train, X_train)
results = model.fit()
results.params
CRIM      -0.109867
ZN         0.045855
INDUS     -0.054801
CHAS       3.758792
NOX       -5.285538
RM         6.267853
AGE       -0.022554
DIS       -1.169496
RAD        0.221785
TAX       -0.010410
PTRATIO   -0.447963
B          0.016474
LSTAT     -0.259210
dtype: float64
results.summary()
OLS Regression Results
Dep. Variable: MEDV R-squared: 0.958
Model: OLS Adj. R-squared: 0.957
Method: Least Squares F-statistic: 575.3
Date: Fri, 07 Jun 2019 Prob (F-statistic): 7.10e-216
Time: 16:38:39 Log-Likelihood: -1025.5
No. Observations: 339 AIC: 2077.
Df Residuals: 326 BIC: 2127.
Df Model: 13
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
CRIM -0.1099 0.039 -2.845 0.005 -0.186 -0.034
ZN 0.0459 0.018 2.543 0.011 0.010 0.081
INDUS -0.0548 0.079 -0.697 0.486 -0.209 0.100
CHAS 3.7588 1.116 3.370 0.001 1.564 5.953
NOX -5.2855 4.398 -1.202 0.230 -13.938 3.367
RM 6.2679 0.405 15.461 0.000 5.470 7.065
AGE -0.0226 0.017 -1.325 0.186 -0.056 0.011
DIS -1.1695 0.249 -4.692 0.000 -1.660 -0.679
RAD 0.2218 0.083 2.672 0.008 0.058 0.385
TAX -0.0104 0.005 -2.155 0.032 -0.020 -0.001
PTRATIO -0.4480 0.137 -3.261 0.001 -0.718 -0.178
B 0.0165 0.003 4.767 0.000 0.010 0.023
LSTAT -0.2592 0.065 -3.959 0.000 -0.388 -0.130
Omnibus: 170.276 Durbin-Watson: 1.981
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1726.398
Skew: 1.839 Prob(JB): 0.00
Kurtosis: 13.426 Cond. No. 8.91e+03


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.91e+03. This might indicate that there are
strong multicollinearity or other numerical problems.
model = sm.OLS(y,X.drop("LSTAT", axis=1))
results = model.fit()
results.summary()
OLS Regression Results
Dep. Variable: MEDV R-squared: 0.954
Model: OLS Adj. R-squared: 0.953
Method: Least Squares F-statistic: 846.6
Date: Fri, 07 Jun 2019 Prob (F-statistic): 2.38e-320
Time: 16:38:39 Log-Likelihood: -1556.1
No. Observations: 506 AIC: 3136.
Df Residuals: 494 BIC: 3187.
Df Model: 12
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
CRIM -0.1439 0.036 -3.990 0.000 -0.215 -0.073
ZN 0.0413 0.015 2.696 0.007 0.011 0.071
INDUS -0.0370 0.068 -0.540 0.589 -0.172 0.098
CHAS 3.2525 0.961 3.384 0.001 1.364 5.141
NOX -10.8653 3.422 -3.175 0.002 -17.590 -4.141
RM 7.1436 0.289 24.734 0.000 6.576 7.711
AGE -0.0449 0.014 -3.235 0.001 -0.072 -0.018
DIS -1.2292 0.206 -5.980 0.000 -1.633 -0.825
RAD 0.2008 0.071 2.829 0.005 0.061 0.340
TAX -0.0100 0.004 -2.391 0.017 -0.018 -0.002
PTRATIO -0.6575 0.112 -5.881 0.000 -0.877 -0.438
B 0.0165 0.003 5.779 0.000 0.011 0.022
Omnibus: 277.013 Durbin-Watson: 0.927
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3084.310
Skew: 2.148 Prob(JB): 0.00
Kurtosis: 14.307 Cond. No. 8.13e+03


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.13e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

TPOT

TPOT est un module d’apprentissage automatique.

try:
    from tpot import TPOTRegressor
except ImportError:
    # for sklearn 0.22
    import sklearn.preprocessing
    from sklearn.impute import SimpleImputer
    sklearn.preprocessing.Imputer = SimpleImputer
    from tpot import TPOTRegressor

tpot = TPOTRegressor(generations=2, population_size=50, verbosity=2)
tpot.fit(X_train, y_train)
print(tpot.score(X_test, y_test))
tpot.export('tpot_boston_pipeline.py')
HBox(children=(IntProgress(value=0, description='Optimization Progress', max=150, style=ProgressStyle(descript…
Generation 1 - Current best internal CV score: -10.19955600172555
Generation 2 - Current best internal CV score: -10.19955600172555

