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| ### (1) Generate simulated data | |
| import numpy.random as rnd | |
| import gradio as gr | |
| import matplotlib | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| import pandas as pd | |
| from sklearn.linear_model import LinearRegression | |
| import sympy as sp | |
| np.random.seed(42) | |
| m = 100 | |
| X1 = 6 * np.random.rand(m,1) - 3 | |
| X2 = X1 ** 2 | |
| y = X1 + 0.5 * X2 + 4 + np.random.randn(m,1) | |
| m = 50 | |
| X1_test = 6 * np.random.rand(m,1) - 3 | |
| X2_test = X1_test ** 2 | |
| y_test = X1_test + 0.5 * X2_test + 4 + np.random.randn(m,1) | |
| import pandas as pd | |
| data = pd.DataFrame({'y': y.flatten(), 'X1': X1.flatten(), 'X2': X2.flatten()}, columns=['y', 'X1', 'X2'],) | |
| data | |
| def draw_polynomial(degree=2): | |
| from sklearn.preprocessing import PolynomialFeatures | |
| poly_features = PolynomialFeatures(degree=degree, include_bias=False) | |
| X_poly = poly_features.fit_transform(X1) | |
| from sklearn.linear_model import LinearRegression | |
| lin_reg = LinearRegression() | |
| lin_reg.fit(X_poly, y) | |
| lin_reg.intercept_, lin_reg.coef_ | |
| # Sample polynomial coefficients | |
| coefficients = list(lin_reg.intercept_)+list(lin_reg.coef_[0]) | |
| coefficients = [np.round(val,3) for val in coefficients] | |
| print("coefficients: ",coefficients) | |
| # Create a symbolic variable for x | |
| x = sp.symbols('x') | |
| # Create the symbolic polynomial expression | |
| polynomial_expr = sum(coeff * x**power for power, coeff in enumerate(coefficients)) | |
| # Convert the symbolic expression to a LaTeX string | |
| latex_expression = sp.latex(polynomial_expr, mode='inline') | |
| latex_expression = 'y = '+latex_expression.replace('$','') | |
| ## Visualized fitted quadratic line on training/testing data | |
| X_new=np.linspace(-3, 3, 100).reshape(100, 1) | |
| X_new_poly = poly_features.transform(X_new) | |
| y_new = lin_reg.predict(X_new_poly) | |
| ### get training error using polynomial model | |
| X_poly = poly_features.transform(X1) | |
| y_predict = lin_reg.predict(X_poly) | |
| y_predict | |
| train_error = np.mean((y_predict - y)**2) | |
| print("train_error: ",train_error) | |
| ### get testing error using polynomial model | |
| X_test_poly = poly_features.transform(X1_test) | |
| y_test_predict = lin_reg.predict(X_test_poly) | |
| y_test_predict | |
| test_error = np.mean((y_test_predict - y_test)**2) | |
| print("test_error: ",test_error) | |
| X = np.array([[train_error,test_error]]) | |
| results = pd.DataFrame(X, columns=['Training Error','Test Error']) | |
| fig = plt.figure(figsize=(12,10)) | |
| plt.subplot(2,1,1) | |
| plt.plot(X1, y, "b.") | |
| plt.plot(X1_test, y_test, "g.", markersize=12) | |
| plt.plot(X_new, y_new, "r-", linewidth=2, label="Predictions") | |
| plt.xlabel("$x_1$", fontsize=18) | |
| plt.ylabel("$y$", rotation=0, fontsize=18) | |
| plt.legend(loc="upper left", fontsize=14) | |
| plt.axis([-3, 3, 0, 10]) | |
| plt.subplot(2,1,2) | |
| plt.plot([i+1 for i in range(0, len(lin_reg.coef_[0]))], lin_reg.coef_[0], 'r-') | |
| plt.xlabel("Parameters", fontsize=14) | |
| plt.ylabel("Values", fontsize=14) | |
| plt.xticks([i+1 for i in range(0, len(lin_reg.coef_[0]))], [i+1 for i in range(0, len(lin_reg.coef_[0]))]) | |
| plt.xlim(0,len(lin_reg.coef_[0])+1) | |
| #plt.show() | |
| fig.tight_layout() | |
| plt.savefig('plot_line.png', dpi=300) | |
| return latex_expression, results, 'plot_line.png' | |
| #### Define input component | |
| input_degree = gr.inputs.Slider(1, 27, step=1, default=2, label='Degree of Polynomial Regression') | |
| #### Define output component | |
| set_formula = gr.outputs.Textbox(label ='Polynomial Model') | |
| set_output = gr.outputs.Dataframe(type='pandas', label ='Evaluation Results') | |
| output_plot1 = gr.outputs.Image(label="Regression plot", type='pil') | |
| ### configure gradio, detailed can be found at https://www.gradio.app/docs/#i_slider | |
| interface = gr.Interface(fn=draw_polynomial, | |
| inputs=[input_degree], | |
| outputs=[set_formula, set_output, output_plot1], | |
| title="CSCI4750/5750: Polynomial Regression models \n (Model Complexity)", | |
| theme = 'huggingface', | |
| layout = 'vertical' | |
| ) | |
| interface.launch(debug=True) | |