### CSCI 4750/5750: regression models and gradient descent ### 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 gradient_descent(intercept=4, slope=3, intercept_random=4, slope_random=3, gradient_descent=False, learning_rate= 0.01, iteration=100): ### (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=(12,20)) plt.subplot(3,1,1) 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") ### (4.3) Apply gradient desc if gradient_descent: b = intercept_random w = slope_random lr = learning_rate # learning rate iteration = iteration # Store initial values for plotting. b_history = [b] w_history = [w] train_mse = [] # Iterations for i in range(iteration): b_grad = 0.0 w_grad = 0.0 for n in range(len(X)): b_grad = b_grad - (y[n,0] - b - w*X[n,0])*1.0 w_grad = w_grad - (y[n,0] - b - w*X[n,0])*X[n,0] b_grad /= len(X) w_grad /= len(X) # Update parameters. b = b - lr * b_grad w = w - lr * w_grad # Store parameters for plotting b_history.append(b) w_history.append(w) train_mse.append(cal_mse(X,y,b,w)) if i == int(iteration/4): X_tmp = np.array([[0], [2]]) X_tmp_b = np.c_[np.ones((2, 1)), X_tmp] # add x0 = 1 to each instance y_predict_tmp = X_tmp_b.dot(np.array([b, w])) plt.plot(X_tmp, y_predict_tmp, "brown", linewidth=2, label = "Fitted line in iteration "+str(i)) if i == int(iteration/3): X_tmp = np.array([[0], [2]]) X_tmp_b = np.c_[np.ones((2, 1)), X_tmp] # add x0 = 1 to each instance y_predict_tmp = X_tmp_b.dot(np.array([b, w])) plt.plot(X_tmp, y_predict_tmp, "blue", linewidth=2, label = "Fitted line in iteration "+str(i)) if i == int(iteration/2): X_tmp = np.array([[0], [2]]) X_tmp_b = np.c_[np.ones((2, 1)), X_tmp] # add x0 = 1 to each instance y_predict_tmp = X_tmp_b.dot(np.array([b, w])) plt.plot(X_tmp, y_predict_tmp, "gray", linewidth=2, label = "Fitted line in iteration "+str(i)) if i == int(iteration-1): X_tmp = np.array([[0], [2]]) X_tmp_b = np.c_[np.ones((2, 1)), X_tmp] # add x0 = 1 to each instance y_predict_tmp = X_tmp_b.dot(np.array([b, w])) plt.plot(X_tmp, y_predict_tmp, "black", linewidth=2, label = "Fitted line in iteration "+str(i)) 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(3,1,2) ### (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) ### (5.7) draw gradient updates if gradient_descent: plt.plot(b_history, w_history, 'o-', ms=3, lw=1.5, color='black') plt.title("Visualization of Gradient Descent Process", fontsize=22) plt.xlabel("$Intercept$", fontsize=22) plt.ylabel("$Slope$", rotation=0, fontsize=22) plt.xticks(fontsize=18) plt.yticks(fontsize=18) plt.xlim(-10,10) plt.ylim(-10,10) ### 6. Visualize the learning curves if gradient_descent: plt.subplot(3,1,3) plt.plot(train_mse,label="train_loss (lr="+str(learning_rate)+")") plt.xlabel('Iteration',fontweight="bold",fontsize = 22) plt.ylabel('Loss',fontweight="bold",fontsize = 22) plt.title("Learning curve: Loss VS Epochs",fontweight="bold",fontsize = 22) plt.legend(fontsize=18) 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=-4.5, label='(Random) Slope') input_gradients = gr.inputs.Checkbox(label="Apply Gradient Descent") input_learningrate = gr.inputs.Slider(0,1, step=0.001, default=0.005, label='Learning Rate') input_interation = gr.inputs.Slider(1, 1000, step=2, default=150, label='Iteration') #### 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=gradient_descent, inputs=[input_intercept, input_slope, input_intercept_random, input_slope_random, input_gradients, input_learningrate, input_interation], outputs=[output_plot1], examples_per_page = 2, examples = [[4, 3, -7, -5, True, 0.0001, 100], [1, 2, -7, -8, False, 0.0001, 100]], title="CSCI4750/5750: Regression models \n (Function approximation by Gradient Descent)", description= "Click examples to generate random dataset and select gradient descent parameters", theme = 'huggingface', layout = 'vertical' ) interface.launch(debug=True)