Best pipeline: XGBRegressor(StandardScaler(input_matrix), learning_rate=0.1, max_depth=9, min_child_weight=2, n_estimators=100, nthread=1, subsample=0.8)
-9.01100125963658

Le module optimise les hyperparamètres, parfois un peu trop à en juger la mauvaise performance obtenue sur la base de test.

r2_score(y_train, tpot.predict(X_train))
0.9994364901579464
r2_score(y_test, tpot.predict(X_test))
0.8978805496355459

Feature importance pour une observations

On reprend la première random forest et on utilise le module treeinterpreter.

clr = RandomForestRegressor()
clr.fit(X, y)
RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,
                      max_features='auto', max_leaf_nodes=None,
                      min_impurity_decrease=0.0, min_impurity_split=None,
                      min_samples_leaf=1, min_samples_split=2,
                      min_weight_fraction_leaf=0.0, n_estimators=100,
                      n_jobs=None, oob_score=False, random_state=None,
                      verbose=0, warm_start=False)
from treeinterpreter import treeinterpreter as ti
prediction, bias, contributions = ti.predict(clr, X_test)
for i in range(min(2, X_train.shape[0])):
    print("Instance", i)
    print("Bias (trainset mean)", bias[i])
    print("Feature contributions:")
    for c, feature in sorted(zip(contributions[i], df.columns),
                             key=lambda x: -abs(x[0])):
        print(feature, round(c, 2))
    print( "-"*20)
Instance 0
Bias (trainset mean) 22.527195652173905
Feature contributions:
RM 7.53
LSTAT 1.58
TAX -0.64
PTRATIO 0.6
DIS -0.4
INDUS 0.19
RAD -0.18
AGE 0.13
ZN 0.12
CRIM 0.07
NOX 0.06
B -0.01
CHAS -0.01
--------------------
Instance 1
Bias (trainset mean) 22.527195652173905
Feature contributions:
LSTAT -5.04
RM -1.64
B -0.9
NOX -0.89
CRIM -0.81
DIS 0.64
AGE 0.17
PTRATIO -0.07
TAX -0.04
CHAS -0.02
INDUS -0.0
ZN 0.0
RAD 0.0
--------------------

Problème 2 : série temporelle

On prend une série sur Google Trends, dans notre cas, c’est la requête tennis live. On compare une approche linéaire et une approche non linéaire.

Approche linéaire

import pandas
df = pandas.read_csv("data/multiTimeline.csv", skiprows=1)
df.columns= ["Semaine", "compte"]
df["SemaineDt"] = pandas.to_datetime(df.Semaine)
df=df.set_index("SemaineDt")
df["compte"] = df["compte"].astype(float)
df.head()
Semaine compte
SemaineDt
2012-07-01 2012-07-01 70.0
2012-07-08 2012-07-08 49.0
2012-07-15 2012-07-15 18.0
2012-07-22 2012-07-22 22.0
2012-07-29 2012-07-29 88.0
%matplotlib inline
df.plot()
<matplotlib.axes._subplots.AxesSubplot at 0x19c15163358>
../_images/2017_session6_40_1.png
from statsmodels.tsa.arima_model import ARIMA
arma_mod = ARIMA(df["compte"].as_matrix(), order=(6 ,1, 1))
res = arma_mod.fit()
res.params
c:Python372_x64libsite-packagesipykernel_launcher.py:2: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.
array([ 0.00418581,  0.59035757, -0.32540695,  0.23286807, -0.03300838,
        0.06434307, -0.07204017, -0.99999983])
res.summary()
ARIMA Model Results
Dep. Variable: D.y No. Observations: 259
Model: ARIMA(6, 1, 1) Log Likelihood -1055.581
Method: css-mle S.D. of innovations 14.116
Date: Fri, 07 Jun 2019 AIC 2129.161
Time: 16:45:54 BIC 2161.173
Sample: 1 HQIC 2142.032
coef std err z P>|z| [0.025 0.975]
const 0.0042 0.021 0.196 0.845 -0.038 0.046
ar.L1.D.y 0.5904 0.063 9.431 0.000 0.468 0.713
ar.L2.D.y -0.3254 0.072 -4.507 0.000 -0.467 -0.184
ar.L3.D.y 0.2329 0.075 3.097 0.002 0.085 0.380
ar.L4.D.y -0.0330 0.076 -0.433 0.665 -0.182 0.116
ar.L5.D.y 0.0643 0.076 0.842 0.400 -0.085 0.214
ar.L6.D.y -0.0720 0.066 -1.096 0.274 -0.201 0.057
ma.L1.D.y -1.0000 0.010 -96.075 0.000 -1.020 -0.980
Roots
Real Imaginary Modulus Frequency
AR.1 -1.2011 -1.2144j 1.7080 -0.3741
AR.2 -1.2011 +1.2144j 1.7080 0.3741
AR.3 0.1840 -1.4018j 1.4138 -0.2292
AR.4 0.1840 +1.4018j 1.4138 0.2292
AR.5 1.4636 -0.4882j 1.5429 -0.0512
AR.6 1.4636 +0.4882j 1.5429 0.0512
MA.1 1.0000 +0.0000j 1.0000 0.0000

