train/valid loss = NAN when loss = "mean_squared_error" due to exploding values

[OmaymaS]

This issue is based on a question raised during the workshop.

Problem

loss values appear to be nan when the loss parameter is set to "mean_squared_error" as shown below.

dl-keras-tf/materials/03-recipe/02-mini-project-ames.Rmd

Line 224 in 3dca65d

model %>% compile(

model %>% compile(
    optimizer_sgd(lr = 0.1),
    loss = "mean_squared_error",
    metrics = "mae"
  )

history <- model %>% fit(
  x_train,
  y_train
  batch_size = 16,
  validation_split = 0.2)

Train on 1640 samples, validate on 411 samples
Epoch 1/10
1640/1640 [==============================] - 1s 397us/sample - loss: nan - mae: nan - val_loss: nan - val_mae: nan
Epoch 2/10
1640/1640 [==============================] - 1s 447us/sample - loss: nan - mae: nan - val_loss: nan - val_mae: nan
Epoch 3/10
1640/1640 [==============================] - 0s 268us/sample - loss: nan - mae: nan - val_loss: nan - val_mae: nan
Epoch 4/10
1640/1640 [==============================] - 1s 382us/sample - loss: nan - mae: nan - val_loss: nan - val_mae: nan

Reason

This is probably related to the range of the predicted value (sales price) which reaches ~ 755000. When the error gets squared, the sum explodes! That's why msle was recommended in the instructions and not mean_squared_error.

[bradleyboehmke]

Yeah, this seems to be an issue with regression models. See this Stackoverflow discussion: https://stackoverflow.com/questions/37232782/nan-loss-when-training-regression-network.

I think there are a few things to consider here:

1. Since you used MSE instead of MSLE, the target values have a large, unbounded range. Using neural nets on large unbounded regression problems can be prone to exploding gradients. Consequently, when we use MSLE we somewhat bound our target values since we log transform prior to computing the loss (which gets used for computing the gradient). This would be a good reason to scale the response if you preferred to use MSE.

2. The optimizer can help control this. For example, using RMSProp and Adam with MSE actually works fine so they seem to help control the gradient descent process. SGD on the other hand, has a harder time. However, when I could control the exploding gradients by using an extremely small learning rate (0.000001).

[dougmet]

One group changed the units to millions $ (/1e6) which kept the context but had the benefit of scaling.