2018-10-09 Ensemble, Gradient, Boosting…

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Le noteboook explore quelques particularités des algorithmes d’apprentissage pour expliquer certains résultats numériques. L’algoithme AdaBoost surpondère les exemples sur lequel un modèle fait des erreurs.

from jyquickhelper import add_notebook_menu
add_notebook_menu()

%matplotlib inline

Skewed split train test

Lorsqu’une classe est sous représentée, il est difficile de prédire les résultats d’un modèle de machine learning.

import numpy, numpy.random
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.neural_network import MLPClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
from sklearn.metrics import confusion_matrix

N = 1000

res = []

for n in [1, 2, 5, 10, 20, 50, 80, 90, 100, 110]:
    print("n=", n)
    for k in range(10):

        X = numpy.zeros((N, 2))
        X[:, 0] = numpy.random.randint(0, 2, (N,))
        X[:, 1] = numpy.random.randint(0, n+1, (N,))
        Y = X[:, 0] + X[:, 1] + numpy.random.normal(size=(N,)) / 2
        Y[Y < 1.5] = 0
        Y[Y >= 1.5] = 1

        X_train, X_test, y_train, y_test = train_test_split(X, Y)

        stat = dict(N=N, n=n, ratio_train=y_train.sum()/y_train.shape[0],
                    k=k, ratio_test=y_test.sum()/y_test.shape[0])

        for model in [LogisticRegression(solver="liblinear"),
                      MLPClassifier(max_iter=500),
                      RandomForestClassifier(n_estimators=10),
                      AdaBoostClassifier(DecisionTreeClassifier(), n_estimators=10)]:
            obs = stat.copy()
            obs["model"] = model.__class__.__name__
            if obs["model"] == "AdaBoostClassifier":
                obs["model"] = "AdaB-" + model.base_estimator.__class__.__name__
            try:
                model.fit(X_train, y_train)
            except ValueError as e:
                obs["erreur"] = str(e)
                res.append(obs)
                continue
            sc = model.score(X_test, y_test)
            obs["accuracy"] = sc
            conf = confusion_matrix(y_test, model.predict(X_test))
            try:
                obs["Error-0|1"] = conf[0, 1] / conf[0, :].sum()
                obs["Error-1|0"] = conf[1, 0] / conf[1, :].sum()
            except Exception:
                pass
            res.append(obs)

n= 1
n= 2
n= 5
n= 10
n= 20
n= 50
n= 80
n= 90
n= 100

c:python370_x64libsite-packagesipykernel_launcher.py:47: RuntimeWarning: invalid value encountered in longlong_scalars
c:python370_x64libsite-packagesipykernel_launcher.py:47: RuntimeWarning: invalid value encountered in longlong_scalars

n= 110

from pandas import DataFrame
df = DataFrame(res)
df = df.sort_values(['n', 'model', 'model', "k"]).reset_index(drop=True)
df["diff_ratio"] = (df["ratio_test"] - df["ratio_train"]).abs()
df.head(n=5)

	Error-0|1	Error-1|0	N	accuracy	k	model	n	ratio_test	ratio_train	diff_ratio
0	0.061798	0.208333	1000	0.896	0	AdaB-DecisionTreeClassifier	1	0.288	0.237333	0.050667
1	0.040230	0.302632	1000	0.880	1	AdaB-DecisionTreeClassifier	1	0.304	0.284000	0.020000
2	0.081395	0.256410	1000	0.864	2	AdaB-DecisionTreeClassifier	1	0.312	0.293333	0.018667
3	0.062147	0.342466	1000	0.856	3	AdaB-DecisionTreeClassifier	1	0.292	0.342667	0.050667
4	0.049180	0.298507	1000	0.884	4	AdaB-DecisionTreeClassifier	1	0.268	0.290667	0.022667

df.tail(n=5)

	Error-0|1	Error-1|0	N	accuracy	k	model	n	ratio_test	ratio_train	diff_ratio
395	0.00	0.0	1000	1.000	5	RandomForestClassifier	110	0.996	0.977333	0.018667
396	0.00	0.0	1000	1.000	6	RandomForestClassifier	110	0.972	0.990667	0.018667
397	0.00	0.0	1000	1.000	7	RandomForestClassifier	110	0.980	0.985333	0.005333
398	0.00	0.0	1000	1.000	8	RandomForestClassifier	110	0.988	0.980000	0.008000
399	0.25	0.0	1000	0.996	9	RandomForestClassifier	110	0.984	0.988000	0.004000

La répartition train/test est loin d’être statisfaisante lorsqu’il existe une classe sous représentée.

