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I'm trying to figure out the following situation which is almost the same as in this post here

Time series with multiple subjects and multiple variables

Subject  Week   x1  x2  x3  x4  x5  y1
A        1      .5  .6  .7  .8  .7  10
B        1      .3  .6  .2  .1  .3  8
C        1      .3  .1  .2  .3  .2  6  
A        2      .1  .9  1.5 .8  .7  5
B        2      .3  .6  .3  .1  .3  2
D        2      .3  .1  .4  .3  .5  10  

I have a time-series matrix with different output variables (~ 12000) which (often but not always) change every day due to an algorithm I'm not aware of.

Each of them has multiple input values I'm trying to regress their values from.

Now here is the reason why I'm posting this again: I know that there is an underlying pattern since this data was generated by an algorithm. So there must be an exact pattern in order to predict the output variables with the data I have. Which is why i'd like to avoid estimating too much with dlm but rather reverse-engineer it with a machine-learning algorithm if that is possible.

But my question becomes: How do I tell a model, that certain rows are related?

I believe this information is critical and the model should know that the columns are not thought of as A,B,C,D,A,B,C,D but AA,BB,CC,DD when trying to figure out how to predict the output variable.

How can I tell an algorithm about it and what kind of algorithm should I try? - Optimally I want to extract the underlying rules from the model in order to completely understand it.

Would be happy about any kind of help or hint!

Best,

Heinrich

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    $\begingroup$ My random number generator uses a (deterministic) algorithm, too--but it is constructed specifically not to have any "underlying pattern"! That is why, if you want the success of your effort to be the result of anything but luck, you should begin by considering what kinds of operations this "algorithm" might be performing and what its objective is. $\endgroup$ – whuber Jun 14 '16 at 19:08

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