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Lets say I have a limited amount of training data (1000 documents each having 10000 values) and after learning with those, the program is basically not allowed to fail.

From what I've read, even very easy tasks take a machine learning algorithm several thousand learning cycles until it is about 98% reliable.

Which parameters need to be tweaked so that even with many many values, the program can make reliable decisions?

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If your question is about supervised learning, than ten million training points are enough in most of the cases. Besides, I think your question is too broad. There are a lot of parameters which can influence the accuracy. Like which algorithm you want to use. Which approximator and its topology, the hyperparameters etc.

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