matthieubulte/statinf

Python Library for Econometrics and Advanced Statistics

STATINF

statinf is a library for statistics and causal inference. It provides main the statistical models ranging from the traditional OLS to Neural Networks.

Regressions

OLS

statinf comes with the OLS regression implemented with the analytical formula:

from statinf.regressions.LinearModels import OLS
from statinf.data.GenerateData import generate_dataset

# Generate a synthetic dataset
data = generate_dataset(coeffs=[1.2556, -6.465, 1.665414, 1.5444], n=1000, std_dev=1.6)

# We set the OLS formula
formula = "Y ~ X0 + X1 + X2 + X3"
# We fit the OLS with the data, the formula and without intercept
ols = OLS(formula, df, fit_intercept=True)

ols.summary()

The output:

=========================================================================
                               OLS summary                               
=========================================================================
| R² = 0.99129                  | Adjusted-R² = 0.99126
| n  =   1000                   | p =     4
| Fisher = 37790.52477                         
=========================================================================
Variables  Coefficients  Standard Errors    t values  Probabilites
       X0      1.234759         0.020300   60.824688           0.0
       X1     -6.475338         0.009052 -715.327289           0.0
       X2      1.662661         0.020141   82.552778           0.0
       X3      1.519622         0.020319   74.787592           0.0

Logistic regression

The logistic regression can be used for binary classification where follows a Bernoulli distribution. With being the matrix of regressors, we have:

We then implement the regression with:

from statinf.regressions.glm import GLM
from statinf.data.GenerateData import generate_dataset

# Generate a synthetic dataset
data = generate_dataset(coeffs=[1.2556, -6.465, 1.665414, -1.5444], n=2500, std_dev=10.5, binary=True)

# We split data into train/test/application
train = data.iloc[0:1000]
test = data.iloc[1001:2000]


# We set the linear formula for Xb
formula = "Y ~ X0 + X1 + X2 + X3"
logit = GLM(formula, train, test_set=test)

# Fit the model
logit.fit(plot=True, epochs=1000, verbose=True)

logit.get_weights()

The ouput:

{'weights': array([ 0.00999791, -0.03512158,  0.00404969, -0.01669436]), 'bias': array(-0.12849798)}

Deep Learning

Multi Layer Perceptron

You can train a Neural Network using the MLP class. The below example shows how to train an MLP with 1 single linear layer. It is equivalent to implement an OLS with Gradient Descent.

from statinf.data.GenerateData import generate_dataset
from statinf.ml.neuralnetwork import MLP, Layer

# Generate the synthetic dataset
data = generate_dataset(coeffs=[1.2556, -6.465, 1.665414, 1.5444], n=1000, std_dev=1.6)

Y = ['Y']
X = [c for c in data.columns if c not in Y]

# Initialize the network and its architecture
nn = MLP()
nn.add(Layer(4, 1, activation='linear'))

# Train the neural network
nn.train(data=data, X=X, Y=Y, epochs=1, learning_rate=0.001)

# Extract the network's weights
print(nn.get_weights())

Output:

{'weights 0': array([[ 1.32005564],
       [-6.38121934],
       [ 1.64515704],
       [ 1.48571785]]), 'bias 0': array([0.81190412])}