df[df.n==100][["n", "ratio_test", "ratio_train"]].head(n=10)

	n	ratio_test	ratio_train
320	100	1.000	0.986667
321	100	0.980	0.984000
322	100	0.984	0.984000
323	100	0.972	0.980000
324	100	0.984	0.981333
325	100	0.976	0.984000
326	100	0.984	0.990667
327	100	0.984	0.988000
328	100	0.980	0.989333
329	100	0.992	0.982667

#df.to_excel("data.xlsx")

columns = ["n", "N", "model"]
agg = df.groupby(columns, as_index=False).mean().sort_values(["n", "model"]).reset_index(drop=True)
agg.tail()

	n	N	model	Error-0|1	Error-1|0	accuracy	k	ratio_test	ratio_train	diff_ratio
35	100	1000	RandomForestClassifier	0.050000	0.002434	0.9968	4.5	0.9836	0.985067	0.006533
36	110	1000	AdaB-DecisionTreeClassifier	0.050000	0.002031	0.9972	4.5	0.9852	0.984667	0.007733
37	110	1000	LogisticRegression	0.261905	0.001216	0.9956	4.5	0.9852	0.984667	0.007733
38	110	1000	MLPClassifier	0.241905	0.001216	0.9948	4.5	0.9852	0.984667	0.007733
39	110	1000	RandomForestClassifier	0.083333	0.001626	0.9972	4.5	0.9852	0.984667	0.007733

import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 2, figsize=(10,4))
agg.plot(x="n", y="diff_ratio", ax=ax[0])
agg.plot(x="n", y="ratio_train", ax=ax[1])
agg.plot(x="n", y="ratio_test", ax=ax[1])
ax[0].set_title("Maximum difference between\nratio of first class on train and test")
ax[1].set_title("Ratio of first class on train and test")
ax[0].legend();

Une astuce pour éviter les doublons avant d’effecturer un pivot.

agg2 = agg.copy()
agg2["ratio_test2"] = agg2["ratio_test"] + agg2["n"] / 100000

import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 3, figsize=(14,4))
agg2.pivot("ratio_test2", "model", "accuracy").plot(ax=ax[0])
agg2.pivot("ratio_test2", "model", "Error-0|1").plot(ax=ax[1])
agg2.pivot("ratio_test2", "model", "Error-1|0").plot(ax=ax[2])
ax[0].plot([0.5, 1.0], [0.5, 1.0], '--', label="constant")
ax[0].set_title("Accuracy")
ax[1].set_title("Error-0|1")
ax[2].set_title("Error-1|0")
ax[0].legend();

agg2.pivot("ratio_test2", "model", "Error-0|1")

model	AdaB-DecisionTreeClassifier	LogisticRegression	MLPClassifier	RandomForestClassifier
ratio_test2
0.28801	0.052915	0.052915	0.052915	0.052915
0.49002	0.099708	0.099708	0.099708	0.099708
0.75445	0.096037	0.096037	0.096037	0.096037
0.84490	0.083750	0.083750	0.083750	0.083750
0.92100	0.132553	0.132553	0.165886	0.170648
0.97010	0.103611	0.193611	0.173611	0.103611
0.98400	0.230000	0.336667	0.336667	0.280000
0.98460	0.050000	0.270370	0.150000	0.050000
0.98630	0.050000	0.261905	0.241905	0.083333
0.98770	0.100000	0.383333	0.133333	0.116667

Le modèle AdaBoost construit 10 arbres tout comme la forêt aléatoire à ceci près que le poids associé à chacun des arbres des différents et non uniforme.

Apprentissage continu

Apprendre une forêt aléatoire, puis ajouter un arbre, encore un tout en gardant le résultat des apprentissages précédents.

from sklearn.datasets import load_boston
boston = load_boston()
X, y = boston.data, boston.target

X_train, X_test, y_train, y_test = train_test_split(X, y)

from sklearn.ensemble import RandomForestRegressor

model = None
res = []
for i in range(0, 20):
    if model is None:
        model = RandomForestRegressor(n_estimators=1, warm_start=True)
    else:
        model.set_params(**dict(n_estimators=model.n_estimators+1))
    model.fit(X_train, y_train)
    score = model.score(X_test, y_test)
    res.append(dict(n_estimators=model.n_estimators, score=score))

df = DataFrame(res)
df.head()

	n_estimators	score
0	1	0.584034
1	2	0.760666
2	3	0.824477
3	4	0.811059
4	5	0.818055

ax = df.plot(x="n_estimators", y="score")
ax.set_title("Apprentissage continu\nmesure de la performance à chaque itération");