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prediction1, bias1, contributions1 = ti.predict(rf, np.array([selected_df[0]]), joint_contribution=True)
prediction2, bias2, contributions2 = ti.predict(rf, np.array([selected_df[1]]), joint_contribution=True)

aggregated_contributions1 = utils.aggregated_contribution(contributions1)
aggregated_contributions2 = utils.aggregated_contribution(contributions2)

res = []
for k in set(aggregated_contributions1.keys()).union(
              set(aggregated_contributions2.keys())):
    res.append(([X_train.columns[index] for index in k] , 

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import lime
import lime.lime_tabular

explainer = lime.lime_tabular.LimeTabularExplainer(X_train.values,
                                                   mode = 'regression',
                                                   feature_names = X_train.columns,
                                                   categorical_features = [3], 
                                                   categorical_names = ['CHAS'], 
                                                   discretize_continuous = True)
                                                   

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mat = scipy.io.loadmat('cover.mat')
X = pd.DataFrame(mat['X'])
y = pd.Series([x[0] for x in mat['y']])

# define % of anomalies
anomalies_ratio = 0.009

if_sk = IsolationForest(n_estimators = 100, 
                        max_samples = 256,
                        contamination = anomalies_ratio, 

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if_eif = iso.iForest(X.values, 
                     ntrees = 100, 
                     sample_size = 256, 
                     ExtensionLevel = 0)

# calculate anomaly scores
anomaly_scores = if_eif.compute_paths(X_in = X.values)
# sort the scores
anomaly_scores_sorted = np.argsort(anomaly_scores)
# retrieve indices of anomalous observations

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def pp_plot(x, dist, line=True, ax=None):
    '''
    Function for comparing empirical data to a theoretical distribution by using a P-P plot.
    
    Params:
    x - empirical data
    dist - distribution object from scipy.stats; for example scipy.stats.norm(0, 1)
    line - boolean; specify if the reference line (y=x) should be drawn on the plot
    ax - specified ax for subplots, None is standalone
    '''

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fig, ax = plt.subplots(1, 2, figsize=(15, 8))

fig.suptitle('PP-plots', fontsize=22)

sm.ProbPlot(rv_norm, scs.norm, loc=0, scale=1).ppplot(line='45', ax=ax[0])
ax[0].set_title('Statsmodels', fontsize=16)

pp_plot(rv_norm, scs.norm(loc=0, scale=1), ax=ax[1])
ax[1].set_title('pp_plot', fontsize=16)

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fig, ax = plt.subplots(1, 2, figsize=(15, 8))

sm.ProbPlot(rv_skew_norm).qqplot(line='s', ax=ax[0]);
ax[0].set_title('Q-Q plot (vs. Normal)', fontsize=16)

sns.distplot(rv_std_norm, kde=False, norm_hist=True, color='blue', label='Standard Normal', ax=ax[1])                                    
sns.distplot(rv_skew_norm, kde=False, norm_hist=True, color='red', label='Skew Normal $\\alpha = 5$', ax=ax[1])
plt.title('Comparison of distributions', fontsize=16)
plt.legend();

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sm.ProbPlot(rv_skew_norm, scs.skewnorm, distargs=(5, )).qqplot(line='s');
plt.title('Q-Q plot (vs. Skew Normal)', fontsize=16);

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fig, ax = plt.subplots(1, 2, figsize=(15, 8))

pp_x = sm.ProbPlot(rv_skew_norm, fit=False)
pp_y = sm.ProbPlot(rv_std_norm, fit=False)
fig = pp_x.qqplot(line='s', other=pp_y, ax=ax[0])
ax[0].set_title('Q-Q plot (vs. Standard Normal)', fontsize=16)

sns.distplot(rv_std_norm, kde=False, norm_hist=True, color='blue', label='Standard Normal', ax=ax[1])                                    
sns.distplot(rv_skew_norm, kde=False, norm_hist=True, color='red', label='Skew Normal $\\alpha = 5$', ax=ax[1])
plt.title('Comparison of distributions', fontsize=16)

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import pandas as pd
from sklearn.datasets import load_boston

# load data
boston = load_boston()
X = pd.DataFrame(boston.data, columns=boston.feature_names)
X.drop('CHAS', axis=1, inplace=True)
y = pd.Series(boston.target, name='MEDV')

# inspect data