Méthode non linéaire

On construire la matrice des séries décalées. Cette méthode permet de sortir du cadre linéaire et d’ajouter d’autres variables.

from statsmodels.tsa.tsatools import lagmat
lag = 8
X = lagmat(df["compte"], lag)
lagged = df.copy()
for c in range(1,lag+1):
    lagged["lag%d" % c] = X[:, c-1]
pandas.concat([lagged.head(), lagged.tail()])
Semaine compte lag1 lag2 lag3 lag4 lag5 lag6 lag7 lag8
SemaineDt
2012-07-01 2012-07-01 70.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2012-07-08 2012-07-08 49.0 70.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2012-07-15 2012-07-15 18.0 49.0 70.0 0.0 0.0 0.0 0.0 0.0 0.0
2012-07-22 2012-07-22 22.0 18.0 49.0 70.0 0.0 0.0 0.0 0.0 0.0
2012-07-29 2012-07-29 88.0 22.0 18.0 49.0 70.0 0.0 0.0 0.0 0.0
2017-05-21 2017-05-21 23.0 40.0 35.0 21.0 29.0 27.0 14.0 23.0 40.0
2017-05-28 2017-05-28 44.0 23.0 40.0 35.0 21.0 29.0 27.0 14.0 23.0
2017-06-04 2017-06-04 55.0 44.0 23.0 40.0 35.0 21.0 29.0 27.0 14.0
2017-06-11 2017-06-11 28.0 55.0 44.0 23.0 40.0 35.0 21.0 29.0 27.0
2017-06-18 2017-06-18 28.0 28.0 55.0 44.0 23.0 40.0 35.0 21.0 29.0
xc = ["lag%d" % i for i in range(1,lag+1)]
split = 0.66
isplit = int(len(lagged) * split)
xt = lagged[10:][xc]
yt = lagged[10:]["compte"]
X_train, y_train, X_test, y_test = xt[:isplit], yt[:isplit], xt[isplit:], yt[isplit:]
from sklearn.ensemble import RandomForestRegressor
clr = RandomForestRegressor()
clr.fit(X_train, y_train)
RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,
                      max_features='auto', max_leaf_nodes=None,
                      min_impurity_decrease=0.0, min_impurity_split=None,
                      min_samples_leaf=1, min_samples_split=2,
                      min_weight_fraction_leaf=0.0, n_estimators=100,
                      n_jobs=None, oob_score=False, random_state=None,
                      verbose=0, warm_start=False)
from sklearn.metrics import r2_score
r2 = r2_score(y_test.as_matrix(), clr.predict(X_test))
r2
c:Python372_x64libsite-packagesipykernel_launcher.py:2: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.
0.4878325848907805
plt.scatter(y_test.as_matrix(), clr.predict(X_test));
c:Python372_x64libsite-packagesipykernel_launcher.py:1: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.
  """Entry point for launching an IPython kernel.
<matplotlib.collections.PathCollection at 0x19c26b9a2e8>
../_images/2017_session6_48_2.png

Texte

On cherche à comparer une LDA avec word2vec et kmeans et les données qui sont sur ensae_teaching_cs/src/ensae_teaching_cs/data/data_web/.

from ensae_teaching_cs.data import twitter_zip
df = twitter_zip(as_df=True)
df.head(n=2).T
0 1
index 776066992054861825 776067660979245056
nb_user_mentions 0 0
nb_extended_entities 0 0
nb_hashtags 1 1
geo NaN NaN
text_hashtags , SiJétaisPrésident , SiJétaisPrésident
annee 2016 2016
delimit_mention NaN NaN
lang fr fr
id_str 7.76067e+17 7.76068e+17
text_mention NaN NaN
retweet_count 4 5
favorite_count 3 8
type_extended_entities [] []
text #SiJétaisPrésident se serait la fin du monde..... #SiJétaisPrésident je donnerai plus de vacance...
nb_user_photos 0 0
nb_urls 0 0
nb_symbols 0 0
created_at Wed Sep 14 14:36:04 +0000 2016 Wed Sep 14 14:38:43 +0000 2016
delimit_hash , 0, 18 , 0, 18

