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| ### CSCI 4750/5750: regression models | |
| import gradio as gr | |
| import matplotlib | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| from sklearn.linear_model import LinearRegression | |
| def cal_mse(X,y,b,w): | |
| thetas = np.array([[b], [w]]) | |
| X_b = np.c_[np.ones((len(X), 1)), X] # add x0 = 1 to each instance | |
| y_predict = X_b.dot(thetas) | |
| mse = np.mean((y_predict-y)**2) | |
| return mse | |
| def plot_regression(intercept=4, slope=3, intercept_random=4, slope_random=3, multi_line=False): | |
| ### (1) generate simulated data points | |
| X = 2 * np.random.rand(100, 1) | |
| y = intercept + slope * X + np.random.randn(100, 1) | |
| ### (2) fit regression model | |
| lin_reg = LinearRegression() | |
| lin_reg.fit(X, y) | |
| ### (3) make a prediction on training data | |
| y_predict = lin_reg.predict(X) | |
| y_predict | |
| ### (4) Draw baseline linear Line | |
| fig = plt.figure(figsize=(12,12)) | |
| plt.subplot(2,1,1) | |
| plt.plot(X, y_predict, "r-", linewidth=2, label = "Line of best fit") | |
| plt.plot(X, y, "b.") | |
| ### (4.2) Draw random line | |
| if intercept_random != intercept or slope_random != slope: #avoid overlap | |
| X_new = np.array([[0], [2]]) | |
| X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance | |
| y_predict = X_new_b.dot(np.array([intercept_random, slope_random])) | |
| plt.plot(X_new, y_predict, "g-", linewidth=2, label = "Random line") | |
| if multi_line: | |
| X_new = np.array([[0], [2]]) | |
| X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance | |
| ### (4.3) generate grid of parameters and plot multiple lines | |
| b = np.arange(-8,8,0.1) #bias | |
| w = np.arange(-8,8,0.1) #weight | |
| ### select random weights/bias for visualization | |
| w_random = w[np.random.choice(range(len(w)), 10)] | |
| b_random = b[np.random.choice(range(len(b)), 10)] | |
| for i in range(len(w_random)): | |
| y_predict = X_new_b.dot(np.array([b_random[i], w_random[i]])) | |
| plt.plot(X_new, y_predict, "g-", linewidth=2) | |
| plt.xlabel("$x_1$", fontsize=22) | |
| plt.ylabel("$y$", rotation=0, fontsize=22) | |
| plt.xticks(fontsize=18) | |
| plt.yticks(fontsize=18) | |
| plt.axis([np.min(X)*0.1, np.max(X)*1.1, np.min(y)*0.1, np.max(y)*1.1]) | |
| plt.title("Linear Regression model predictions", fontsize=22) | |
| plt.legend(fontsize=18) | |
| ### (5) Visualize loss function | |
| plt.subplot(2,1,2) | |
| ### (5.1) generate grid of parameters | |
| b = np.arange(-10,10,0.1) #bias | |
| w = np.arange(-10,10,0.1) #weight | |
| ### (5.2) Calculate MSE over parameters | |
| Z = np.zeros((len(w), len(b))) | |
| for i in range(len(w)): | |
| for j in range(len(b)): | |
| w0 = w[i] | |
| b0 = b[j] | |
| Z[i][j] = cal_mse(X, y, b0, w0) | |
| ### (5.3) Get optimal parameters | |
| theta0_best = lin_reg.intercept_[0] | |
| theta1_best = lin_reg.coef_[0][0] | |
| ### (5.4) Draw the contour graph | |
| plt.contourf(b,w,Z, 50, alpha=0.5, cmap=plt.get_cmap('jet')) | |
| ### (5.5) Add optimal loss | |
| plt.plot(theta0_best, theta1_best, 'x', ms=12, markeredgewidth=3, color='orange') | |
| plt.text(theta0_best, theta1_best,'MSE:'+str(np.round(cal_mse(X,y,theta0_best, theta1_best),2)), color='red', fontsize=22) | |
| ### (5.6) Add loss of random lines | |
| if intercept_random != intercept or slope_random != slope: #avoid overlap | |
| plt.plot(intercept_random, slope_random, 'o', ms=5, markeredgewidth=3, color='orange') | |
| plt.text(intercept_random, slope_random,'MSE:'+str(np.round(cal_mse(X,y,intercept_random, slope_random),2)), fontsize=22) | |
| if multi_line: | |
| for i in range(len(w_random)): | |
| plt.plot(b_random[i], w_random[i], 'o', ms=5, markeredgewidth=3, color='orange') | |
| plt.text(b_random[i], w_random[i],'MSE:'+str(np.round(cal_mse(X,y,b_random[i], w_random[i]),2)), fontsize=22) | |
| plt.title("Visualization of Loss function over parameters", fontsize=22) | |
| plt.xlabel("$Intercept$", fontsize=22) | |
| plt.ylabel("$Slope$", rotation=0, fontsize=22) | |
| plt.xticks(fontsize=18) | |
| plt.yticks(fontsize=18) | |
| #plt.show() | |
| fig.tight_layout() | |
| plt.savefig('plot_line.png', dpi=300) | |
| return 'plot_line.png' | |
| #### Define input component | |
| input_intercept = gr.inputs.Slider(1, 8, step=0.5, default=4, label='(Baseline) Intercept') | |
| input_slope = gr.inputs.Slider(-8, 8, step=0.5, default=2.8, label='(Baseline) Slope') | |
| input_intercept_random = gr.inputs.Slider(-8, 8, step=0.5, default=4, label='(Random) Intercept') | |
| input_slope_random = gr.inputs.Slider(-8, 8, step=0.5, default=2.8, label='(Random) Slope') | |
| input_random_plots = gr.inputs.Checkbox(label="Draw multiple lines") | |
| #### Define output component | |
| output_plot1 = gr.outputs.Image(label="Regression plot") | |
| ### configure gradio, detailed can be found at https://www.gradio.app/docs/#i_slider | |
| interface = gr.Interface(fn=plot_regression, | |
| inputs=[input_intercept, input_slope, input_intercept_random, input_slope_random, input_random_plots], | |
| outputs=[output_plot1], | |
| examples_per_page = 2, | |
| examples = [[4, 3, 2, 1, True], [1, 2, 3, 4, False]], | |
| title="CSCI4750/5750: Regression models", | |
| description= "Click examples to generate random dataset", | |
| theme = 'huggingface', | |
| layout = 'vertical' | |
| ) | |
| interface.launch(debug=True) | |