Issue
I am trying to build a model to predict house prices.
I have some features X (no. of bathrooms , etc.) and target Y (ranging around $300,000 to $800,000)
I have used sklearn's Standard Scaler to standardize Y before fitting it to the model.
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
I am having trouble trying to interpret the results -- what does a MSE of 0.617454319755 mean?
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]))
I apologise for sounding silly as I am starting out!
Solution
I apologise for sounding silly as I am starting out!
Do not; this is a subtle issue of great importance, which is usually (and regrettably) omitted in tutorials and introductory expositions.
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:
- Transform back your predictions to the initial scale of the original data
- Get the MSE between these invert-transformed predictions and the original data
- Take the square root of the result
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).
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]])
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 ]
The MSE reported by Keras is actually the scaled MSE, i.e.:
MSE_scaled = mean_squared_error(Y_train, prediction)
MSE_scaled
# 0.052299712818541934
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
So, in our case, if our initial Y were US dollars, the actual error in the same units (dollars) would be 0.32 (dollars).
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])
Answered By - desertnaut
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