non linear regression python

Imam-Zamana answered on May 31, 2024 Popularity 3/10 Helpfulness 1/10

answer non linear regression python

non linear regression python

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import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import statsmodels.api as sm
from statsmodels.base.model import GenericLikelihoodModel
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline

# Generate synthetic data
np.random.seed(0)
x_data = np.linspace(0, 4, 50)
y_data = 2.5 * np.exp(-1.3 * x_data) + 0.5 + 0.2 * np.random.normal(size=len(x_data))
x_data_reshaped = x_data[:, np.newaxis]  # For sklearn

# 1. Using scipy.optimize.curve_fit
def model(x, a, b, c):
    return a * np.exp(-b * x) + c

popt, pcov = curve_fit(model, x_data, y_data)

image.mefiz.com

# 2. Using statsmodels
class NonLinearModel(GenericLikelihoodModel):
    def __init__(self, endog, exog, **kwargs):
        super(NonLinearModel, self).__init__(endog, exog, **kwargs)

    def nloglikeobs(self, params):
        a, b, c = params
        y_pred = a * np.exp(-b * self.exog) + c
        resid = self.endog - y_pred
        return 0.5 * (resid ** 2)

    def fit(self, start_params=None, maxiter=10000, method='nm', **kwargs):
        if start_params is None:
            start_params = np.array([1.0, 1.0, 1.0])
        return super(NonLinearModel, self).fit(start_params=start_params, maxiter=maxiter, method=method, **kwargs)

nlm = NonLinearModel(y_data, x_data)
result = nlm.fit()

# 3. Using sklearn with Polynomial Features
degree = 4
poly_model = make_pipeline(PolynomialFeatures(degree), LinearRegression())
poly_model.fit(x_data_reshaped, y_data)

# Plot results
plt.figure(figsize=(12, 8))

# Original Data
plt.scatter(x_data, y_data, label='Data', color='blue')

# scipy.optimize.curve_fit
plt.plot(x_data, model(x_data, *popt), label='scipy.optimize.curve_fit', color='red')

# statsmodels
plt.plot(x_data, result.predict(x_data), label='statsmodels', color='green')

# sklearn Polynomial Regression
plt.plot(x_data, poly_model.predict(x_data_reshaped), label='sklearn Polynomial Regression', color='purple')

plt.legend()
plt.xlabel('x')
plt.ylabel('y')
plt.title('Non-linear Regression using different methods')
plt.show()

Popularity 3/10 Helpfulness 1/10 Language python

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Tags: non-linear-regression python

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Contributed on May 31 2024

Imam-Zamana

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non linear regression python

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