我打算在 Spark 中使用线性回归。首先，我查看了官方文档 ( which you can find here ) 中的示例
我还发现了 this question on stackoverflow ，这和我的问题本质上是一样的。答案建议调整步长，我也尝试这样做，但是结果仍然像不调整步长一样随机。我使用的代码如下所示:
from pyspark.mllib.regression import LabeledPoint, LinearRegressionWithSGD, LinearRegressionModel
# Load and parse the data
def parsePoint(line):
values = [float(x) for x in line.replace(',', ' ').split(' ')]
return LabeledPoint(values[0], values[1:])
data = sc.textFile("data/mllib/ridge-data/lpsa.data")
parsedData = data.map(parsePoint)
# Build the model
model = LinearRegressionWithSGD.train(parsedData,100000,0.01)
# Evaluate the model on training data
valuesAndPreds = parsedData.map(lambda p: (p.label, model.predict(p.features)))
MSE = valuesAndPreds.map(lambda (v, p): (v - p)**2).reduce(lambda x, y: x + y) / valuesAndPreds.count()
print("Mean Squared Error = " + str(MSE))
结果如下:
(Expected Label, Predicted Label)
(-0.4307829, -0.7824231588143065)
(-0.1625189, -0.6234287565006766)
(-0.1625189, -0.41979307020176226)
(-0.1625189, -0.6517649080382241)
(0.3715636, -0.38543073492870156)
(0.7654678, -0.7329426818746223)
(0.8544153, -0.33273378445315)
(1.2669476, -0.36663240056848917)
(1.2669476, -0.47541427992967517)
(1.2669476, -0.1887811811672498)
(1.3480731, -0.28646712964591936)
(1.446919, -0.3425075015127807)
(1.4701758, -0.14055275401870437)
(1.4929041, -0.06819303631450688)
(1.5581446, -0.772558163357755)
(1.5993876, -0.19251656391040356)
(1.6389967, -0.38105697301968594)
(1.6956156, -0.5409707504639943)
(1.7137979, 0.14914490255841997)
(1.8000583, -0.0008818203337740971)
(1.8484548, 0.06478505759587616)
(1.8946169, -0.0685096804502884)
(1.9242487, -0.14607596025743624)
(2.008214, -0.24904211817187422)
(2.0476928, -0.4686214015035236)
(2.1575593, 0.14845590638215034)
(2.1916535, -0.5140996125798528)
(2.2137539, 0.6278134417345228)
(2.2772673, -0.35049969044209983)
(2.2975726, -0.06036824276546304)
(2.3272777, -0.18585219083806218)
(2.5217206, -0.03167349168036536)
(2.5533438, -0.1611040092884861)
(2.5687881, 1.1032200139582564)
(2.6567569, 0.04975777739217784)
(2.677591, -0.01426285133724671)
(2.7180005, 0.07853368755223371)
(2.7942279, -0.4071930969456503)
(2.8063861, 0.000492545291049501)
(2.8124102, -0.019947344959659177)
(2.8419982, 0.03023139779978133)
(2.8535925, 0.5421291261646886)
(2.9204698, 0.3923068894170366)
(2.9626924, 0.21639267973240908)
(2.9626924, -0.22540434628281075)
(2.9729753, 0.2363938458250126)
(3.0130809, 0.35136961387278565)
(3.0373539, 0.013876918415846595)
(3.2752562, 0.49970959078043126)
(3.3375474, 0.5436323480304672)
(3.3928291, 0.48746004196839055)
(3.4355988, 0.3350764608584778)
(3.4578927, 0.6127634045652381)
(3.5160131, -0.03781697409079157)
(3.5307626, 0.2129806543371961)
(3.5652984, 0.5528805608876549)
(3.5876769, 0.06299042506665305)
(3.6309855, 0.5648082098866389)
(3.6800909, -0.1588172848952902)
(3.7123518, 0.1635062564072022)
(3.9843437, 0.7827244309795267)
(3.993603, 0.6049246406551748)
(4.029806, 0.06372113813964088)
(4.1295508, 0.24281029469705093)
(4.3851468, 0.5906868686740623)
(4.6844434, 0.4055055537895428)
(5.477509, 0.7335244827296759)
Mean Squared Error = 6.83550847274
那么，我错过了什么？由于数据来自官方 spark 文档，我猜它应该适合对其应用线性回归(并至少获得相当好的预测)？
请您参考如下方法:
对于初学者来说，您错过了拦截。而自变量的平均值接近于零:
parsedData.map(lambda lp: lp.features).mean()
## DenseVector([-0.031, -0.0066, 0.1182, -0.0199, 0.0178, -0.0249,
## -0.0294, 0.0669]
因变量的平均值与它相去甚远:
parsedData.map(lambda lp: lp.label).mean()
## 2.452345085074627
在这种情况下强制回归线通过原点是没有意义的。那么让我们看看 LinearRegressionWithSGD 如何使用默认参数和添加的截距执行:
model = LinearRegressionWithSGD.train(parsedData, intercept=True)
valuesAndPreds = (parsedData.map(lambda p: (p.label, model.predict(p.features))))
valuesAndPreds.map(lambda vp: (vp[0] - vp[1]) ** 2).mean()
## 0.44005904185432504
让我们将其与解析解进行比较
import numpy as np
from sklearn import linear_model
features = np.array(parsedData.map(lambda lp: lp.features.toArray()).collect())
labels = np.array(parsedData.map(lambda lp: lp.label).collect())
lm = linear_model.LinearRegression()
lm.fit(features, labels)
np.mean((lm.predict(features) - labels) ** 2)
## 0.43919976805833411
如您所见，使用 LinearRegressionWithSGD 获得的结果几乎是最优的。
您可以添加网格搜索，但在这种特殊情况下可能没有任何收获。
