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| def homework06_solution(theta0, theta1, theta2, learning_rate): | |
| import numpy as np | |
| import pandas as pd | |
| def logistic_predict(b0, b1, b2, x1, x2): | |
| z = b0 + b1*x1 + b2*x2 | |
| p = 1 / (1 + np.exp(-z)) | |
| return p | |
| def binary_cross_entropy(X, y, parameter_list): | |
| entropy_loss = 0 | |
| for n in range(0,len(X)): | |
| # calculate the linear output given the current weights | |
| z = parameter_list[0] + parameter_list[1]*X[n][0]+ parameter_list[2]*X[n][1] | |
| # calculate sigmoid output given z | |
| p = 1 / (1 + np.exp(-z)) | |
| # calculate the binary cross-entropy | |
| predict_1 = y[n] * np.log(p) | |
| predict_0 = (1-y[n]) * np.log(1-p) | |
| entropy_loss += -(predict_1 + predict_0) / len(X) | |
| return entropy_loss | |
| def get_logistic_results(data, theta0, theta1, theta2): | |
| ## (2) make logistic 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 = logistic_predict(theta0, theta1, theta2, x1, x2) | |
| y_hat_list.append(y_hat) | |
| ## (3) calculate gradients | |
| theta0_grad = theta0_grad - 1/len(data)*(y - y_hat)*1.0 | |
| theta1_grad = theta1_grad - 1/len(data)*(y - y_hat)*x1 | |
| theta2_grad = theta2_grad - 1/len(data)*(y - y_hat)*x2 | |
| data['y_hat'] = y_hat_list | |
| data['y-y_hat'] = data['y'] - data['y_hat'] | |
| data['(y-y_hat)*x_1'] = data['y-y_hat']*data.iloc[:,0] | |
| data['(y-y_hat)*x_2'] = data['y-y_hat']*data.iloc[:,1] | |
| return data, theta0_grad, theta1_grad, theta2_grad | |
| ## (1) load data | |
| X = np.array([[9,9], [0,0], [8,6], [3,3], [7,8], [0.5,0.5], [5,6], [6,7]]) | |
| y = [1,0,1,0,1,0,1,1] | |
| data = pd.DataFrame(X, columns=['X1','X2']) | |
| data['y'] = y | |
| ## (2) get regression table, gradients q3.2 | |
| data, theta0_grad, theta1_grad, theta2_grad = get_logistic_results(data, theta0, theta1, theta2) | |
| ### (3) summarize gradient results for question 3.2 | |
| data_t = data.T | |
| data_t = data_t.round(5) | |
| data_t.insert(loc=0, column='Name', value=['X1', 'X2', 'y', 'y_hat', 'y-y_hat', '(y-y_hat)*x_1', '(y-y_hat)*x_2']) | |
| ### (4) summarize gradient results for question 3b | |
| q3_loss = binary_cross_entropy(X, y, [theta0, theta1, theta2]) | |
| ### summarize gradient results for question Q3.3 | |
| ### update parameter using gradient descent Q3.4 | |
| theta0_new = theta0 - learning_rate*theta0_grad | |
| theta1_new = theta1 - learning_rate*theta1_grad | |
| theta2_new = theta2 - learning_rate*theta2_grad | |
| ### (6) summarize gradient results for question 3.4 | |
| q3_loss_new = binary_cross_entropy(X, y, [theta0_new, theta1_new, theta2_new]) | |
| ### (7) return all results for Gradio visualization | |
| data_final = data_t.T | |
| print(data_final['y-y_hat'].values[1:]) | |
| y_diff_sum = data_final['y-y_hat'].values[1:].sum() | |
| y_diff_x1_sum = data_final['(y-y_hat)*x_1'].values[1:].sum() | |
| y_diff_x2_sum = data_final['(y-y_hat)*x_2'].values[1:].sum() | |
| return data_t.T, q3_loss, y_diff_sum, y_diff_x1_sum, y_diff_x2_sum, theta0_grad, theta1_grad , theta2_grad, theta0_new, theta1_new, theta2_new, q3_loss_new | |
| 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 3.2') | |
| set_output_q3b = gr.outputs.Textbox(label ='Question 3.1: Initial BCE loss') | |
| set_output_q3c = gr.outputs.Textbox(label ='Question 3.2: sum(y-y_hat)') | |
| set_output_q3d = gr.outputs.Textbox(label ='Question 3.2: sum((y-y_hat)*x_1)') | |
| set_output_q3e = gr.outputs.Textbox(label ='Question 3.2: sum((y-y_hat)*x_2)') | |
| set_output_q4a0 = gr.outputs.Textbox(label ='Question 3.3: theta0_grad') | |
| set_output_q4a1 = gr.outputs.Textbox(label ='Question 3.3: theta1_grad') | |
| set_output_q4a2 = gr.outputs.Textbox(label ='Question 3.3: theta2_grad') | |
| set_output_q4b0 = gr.outputs.Textbox(label ='Question 3.4: theta0_new: updated by gradient descent') | |
| set_output_q4b1 = gr.outputs.Textbox(label ='Question 3.4: theta1_new: updated by gradient descent') | |
| set_output_q4b2 = gr.outputs.Textbox(label ='Question 3.4: theta2_new: updated by gradient descent') | |
| set_output_q4b4 = gr.outputs.Textbox(label ='Question 4 (4): New BCE after update the parameters using gradient descent') | |
| ### configure Gradio | |
| interface = gr.Interface(fn=homework06_solution, | |
| inputs=[set_theta0, set_theta1, set_theta2, set_ita], | |
| outputs=[set_output_q3a, set_output_q3b, set_output_q3c, set_output_q3d, set_output_q3e, | |
| set_output_q4a0, set_output_q4a1, set_output_q4a2, | |
| set_output_q4b0, set_output_q4b1, set_output_q4b2, | |
| set_output_q4b4], | |
| title="CSCI4750/5750(hw06): Linear Regression/Optimization", | |
| description= "Click examples below for a quick demo", | |
| theme = 'huggingface', | |
| layout = 'horizontal', | |
| live=True | |
| ) | |
| interface.launch(debug=True) |