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What type of neural network should I be using for different sized inputs?

I am trying to build a neural network to help predict an NBA player's overall fantasy production score for a season. What I have done for every season of the player's career is use a certain set of stats to arrive at an overall production score for that season. I would like to build some type of regression model that can predict say, the next three years of the player's production score.

Example inputs, where each array is a player's career production numbers:

[22.3, 44, 33.1],

[10, 16.2, 42, 67, 54.3, 68.9, 62, 43, 12],

[45, 79, 58, 54, 42],

[12, 24],

[33, 67, 72, 80.3, 94.6, 74]

Most neural networks that I have seen expect the same amount of features for the inputs but in this case, every player will have a different number of inputs based on how many seasons they have played. I have seen people suggest to zero out the missing data values but I do not want to do that because the NN would start expecting a huge decline in production after just a couple seasons, and zero is a meaningful value in regards to the production score.

Is there a neural network that can handle the varying input lengths of each player? And will it use the career length of the player to help predict the player's future production score?

This is exactly the kind of issue that recurrent neural networks were built for! A recurrent neural network takes series inputs, and has only one node that is shared/repeated for each time-step in the series. It can handle variable sized inputs, but do note that if you are unwilling to zero-pad the inputs, you will inevitably have to run each input one at a time. There is no way to vectorize a jagged input matrix. If you don't have too much data, this won't be much of an issue though. Take a look here for some more information.

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