推荐系统评测指标
• 预测准确度
• 用户满意度
• 覆盖率
• 多样性
• 惊喜度
• 信任度
• 实时性
• 健壮性
• 商业目标
推荐准确度评测
• 评分预测
很多网站都有让用户给物品打分的功能，如果知道用户对物品的历史评分，就可以从中学习一个兴趣模型，从而预测用户对新物品的评分
– 评分预测的准确度一般用均方根误差（RMSE）或平均绝对误差（MAE）计算
• Top-N推荐
– 网站提供推荐服务时，一般是给用户一个个性化的推荐列表，这种推荐叫做
Top-N推荐
– Top-N推荐的预测准确率一般用精确率（precision）和召回率（recall）来度量
准确率、精确率和召回率
机 器 学 习 基 础
• 经验风险
– 模型 f(X) 关于训练数据集的平均损失称为经验风险（empirial risk），记作 Remp
• 经验风险最小化（Empirical Risk Minimization，ERM）
– 这一策略认为，经验风险最小的模型就是最优的模型
– 样本足够大时，ERM 有很好的学习效果，因为有足够多的“经验”
– 样本较小时，ERM 就会出现一些问题
训练误差和测试误差
• 训练误差
– 训练误差（training error）是关于训练集的平均损失。
– 训练误差的大小，可以用来判断给定问题是否容易学习，但本质上并不重要
• 测试误差
– 测试误差（testing error）是关于测试集的平均损失。
– 测试误差真正反映了模型对未知数据的预测能力，这种能力一般被称为 泛化能力
0. 引入依赖
import numpy as np
import matplotlib.pyplot as plt
1. 导入数据（data.csv）
32.502345269453031,31.70700584656992
53.426804033275019,68.77759598163891
61.530358025636438,62.562382297945803
47.475639634786098,71.546632233567777
59.813207869512318,87.230925133687393
55.142188413943821,78.211518270799232
52.211796692214001,79.64197304980874
39.299566694317065,59.171489321869508
48.10504169176825,75.331242297063056
52.550014442733818,71.300879886850353
45.419730144973755,55.165677145959123
54.351634881228918,82.478846757497919
44.164049496773352,62.008923245725825
58.16847071685779,75.392870425994957
56.727208057096611,81.43619215887864
48.955888566093719,60.723602440673965
44.687196231480904,82.892503731453715
60.297326851333466,97.379896862166078
45.618643772955828,48.847153317355072
38.816817537445637,56.877213186268506
66.189816606752601,83.878564664602763
65.41605174513407,118.59121730252249
47.48120860786787,57.251819462268969
41.57564261748702,51.391744079832307
51.84518690563943,75.380651665312357
59.370822011089523,74.765564032151374
57.31000343834809,95.455052922574737
63.615561251453308,95.229366017555307
46.737619407976972,79.052406169565586
50.556760148547767,83.432071421323712
52.223996085553047,63.358790317497878
35.567830047746632,41.412885303700563
42.436476944055642,76.617341280074044
58.16454011019286,96.769566426108199
57.504447615341789,74.084130116602523
45.440530725319981,66.588144414228594
61.89622268029126,77.768482417793024
33.093831736163963,50.719588912312084
36.436009511386871,62.124570818071781
37.675654860850742,60.810246649902211
44.555608383275356,52.682983366387781
43.318282631865721,58.569824717692867
50.073145632289034,82.905981485070512
43.870612645218372,61.424709804339123
62.997480747553091,115.24415280079529
32.669043763467187,45.570588823376085
40.166899008703702,54.084054796223612
53.575077531673656,87.994452758110413
33.864214971778239,52.725494375900425
64.707138666121296,93.576118692658241
38.119824026822805,80.166275447370964
44.502538064645101,65.101711570560326
40.599538384552318,65.562301260400375
41.720676356341293,65.280886920822823
51.088634678336796,73.434641546324301
55.078095904923202,71.13972785861894
41.377726534895203,79.102829683549857
62.494697427269791,86.520538440347153
49.203887540826003,84.742697807826218
41.102685187349664,59.358850248624933
41.182016105169822,61.684037524833627
50.186389494880601,69.847604158249183
52.378446219236217,86.098291205774103
50.135485486286122,59.108839267699643
33.644706006191782,69.89968164362763
39.557901222906828,44.862490711164398
56.130388816875467,85.498067778840223
57.362052133238237,95.536686846467219
60.269214393997906,70.251934419771587
35.678093889410732,52.721734964774988
31.588116998132829,50.392670135079896
53.66093226167304,63.642398775657753
46.682228649471917,72.247251068662365
43.107820219102464,57.812512976181402
70.34607561504933,104.25710158543822
44.492855880854073,86.642020318822006
57.50453330326841,91.486778000110135
36.930076609191808,55.231660886212836
55.805733357942742,79.550436678507609
38.954769073377065,44.847124242467601
