如何在 Keras Regressor 中解释 MSE [英] How to interpret MSE in Keras Regressor

问题描述

我正在尝试建立一个模型来预测房价.

I am trying to build a model to predict house prices.

我有一些功能 X(浴室数量等)和目标 Y(范围在 300,000 美元到 800,000 美元之间)

I have some features X (no. of bathrooms , etc.) and target Y (ranging around $300,000 to $800,000)

在将 Y 拟合到模型之前，我使用了 sklearn 的 Standard Scaler 对其进行了标准化.

I have used sklearn's Standard Scaler to standardize Y before fitting it to the model.

这是我的 Keras 模型:

Here is my Keras model:

def build_model():
    model = Sequential()
    model.add(Dense(36, input_dim=36, activation='relu'))
    model.add(Dense(18, input_dim=36, activation='relu'))
    model.add(Dense(1, activation='sigmoid'))
    model.compile(loss='mse', optimizer='sgd', metrics=['mae','mse'])
    return model

我在尝试解释结果时遇到问题——0.617454319755 的 MSE 是什么意思?

I am having trouble trying to interpret the results -- what does a MSE of 0.617454319755 mean?

我是否必须对这个数字进行逆变换，然后对结果求平方，得到 741.55 美元的错误率?

Do I have to inverse transform this number, and square root the results, getting an error rate of 741.55 in dollars?

math.sqrt(sc.inverse_transform([mse]))

对于刚开始时听起来很愚蠢，我深表歉意！

I apologise for sounding silly as I am starting out!

推荐答案

对于刚开始时听起来很愚蠢，我深表歉意！

I apologise for sounding silly as I am starting out!

不要；这是一个非常重要的微妙问题，通常(并且令人遗憾地)在教程和介绍性说明中被省略.

Do not; this is a subtle issue of great importance, which is usually (and regrettably) omitted in tutorials and introductory expositions.

不幸的是，它不像取逆变换 MSE 的平方根那么简单，但也没有那么复杂；基本上你要做的是:

Unfortunately, it is not as simple as taking the square root of the inverse-transformed MSE, but it is not that complicated either; essentially what you have to do is:

1. 将您的预测转换回原始数据的初始规模
2. 获取这些逆变换预测与原始数据之间的 MSE
3. 求结果的平方根

为了获得在您的问题的业务环境中有意义的模型性能指标(例如此处的美元).

in order to get a performance indicator of your model that will be meaningful in the business context of your problem (e.g. US dollars here).

让我们看一个简单的玩具数据示例，省略模型本身(这里无关紧要，实际上可以是任何回归模型 - 不仅仅是 Keras 模型):

Let's see a quick example with toy data, omitting the model itself (which is irrelevant here, and in fact can be any regression model - not only a Keras one):

from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error
import numpy as np

# toy data
X = np.array([[1,2], [3,4], [5,6], [7,8], [9,10]])
Y = np.array([3, 4, 5, 6, 7])

# feature scaling
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X)

# outcome scaling:
sc_Y = StandardScaler()
Y_train = sc_Y.fit_transform(Y.reshape(-1, 1))
Y_train
# array([[-1.41421356],
#        [-0.70710678],
#        [ 0.        ],
#        [ 0.70710678],
#        [ 1.41421356]])

现在，假设我们使用缩放集 X_train 和 Y_train 拟合我们的 Keras 模型(此处未显示)，并获得对训练集的预测:

Now, let's say that we fit our Keras model (not shown here) using the scaled sets X_train and Y_train, and get predictions on the training set:

prediction = model.predict(X_train) # scaled inputs here
print(prediction)
# [-1.4687586  -0.6596055   0.14954728  0.95870024  1.001172  ]

Keras 报告的 MSE 实际上是缩放后的 MSE，即:

The MSE reported by Keras is actually the scaled MSE, i.e.:

MSE_scaled = mean_squared_error(Y_train, prediction)
MSE_scaled
# 0.052299712818541934

虽然我上面描述的 3 个步骤很简单:

while the 3 steps I have described above are simply:

MSE = mean_squared_error(Y, sc_Y.inverse_transform(prediction))  # first 2 steps, combined
MSE
# 0.10459946572909758
np.sqrt(MSE)  # 3rd step
# 0.323418406602187

因此，在我们的例子中，如果我们最初的 Y 是美元，那么相同单位(美元)的实际误差将是 0.32(美元).

So, in our case, if our initial Y were US dollars, the actual error in the same units (dollars) would be 0.32 (dollars).

请注意对缩放 MSE 进行逆变换的幼稚方法会产生非常不同(且不正确)的结果:

Notice how the naive approach of inverse-transforming the scaled MSE would give a very different (and incorrect) result:

np.sqrt(sc_Y.inverse_transform([MSE_scaled]))
# array([2.25254588])

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