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| def homework04_solution(theta0, theta1, theta2, learning_rate): | |
| import numpy as np | |
| import pandas as pd | |
| def linear_predict(b0, b1, b2, x1, x2): | |
| y_hat = b0 + b1*x1 + b2*x2 | |
| return y_hat | |
| def get_linear_results(data, theta0, theta1, theta2): | |
| ## (2) make linear prediction | |
| y_hat_list = [] | |
| theta0_grad = 0 | |
| theta1_grad = 0 | |
| theta2_grad = 0 | |
| for i in range(len(data)): | |
| x1 = data.iloc[i,0] | |
| x2 = data.iloc[i,1] | |
| y = data.iloc[i,2] | |
| y_hat = linear_predict(theta0, theta1, theta2, x1, x2) | |
| y_hat_list.append(y_hat) | |
| ## (3) calculate gradients | |
| theta0_grad = theta0_grad - 2/len(data)*(y - theta0 - theta1*x1 - theta2*x2)*1.0 | |
| theta1_grad = theta1_grad - 2/len(data)*(y - theta0 - theta1*x1 - theta2*x2)*x1 | |
| theta2_grad = theta2_grad - 2/len(data)*(y - theta0 - theta1*x1 - theta2*x2)*x2 | |
| data['y_hat'] = y_hat_list | |
| data['y-y_hat'] = data['y'] - data['y_hat'] | |
| data['(y-y_hat)^2'] = data['y-y_hat']*data['y-y_hat'] | |
| return data, theta0_grad, theta1_grad, theta2_grad | |
| ## (1) load data | |
| X = np.array([[15,20], [30,16], [12,6.5], [13,20], [18,18]]) | |
| y = [4.9, 5.8,6.5,7.3,7.2] | |
| data = pd.DataFrame(X, columns=['X1','X2']) | |
| data['y'] = y | |
| ## (2) get regression table, gradients | |
| data, theta0_grad, theta1_grad, theta2_grad = get_linear_results(data, theta0, theta1, theta2) | |
| ### (3) summarize gradient results for question 3a | |
| data_t = data.T | |
| data_t = data_t.round(2) | |
| data_t.insert(loc=0, column='Name', value=['X1', 'X2', 'y', 'y_hat', 'y-y_hat', '(y-y_hat)^2']) | |
| ### (4) summarize gradient results for question 3b | |
| MSE = data['(y-y_hat)^2'].mean() | |
| q3_mse = MSE | |
| ### summarize gradient results for question 4 (2) | |
| ### update parameter using gradient descent 4 (3) | |
| theta0_new = theta0 - learning_rate*theta0_grad | |
| theta1_new = theta1 - learning_rate*theta1_grad | |
| theta2_new = theta2 - learning_rate*theta2_grad | |
| ### (5) recalculate linear regression table using new gradients | |
| data4,_,_,_ = get_linear_results(data, theta0_new, theta1_new, theta2_new) | |
| ### (6) summarize gradient results for question 4 (4) | |
| MSE = data4['(y-y_hat)^2'].mean() | |
| q4_mse = MSE | |
| ### (7) return all results for Gradio visualization | |
| return data_t, q3_mse, theta0_grad, theta1_grad , theta2_grad, theta0_new, theta1_new, theta2_new, q4_mse | |
| import numpy as np | |
| import gradio as gr | |
| ### configure inputs | |
| set_theta0 = gr.inputs.Number() | |
| set_theta1 = gr.inputs.Number() | |
| set_theta2 = gr.inputs.Number() | |
| set_ita = gr.inputs.Number() | |
| ### configure outputs | |
| set_output_q3a = gr.outputs.Dataframe(type='pandas', label ='Question 3a') | |
| set_output_q3b = gr.outputs.Textbox(label ='Question 3b: Initial MSE loss') | |
| set_output_q4a0 = gr.outputs.Textbox(label ='Question 4 (2): theta0_grad') | |
| set_output_q4a1 = gr.outputs.Textbox(label ='Question 4 (2): theta1_grad') | |
| set_output_q4a2 = gr.outputs.Textbox(label ='Question 4 (2): theta2_grad') | |
| set_output_q4b0 = gr.outputs.Textbox(label ='Question 4 (3): theta0_new: updated by gradient descent') | |
| set_output_q4b1 = gr.outputs.Textbox(label ='Question 4 (3): theta1_new: updated by gradient descent') | |
| set_output_q4b2 = gr.outputs.Textbox(label ='Question 4 (3): theta2_new: updated by gradient descent') | |
| set_output_q4b4 = gr.outputs.Textbox(label ='Question 4 (4): New MSE after update the parameters using gradient descent') | |
| ### configure Gradio | |
| interface = gr.Interface(fn=homework04_solution, | |
| inputs=[set_theta0, set_theta1, set_theta2, set_ita], | |
| outputs=[set_output_q3a, set_output_q3b, | |
| set_output_q4a0, set_output_q4a1, set_output_q4a2, | |
| set_output_q4b0, set_output_q4b1, set_output_q4b2, | |
| set_output_q4b4], | |
| examples_per_page = 2, | |
| examples=[ | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| np.round(np.random.uniform(0, 1, (3,)),2).tolist()+[0.001], | |
| ], | |
| title="CSCI4750/5750(hw04): Linear Regression/Optimization", | |
| description= "Click examples below for a quick demo", | |
| theme = 'huggingface', | |
| layout = 'horizontal', | |
| live=True | |
| ) | |
| interface.launch(debug=True) |