56.901214702247074,80.207523139682763
56.868900661384046,83.14274979204346
34.33312470421609,55.723489260543914
59.04974121466681,77.634182511677864
57.788223993230673,99.051414841748269
54.282328705967409,79.120646274680027
51.088719898979143,69.588897851118475
50.282836348230731,69.510503311494389
44.211741752090113,73.687564318317285
38.005488008060688,61.366904537240131
32.940479942618296,67.170655768995118
53.691639571070056,85.668203145001542
68.76573426962166,114.85387123391394
46.230966498310252,90.123572069967423
68.319360818255362,97.919821035242848
50.030174340312143,81.536990783015028
49.239765342753763,72.111832469615663
50.039575939875988,85.232007342325673
48.149858891028863,66.224957888054632
25.128484647772304,53.454394214850524
在jupyternobook中运行
points = np.genfromtxt('data.csv', delimiter=',')
points[0,0]
# 提取points中的两列数据，分别作为x，y
x = points[:, 0]
y = points[:, 1]
# 用plt画出散点图
plt.scatter(x, y)
plt.show()
2. 定义损失函数
# 损失函数是系数的函数，另外还要传入数据的x，y
def compute_cost(w, b, points):
total_cost = 0
M = len(points)
# 逐点计算平方损失误差，然后求平均数
for i in range(M):
x = points[i, 0]
y = points[i, 1]
total_cost += ( y - w * x - b ) ** 2
#total_cost为平均损失函数
return total_cost/M
简单线性回归（最小二乘法）
3.定义算法拟合函数
# 先定义一个求均值的函数
def average(data):
sum = 0
num = len(data)
for i in range(num):
sum += data[i]
return sum/num
# 定义核心拟合函数
def fit(points):
M = len(points)
x_bar = average(points[:, 0]) #x平均值
sum_yx = 0
sum_x2 = 0
sum_delta = 0
for i in range(M):
x = points[i, 0]
y = points[i, 1]
sum_yx += y * ( x - x_bar )
sum_x2 += x ** 2
# 根据公式计算w
w = sum_yx / ( sum_x2 - M * (x_bar**2) )
for i in range(M):
x = points[i, 0]
y = points[i, 1]
sum_delta += ( y - w * x )
b = sum_delta / M
return w, b
4. 测试
w, b = fit(points)
print("w is: ", w)
print("b is: ", b)
cost = compute_cost(w, b, points)
print("cost is: ", cost)
w is: 1.3224310227553846
b is: 7.991020982269173
cost is: 110.25738346621313
5. 画出拟合曲线
plt.scatter(x, y)
# 针对每一个x，计算出预测的y值
pred_y = w * x + b
plt.plot(x, pred_y, c='r')
plt.show()
简单线性回归（梯度下降法）
3. 定义模型的超参数
alpha = 0.0001 #步长
initial_w = 0
initial_b = 0
num_iter = 10 #迭代次数
4. 定义核心梯度下降算法函数
def grad_desc(points, initial_w, initial_b, alpha, num_iter):
w = initial_w
b = initial_b
# 定义一个list保存所有的损失函数值，用来显示下降的过程
cost_list = []
for i in range(num_iter):
cost_list.append( compute_cost(w, b, points) )
w, b = step_grad_desc( w, b, alpha, points )
return [w, b, cost_list]
def step_grad_desc( current_w, current_b, alpha, points ):
sum_grad_w = 0
sum_grad_b = 0
M = len(points) #点的个数
# 对每个点，代入公式求和
for i in range(M):
x = points[i, 0]
y = points[i, 1]
sum_grad_w += ( current_w * x + current_b - y ) * x
sum_grad_b += current_w * x + current_b - y
# 用公式求当前梯度
grad_w = 2/M * sum_grad_w
grad_b = 2/M * sum_grad_b
# 梯度下降，更新当前的w和b
updated_w = current_w - alpha * grad_w
updated_b = current_b - alpha * grad_b
return updated_w, updated_b
5. 测试：运行梯度下降算法计算最优的w和b
w, b, cost_list = grad_desc( points, initial_w, initial_b, alpha, num_iter )
print("w is: ", w)
print("b is: ", b)
cost = compute_cost(w, b, points)
print("cost is: ", cost)
plt.plot(cost_list)
plt.show()
w is: 1.4774173755483797
b is: 0.02963934787473238
cost is: 112.65585181499748
6. 画出拟合曲线
plt.scatter(x, y)
# 针对每一个x，计算出预测的y值
pred_y = w * x + b
plt.plot(x, pred_y, c='r')
plt.show()
线性回归调sklearn库实现
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
x_new = x.reshape(-1, 1)
y_new = y.reshape(-1, 1)
lr.fit(x_new, y_new)
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,normalize=False)
# 从训练好的模型中提取系数和截距
w = lr.coef_[0][0]
b = lr.intercept_[0]
print("w is: ", w)
print("b is: ", b)
cost = compute_cost(w, b, points)
print("cost is: ", cost)
w is: 1.3224310227553597
b is: 7.991020982270399
cost is: 110.25738346621318
plt.scatter(x, y)
# 针对每一个x，计算出预测的y值
pred_y = w * x + b
plt.plot(x, pred_y, c='r')
plt.show()
