nightingale 2020.4.7

Python library for simplifying statistical analysis and making it more consistent

Nightingale

I named this package Nightingale in honour of Florence Nightingale, the lady with the data.

Table of Contents

• Installation
• Usage
  • Population Proportion
  • Regression
    • Ordinary Least Squares (OLS)
    • Logistic Regression (LogisticRegression)
    • Generalized Estimating Equation (GEE)
  • Evaluation
    • evaluate_regression
    • evaluate_classification
  • Feature Importance
    • get_coefficients
    • get_feature_importances
    • get_model_influence
• References

Installation

You can use pip to install Nightingale:

pip install nightingale

Usage

Shannon's Entropy

from nightingale import entropy
import numpy as np

x = np.random.choice(np.arange(1, 7), size=1000, p=[0.1, 0.05, 0.05, 0.2, 0.4, 0.2])
y = x + np.random.uniform(low=0, high=3, size=1000) < 3 
print('H(x)=', entropy.get_entropy(x))
print('H(y, x)=', entropy.get_conditional_entropy(y, x))
print('G(y, x)=', entropy.get_information_gain(y, x))

output:

H(x)= 2.2398258260443384
H(y, x)= 0.12189402130109395
G(y, x)= 0.2767517685048818

Population Proportion

from nightingale import get_sample_size, PopulationProportion, get_z_score

print('z-score for 0.95 confidence:', get_z_score(confidence=0.95))
print('sample size:', get_sample_size(confidence=0.95, error_margin=0.05, population_size=1000))
print('with 10% group proportion:', get_sample_size(confidence=0.95, error_margin=0.05, population_size=1000, group_proportion=0.1))

population_proportion = PopulationProportion(sample_n=239, group_proportion=0.5)
print('error:', population_proportion.get_error(confidence=0.95))

Regression

Ordinary Least Squares (OLS)

from nightingale.regression import OLS

# import other libraries
import pandas as pd
import numpy as np
from IPython.display import display

# create data
data = pd.DataFrame({
    'x': np.random.normal(size=20, scale=5), 
    'y': np.random.normal(size=20, scale=5),
})
data['z'] = data['x'].values + data['y'].values + np.random.normal(size=20, scale=1)
display(data.head())

# build model
ols = OLS(data=data, formula='z ~ x + y')
print('ols results:')
display(ols.model_table)

print('r-squared:', ols.r_squared)
print('adjusted r-squared:', ols.adjusted_r_squared)

print('\n', 'summary:')
display(ols.summary)

Logistic Regression (LogisticRegression)

Generalized Estimating Equation (GEE)

Evaluation

evaluate_regression

from nightingale.evaluation import evaluate_regression

# import other libraries
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from pandas import DataFrame
from numpy.random import normal
from IPython.display import display

# create the data
num_rows = 1000
num_columns = 10
data = DataFrame({f'x_{i + 1}': normal(size=num_rows) for i in range(num_columns)})
noise = normal(size=num_rows)
data['y'] = noise
for i in range(num_columns):
    data['y'] += data[f'x_{i + 1}']

# split the data into training and test
training, test = train_test_split(data, test_size=0.2, random_state=42)
x_columns = [f'x_{i + 1}' for i in range(num_columns)]
X_training = training[x_columns]
X_test = test[x_columns]

# build regressor
regressor = LinearRegression()
regressor.fit(X_training, training['y'])

# predict
predicted = regressor.predict(test[x_columns])

# evaluate the predictions
display(evaluate_regression(actual=test['y'], predicted=predicted))

output:

{'nmae': 0.03634390112869996,
 'rmse': 1.004360709998502,
 'mae': 0.8091380646812157,
 'mape': 125.73196935352729}

evaluate_classification

This method evaluates a binary classifier based on predictions and actual values.

from nightingale.evaluation import evaluate_classification

# import other libraries
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from pandas import DataFrame
from numpy.random import normal
from IPython.display import display

# create the data
num_rows = 1000
num_columns = 10
data = DataFrame({f'x_{i + 1}': normal(size=num_rows) for i in range(num_columns)})
noise = normal(size=num_rows)
data['y'] = noise
for i in range(num_columns):
    data['y'] += data[f'x_{i + 1}']

data['y_class'] = (data['y'] > 0).astype(int)

# split the data into training and test
training, test = train_test_split(data, test_size=0.2, random_state=42)
x_columns = [f'x_{i + 1}' for i in range(num_columns)]
X_training = training[x_columns]
X_test = test[x_columns]

# build classifier
classifier = LogisticRegression()
classifier.fit(X_training, training['y_class'])

# predict
predicted = classifier.predict(test[x_columns])
display(evaluate_classification(actual=test['y_class'], predicted=predicted))

output:

