---
tags: AI
disqus: HackMD
---

人工智慧 #3
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For the data set in the table below, please implement a multivariate regression program to predict the weights of new samples. Please implement the gradient descent search of the perceptron learning rule by yourself, not calling any library functions. Upload a detail report on how you program the predictor and the running environment of the final program. (Note: Your program should not use any regression library functions from any language environment.)


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import numpy as np
import pandas as pd

def cost_function(X, Y, theta):
    '''計算成本函數'''
    m = len(Y)
    error = X.dot(theta) - Y
    cost = np.sum(error ** 2)/(2*m)
    return cost, error

def batch_gradient_descent(X, Y, theta, alpha, iters):
    '''梯度下降'''
    cost_history = np.zeros(iters)
    m = len(Y)
    for i in range(iters):
        cost, error = cost_function(X, Y, theta)
        gradient = X.T.dot(error) / m
        theta = theta - alpha * gradient
        cost_history[i] = cost
    return theta, cost_history

# In[0]: 先將資料載入pandas.DataFrame  
data = list([[5.0, 45, 77], 
             [5.11, 26, 47], 
             [5.6, 30, 55], 
             [5.9, 34, 59], 
             [4.8, 40, 72], 
             [5.8, 36, 60], 
             [5.3, 19, 40], 
             [5.8, 28, 60], 
             [5.5, 23, 45], 
             [5.6, 32, 58]])

df = pd.DataFrame(columns=('Height', 'Age', 'Weight'), data=data)

# In[1]: 將資料切分為X、Y，其中X作為Feature、Y作為Label
X = df[['Height', 'Age']]
Y = df['Weight']

# In[2]: 資料標準化，採用Z分數標準化(Z-Score Standardization)
# 取平均值
X_mean = X.mean()

# 取標準差
X_std = X.std()

# (X-平均值)/標準差
X = (X - X_mean) / X_std

# 在向量插入偏差列，校準時會乘以偏差列
X = np.c_[np.ones(X.shape[0]), X]

# In[3]: 設定初始係數
theta = np.zeros(X.shape[1])
alpha = 0.005
iterations = 2000

# In[4]: 梯度下降
theta, cost_history = batch_gradient_descent(X, Y, theta, alpha, iterations)

# In[5]: 預測結果
test = (5.5, 38)
Pred = (theta[2] * (test[0] - X_mean[0]) / X_std[0]) + (theta[1] * (test[1] - X_mean[1]) / X_std[1]) + theta[0]
print('Predict:', Pred)