Estatística para Cientistas de Dados
Carregando, aguarde alguns segundos.
6 - Classificação
6.1 - Preparação dos dados
6.2 - Naive Bayes
6.3 - Análise discriminante
Exemplo simples:
loan3000 = pd.read_csv(LOAN3000_CSV)
print(loan3000.head())Alteramos a propriedade outcome.
loan3000.outcome = loan3000.outcome.astype('category')
print(loan3000.head())Calculamos o LDA do empréstimo.
predictors = ['borrower_score', 'payment_inc_ratio']
outcome = 'outcome'
#
X = loan3000[predictors]
y = loan3000[outcome]
#
loan_lda = LinearDiscriminantAnalysis()
loan_lda.fit(X, y)
print(pd.DataFrame(loan_lda.scalings_, index=X.columns))
#
pred = pd.DataFrame(
loan_lda.predict_proba(loan3000[predictors]),
columns=loan_lda.classes_)
print(pred.head())Figura 5-1: use escalas e centro de meios para determinar o limite de decisão.
center = np.mean(loan_lda.means_, axis=0)
slope = - loan_lda.scalings_[0] / loan_lda.scalings_[1]
intercept = center[1] - center[0] * slope
#
# payment_inc_ratio para borrower_score de 0 e 20
#
x_0 = (0 - intercept) / slope
x_20 = (20 - intercept) / slope
#
lda_df = pd.concat([loan3000, pred['default']], axis=1)
print(lda_df.head())Figura:
fig, ax = plt.subplots(figsize=(4, 4))
g = sns.scatterplot(
x='borrower_score', y='payment_inc_ratio',
hue='default', data=lda_df,
palette=sns.diverging_palette(240, 10, n=9, as_cmap=True),
ax=ax, legend=False)
#
ax.set_ylim(0, 20)
ax.set_xlim(0.15, 0.8)
ax.plot((x_0, x_20), (0, 20), linewidth=3)
ax.plot(*loan_lda.means_.transpose())
#
plt.tight_layout()
plt.show()
6.4 - Regressão logística
6.4.1 - Função de Resposta Logística e Logit
p = np.arange(0.01, 1, 0.01)
df = pd.DataFrame({
'p': p,
'logit': np.log(p / (1 - p)),
'odds': p / (1 - p),
})
#
fig, ax = plt.subplots(figsize=(3, 3))
ax.axhline(0, color='grey', linestyle='--')
ax.axvline(0.5, color='grey', linestyle='--')
ax.plot(df['p'], df['logit'])
ax.set_xlabel('Probability')
ax.set_ylabel('logit(p)')
#
plt.tight_layout()
plt.show()
6.4.2 - Regressão Logística e o GLM
6.4.3 - Valores previstos da Regressão Logística
6.4.4 - Interpretando os coeficientes e razões ímpares
fig, ax = plt.subplots(figsize=(3, 3))
ax.plot(df['logit'], df['odds'])
ax.set_xlabel('log(razões ímpares)')
ax.set_ylabel('razões ímpares')
ax.set_xlim(0, 5.1)
ax.set_ylim(-5, 105)
#
plt.tight_layout()
plt.show()
6.4.5 - Avaliação do modelo
6.5 - Ripas (splines)
import statsmodels.formula.api as smf
formula = ('outcome ~ bs(payment_inc_ratio, df=8) + purpose_ + ' +
'home_ + emp_len_ + bs(borrower_score, df=3)')
model = smf.glm(formula=formula, data=loan_data, family=sm.families.Binomial())
results = model.fit()
print(results.summary())Gráfico:
from statsmodels.genmod.generalized_linear_model import GLMResults
def partialResidualPlot(model, df, outcome, feature, fig, ax):
y_actual = [0 if s == 'default' else 1 for s in df[outcome]]
y_pred = model.predict(df)
org_params = model.params.copy()
zero_params = model.params.copy()
# set model parametes of other features to 0
for i, name in enumerate(zero_params.index):
if feature in name:
continue
zero_params[i] = 0.0
model.initialize(model.model, zero_params)
feature_prediction = model.predict(df)
ypartial = -np.log(1/feature_prediction - 1)
ypartial = ypartial - np.mean(ypartial)
model.initialize(model.model, org_params)
results = pd.DataFrame({
'feature': df[feature],
'residual': -2 * (y_actual - y_pred),
'ypartial': ypartial/ 2,
})
results = results.sort_values(by=['feature'])
#
ax.scatter(results.feature, results.residual, marker=".", s=72./fig.dpi)
ax.plot(results.feature, results.ypartial, color='black')
ax.set_xlabel(feature)
ax.set_ylabel(f'Residual + {feature} contribution')
return ax
#
fig, ax = plt.subplots(figsize=(5, 5))
partialResidualPlot(results, loan_data, 'outcome', 'payment_inc_ratio', fig, ax)
ax.set_xlim(0, 25)
ax.set_ylim(-2.5, 2.5)
#
plt.tight_layout()
plt.show()
6.6 - Avaliação de modelos de classificação
6.6.1 - Matriz de confusão
6.6.2 - Precisão, Recall e Especificidade
6.6.3 - Curva ROC
A função `roc_curve` em _Scikit-Learn_ calcula todas as informações necessárias para traçar uma curva ROC.
fpr, tpr, thresholds = roc_curve(
y,
logit_reg.predict_proba(X)[:, 0],
pos_label='default')
roc_df = pd.DataFrame({'recall': tpr, 'specificity': 1 - fpr})
ax = roc_df.plot(x='specificity', y='recall', figsize=(4, 4), legend=False)
ax.set_ylim(0, 1)
ax.set_xlim(1, 0)
ax.plot((1, 0), (0, 1))
ax.set_xlabel('specificity')
ax.set_ylabel('recall')
plt.tight_layout()
plt.show()
6.6.4 - AUC
Accuracy can easily be calculated using the _Scikit-Learn_ function `accuracy_score`.
print(np.sum(roc_df.recall[:-1] * np.diff(1 - roc_df.specificity)))
print(roc_auc_score([1 if yi == 'default' else 0 for yi in y], logit_reg.predict_proba(X)[:, 0]))
fpr, tpr, thresholds = roc_curve(y, logit_reg.predict_proba(X)[:,0],
pos_label='default')
roc_df = pd.DataFrame({'recall': tpr, 'specificity': 1 - fpr})
ax = roc_df.plot(x='specificity', y='recall', figsize=(4, 4), legend=False)
ax.set_ylim(0, 1)
ax.set_xlim(1, 0)
# ax.plot((1, 0), (0, 1))
ax.set_xlabel('specificity')
ax.set_ylabel('recall')
ax.fill_between(roc_df.specificity, 0, roc_df.recall, alpha=0.3)
plt.tight_layout()
plt.show()
6.7 - Estratégias para dados desequilibrados
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