Des mots aux coordonnées - tf-idf

keep = df.text.dropna().index
dfnonan = df.iloc[keep, :]
dfnonan.shape
(5087, 20)
from sklearn.feature_extraction.text import TfidfVectorizer
tfidf_vectorizer = TfidfVectorizer(max_df=0.95, min_df=2, max_features=1000)
tfidf = tfidf_vectorizer.fit_transform(dfnonan["text"])
tfidf[:2, :]
<2x1000 sparse matrix of type '<class 'numpy.float64'>'
    with 21 stored elements in Compressed Sparse Row format>
tfidf[:2, :].todense()
matrix([[0., 0., 0., ..., 0., 0., 0.],
        [0., 0., 0., ..., 0., 0., 0.]])

LDA

from sklearn.decomposition import LatentDirichletAllocation
lda = LatentDirichletAllocation(n_components=10, max_iter=5,
                                learning_method='online',
                                learning_offset=50.,
                                random_state=0)
lda.fit(tfidf)
LatentDirichletAllocation(batch_size=128, doc_topic_prior=None,
                          evaluate_every=-1, learning_decay=0.7,
                          learning_method='online', learning_offset=50.0,
                          max_doc_update_iter=100, max_iter=5,
                          mean_change_tol=0.001, n_components=10, n_jobs=None,
                          perp_tol=0.1, random_state=0, topic_word_prior=None,
                          total_samples=1000000.0, verbose=0)
tf_feature_names = tfidf_vectorizer.get_feature_names()
tf_feature_names[100:103]
['avoir', 'bac', 'bah']
lda.components_.shape
(10, 1000)

On obtient dix vecteurs qui représentent les dix vecteurs associés aux dix clusters. Chaque dimension relié au fait que le mot appartient ou non au cluster.

def print_top_words(model, feature_names, n_top_words):
    for topic_idx, topic in enumerate(model.components_):
        print("Topic #%d:" % topic_idx)
        print(" ".join([feature_names[i]
                        for i in topic.argsort()[:-n_top_words - 1:-1]]))
    print()
print_top_words(lda, tf_feature_names, 10)
Topic #0:
gratuit mcdo supprimerai école soir kebab macdo kfc domicile cc
Topic #1:
macron co https de la est le il et hollande
Topic #2:
sijetaispresident je les de la et le des en pour
Topic #3:
notaires eu organiserais mets carte nouveaux journées installation cache créer
Topic #4:
sijetaispresident interdirais les je ballerines la serait serais bah de
Topic #5:
ministre de sijetaispresident la je premier mort et nommerais président
Topic #6:
cours le supprimerais jour sijetaispresident lundi samedi semaine je vendredi
Topic #7:
port interdirait démissionnerais promesses heure rendrai ballerine mes changement christineboutin
Topic #8:
seraient sijetaispresident gratuits aux les nos putain éducation nationale bonne
Topic #9:
bordel seront légaliserai putes gratuites pizza mot virerais vitesse dutreil

Clustering

from sklearn.cluster import KMeans
km = KMeans(n_clusters=10)
km.fit(tfidf)
KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,
       n_clusters=10, n_init=10, n_jobs=None, precompute_distances='auto',
       random_state=None, tol=0.0001, verbose=0)
km.cluster_centers_.shape
(10, 1000)
def print_top_words(model, feature_names, n_top_words):
    for topic_idx, topic in enumerate(model.cluster_centers_):
        print("Topic #%d:" % topic_idx)
        print(" ".join([feature_names[i]
                        for i in topic.argsort()[:-n_top_words - 1:-1]]))
    print()
print_top_words(km, tf_feature_names, 10)
Topic #0:
ferais je sijetaispresident les en sorte que de et un
Topic #1:
le sijetaispresident je monde et pour de tout des les
Topic #2:
de sijetaispresident la en et des une un plus aurait
Topic #3:
https co macron de la le les via et sijetaispresident
Topic #4:
les sijetaispresident je de et tous des seraient pour ballerines
Topic #5:
serait sijetaispresident la le merde de ça et on dans
Topic #6:
je sijetaispresident la des me et ferai pas en au
Topic #7:
macron est il de pas la hollande le gauche que
Topic #8:
ministre premier nommerais sijetaispresident de je la mickey serait nommerai
Topic #9:
serais je sijetaispresident un pas ne président que la de

Ah les stop words….