{'accuracy': 0.9,
 'precision': 0.9425287356321839,
 'recall': 0.845360824742268,
 'specificity': 0.9514563106796117,
 'negative_predictive_value': 0.8672566371681416,
 'miss_rate': 0.15463917525773196,
 'fall_out': 0.04854368932038835,
 'false_discovery_rate': 0.05747126436781609,
 'false_omission_rate': 0.13274336283185842,
 'threat_score': 0.803921568627451,
 'f1_score': 0.8913043478260869,
 'matthews_correlation_coefficient': 0.8032750843025658,
 'informedness': 0.7968171354218798,
 'markedness': 0.8097853728003255,
 'confusion_matrix': array([[98,  5],
        [15, 82]], dtype=int64),
 'true_negative': 98,
 'false_positive': 5,
 'false_negative': 15,
 'true_positive': 82}

Feature Importance

get_coefficients

This method provides the coefficients of a model (if applicable).

from nightingale.feature_importance import get_coefficients

# import other libraries
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from pandas import DataFrame
from numpy.random import normal
from IPython.display import display

# create the data
num_rows = 1000
num_columns = 10
data = DataFrame({f'x_{i + 1}': normal(size=num_rows) for i in range(num_columns)})
noise = normal(size=num_rows)
data['y'] = noise
for i in range(num_columns):
    data['y'] += data[f'x_{i + 1}'] * (i + 1)

# split the data into training and test
training, test = train_test_split(data, test_size=0.2, random_state=42)
x_columns = [f'x_{i + 1}' for i in range(num_columns)]
X_training = training[x_columns]
X_test = test[x_columns]

# build regressor
regressor = LinearRegression()
regressor.fit(X_training, training['y'])

# show results
display(get_coefficients(model=regressor, columns=x_columns))

output:

{'x_1': 0.9757592681006574,
 'x_2': 2.087658823002798,
 'x_3': 3.029429170607074,
 'x_4': 3.9872397737924814,
 'x_5': 5.017284345652762,
 'x_6': 5.957884804572033,
 'x_7': 7.0112941806800775,
 'x_8': 7.99189170951265,
 'x_9': 9.046356367379428,
 'x_10': 9.994160430237088}

get_feature_importances

This method produces the feature importances of a model (if applicable).

from nightingale.feature_importance import get_feature_importances

# import other libraries
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from pandas import DataFrame
from numpy.random import normal
from IPython.display import display

# create the data
num_rows = 1000
num_columns = 10
data = DataFrame({f'x_{i + 1}': normal(size=num_rows) for i in range(num_columns)})
noise = normal(size=num_rows)
data['y'] = noise
for i in range(num_columns):
    data['y'] += data[f'x_{i + 1}'] * (i + 1)
data['y_class'] = (data['y'] > 0).astype(int)

# split the data into training and test
training, test = train_test_split(data, test_size=0.2, random_state=42)
x_columns = [f'x_{i + 1}' for i in range(num_columns)]
X_training = training[x_columns]
X_test = test[x_columns]

# build classifier
classifier = RandomForestClassifier()
classifier.fit(X_training, training['y_class'])

# show results
display(get_feature_importances(model=classifier, columns=x_columns))

output:

{'x_1': 0.039392558058928634,
 'x_2': 0.045648670987447175,
 'x_3': 0.06830354705691284,
 'x_4': 0.0675098079660134,
 'x_5': 0.09446851464509692,
 'x_6': 0.10764938247312761,
 'x_7': 0.10715124795271348,
 'x_8': 0.13332980023234497,
 'x_9': 0.14531677148789846,
 'x_10': 0.19122969913951648}

get_model_influence

from nightingale.feature_importance import get_model_influence

# import other libraries
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from pandas import DataFrame
from numpy.random import normal
from IPython.display import display

# visualization libraries
from plotnine import ggplot, geom_line, aes, stat_smooth, facet_wrap
from plotnine.data import mtcars
from plotnine import options

# create the data
num_rows = 1000
num_columns = 10
data = DataFrame({f'x_{i + 1}': normal(size=num_rows) for i in range(num_columns)})
noise = normal(size=num_rows)
data['y'] = noise
for i in range(num_columns):
    data['y'] += data[f'x_{i + 1}'] * (i + 1) * (-1) ** i

# split the data into training and test
training, test = train_test_split(data, test_size=0.2, random_state=42)
x_columns = [f'x_{i + 1}' for i in range(num_columns)]
X_training = training[x_columns]
X_test = test[x_columns]

# build random forest regressor
random_forest_regressor = RandomForestRegressor(n_estimators=10)
random_forest_regressor.fit(X_training, training['y'])

# show results
influence = get_model_influence(model=random_forest_regressor, data=test, x_columns=x_columns, num_points=200, num_threads=1, echo=1)
display(influence.head())

# visualize
options.figure_size = 10, 5
ggplot(influence, aes(x='perturbation', y='influence_mean', colour='column')) + geom_line()

References

z-score: https://stackoverflow.com/questions/20864847/probability-to-z-score-and-vice-versa-in-python