# Problem description

To predict a list of values associated with a set of variables.

## Trainset

Trainset has a set of variables X1, X2, X3, ... Xn. In the simplest form, each variable is of type numeric with different ranges. The largest range being 1-100000 and the smallest range being 1-10. Target is a list of numbers(Y) whose range is again 1-100000. The list is of variable length so each observation has varying number of targets. Could assume that the target list is a list of item IDs.

Example of the train subset (X1, X2, X3... Xn => {Y})

Observation1: 2345, 23, 8, ... 99399 => {2345, 98755}

Observation2: 45276, 3, 1, ... 80001 => {7865, 98675, 78954}

and so on...

Prediction

So, prediction is a list of numbers that can vary depending on the variable values.

My thoughts

1. Looks like a multi label classification problem with each label corresponding to a single value in the prediction list.
2. But because the range of the labels is large (i.e. 1-100000), cannot use a classification method.
3. Probably can use multi target regression method to predict a list of targets for an observation in the test set.
4. Assuming Ym is the maximum length of the prediction list in the training set. Could fill the prediction list in Observation1 of the training set as:

Observation1: 2345, 23, 8, ... 99399 => {2345, 98755, 0 , ... 0} (0 representing empty value which is repeated Ym-2 times)

5. Might be worth normalizing all the variables and values in the prediction list.

Questions

1. Am I missing something ? Is this method appropriate for this kind of problem ?
2. The values in the prediction list are identifiers so they do not have a direct correlation with other values & variables in the observation. And this is a concern that worries me. Will it be a major concern if I use a multi target regression ?
3. What kind of methods can I use ? neural network or linear regression ?
4. Because the complete set of targets is known during training, could a clustering method be used as I am trying to predict a cluster of items that correspond to an observation ?
• I am no expert in artificial neural networks (ANNs) but have a gut feeling that an ANN would be the way to go here (a regression 'mapping' from multiple input variables to multiple output variables). I think your points in 4 and 5 are quite sensible. Might be helpful to add the ANN tag to the question to draw the attention of the right audience. Commented Jun 17, 2015 at 9:42
• The variable dimension thing is... Messy. Are you absolutely sure you've formulated the problem correctly? Commented Jun 17, 2015 at 12:19
• @ssdecontrol: If you are referring to multiple targets for each observation when you say 'variable dimension' then I am pretty certain that I formulated the problem correctly. Commented Jun 17, 2015 at 13:55
• @iceBreak it's not just having multiple targets, it's also that the number of targets varies Commented Jun 17, 2015 at 14:52
• @ssdecontrol I formulated this problem from this scenario: The variables used in the problem are parameters defining a particular device used by a person and the targets I am trying to predict are all the cookies associated with it. So variables are things like what type of device it is, country the device belongs to, etc. and each target is an id representing a cookie on that device. So, number of cookies associated a device will vary and I need to predict more than one target for a device. Commented Jun 17, 2015 at 15:35