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I have a dataset containing 40 input columns and 12 output columns (float values).

I suppose it is a regression problem and I am wondering, how to choose the ideal architecture of the neural network? I didn't find examples of neural network regression with multiple outputs. What is the right way to do it?

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To perform regression of twelve variables, you want a neural network that has 12 linear units in its last layer. The number of hidden layers and number of units per hidden layer is totally dependent on your data and the task you are trying to solve. See this thread for more info about neural network architecture design.

Without providing more information about your dataset, we cannot advise you anything more specific. Also, make sure neural network is the right method for your task. There are simpler models that can work better for simpler tasks.

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