今天做了一个山景智能公司的线性回归的题目，做了老半天没做出来，心里非常的着急，最后几分钟做出来了，我都没有预料到。真是惊险又刺激的挑战

加载库和导入数据

import numpy
import sklearn.metrics
x_train = numpy.array([[-0.8 , -0.8 ],
       [-0.8 , -0.48],
       [-0.8 , -0.16],
       [-0.8 ,  0.16],
       [-0.8 ,  0.48],
       [-0.8 ,  0.8 ],
       [-0.48, -0.8 ],
       [-0.48, -0.48],
       [-0.48, -0.16],
       [-0.48,  0.16],
       [-0.48,  0.48],
       [-0.48,  0.8 ],
       [-0.16, -0.8 ],
       [-0.16, -0.48],
       [-0.16, -0.16],
       [-0.16,  0.16],
       [-0.16,  0.48],
       [-0.16,  0.8 ],
       [ 0.16, -0.8 ],
       [ 0.16, -0.48],
       [ 0.16, -0.16],
       [ 0.16,  0.16],
       [ 0.16,  0.48],
       [ 0.16,  0.8 ],
       [ 0.48, -0.8 ],
       [ 0.48, -0.48],
       [ 0.48, -0.16],
       [ 0.48,  0.16],
       [ 0.48,  0.48],
       [ 0.48,  0.8 ],
       [ 0.8 , -0.8 ],
       [ 0.8 , -0.48],
       [ 0.8 , -0.16],
       [ 0.8 ,  0.16],
       [ 0.8 ,  0.48],
       [ 0.8 ,  0.8 ]])
y_train = numpy.array([19.16695052, 13.22042364, 10.06006317, 10.07024508, 13.09231182, 19.28932958, 13.09699286,  7.02510918,  3.77707591,  3.75280753, 6.98970389, 12.95676487, 10.01139805,  3.83283814,  0.75967419, 0.66507218,  4.08057273,  9.83142631, 10.14434347,  3.87253675, 0.48726579,  0.85708327,  3.62700781,  9.98383945, 13.03754723, 6.91194217,  3.80872056,  3.75064037,  6.96504836, 13.03395797, 19.18596309, 13.22441868,  9.97017209,  9.9608034 , 13.03983236, 19.25797367])
x_test = numpy.array([[ 0.60066134,  0.75514525],
       [ 0.62493958,  0.74354012],
       [ 0.68757087,  0.68514481],
       [ 0.70646998,  0.74249948],
       [-0.86394857,  0.22874845],
       [ 0.2215083 ,  0.49629939],
       [ 0.44835169,  0.98975117],
       [-0.76399039, -0.94554732],
       [ 0.39836963, -0.10177351],
       [ 0.91524278,  0.53612187],
       [-0.41065771,  0.56951352],
       [ 0.16812817,  0.7284085 ],
       [ 0.8898741 ,  0.73323525],
       [-0.86431684,  0.12372524],
       [-0.2547392 ,  0.56557855],
       [ 0.45626855, -0.98097258],
       [ 0.01415029,  0.26820149],
       [-0.97811162, -0.2954746 ],
       [ 0.78104109, -0.22334335],
       [-0.60341742,  0.60002444],
       [-0.79763483,  0.29683079],
       [-0.64229142,  0.66181316],
       [ 0.84009633, -0.1485917 ],
       [ 0.46944093,  0.27329434],
       [ 0.41647943, -0.22300934]])
y_test = numpy.array([14.0648327 , 14.1768829 , 14.2222626 , 15.71538637, 11.79833645, 4.46068088, 17.72559463, 21.99815467,  2.53139972, 16.72969738, 7.42901727,  8.35165552, 20.00799747, 11.42873041,  5.70221722, 17.6655741 ,  0.91620557, 15.67473377,  9.98291571, 10.84098305, 10.81040218, 12.7695035 , 10.84929453,  4.34147587,  3.45347178])

评估

def eval_model(true_label, prediction):
  metric = numpy.sqrt(sklearn.metrics.mean_squared_error(true_label, prediction))
  check = lambda x: "达到目标精度" if x < 0.15 else "未达到目标精度"
  print(f"效果：{metric:.2f} {check(metric)}")

要求达到的精度小于0.15

线性回归

import sklearn.linear_model
# model = sklearn.linear_model.LinearRegression()
from sklearn.linear_model import Lasso
from sklearn.preprocessing import PolynomialFeatures
quadratic_featurizer = PolynomialFeatures(degree=2)
X_train_quadratic = quadratic_featurizer.fit_transform(x_train)
X_test_quadratic = quadratic_featurizer.fit_transform(x_test)
model = sklearn.linear_model.LinearRegression()
model.fit(X_train_quadratic, y_train)
pred = model.predict(X_test_quadratic)
eval_model(y_test, pred)

主要用了PolynomialFeatures，
sklearn.preprocessing.PolynomialFeatures 这个类可以进行特征的构造，构造的方式就是特征与特征相乘（自己与自己，自己与其他人），这种方式叫做使用多项式的方式。
例如：有 𝑎、𝑏 两个特征，那么它的 2 次多项式的次数为 [1,𝑎,𝑏,𝑎2,𝑎𝑏,𝑏2]

结果：

效果：0.11 达到目标精度

参考文献

sklearn 的 PolynomialFeatures 的用法