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Suppose I have many vectors which can take on any of three values, 0, 1, 2. These vectors affect an outcome being predicted, Y. Vectors add together: a vector "A" of the value 2 has twice the affect on Y as vector "A" of the value 1, and also vector "A" and other vector "B" add together (that is, there are never interactions between vectors). Some vectors are very correlated with a small number of related vectors, and the degree to which they are correlated is known precisely.

Here is a difficulty: there is a very large number of vectors (features), about 1 million. However, there are only about 100,000 or so feature set --> outcome observations available for training, and there are 10,000 "true" (non-zero) features. Different features have different effect sizes.

What is the optimal machine learning technique to predict Y? I've been told LASSO would be a good choice but I want to hear other methods.

This question is crossposted here, as I'm not sure where this goes. I will update threads will be updated as soon as one gets a result. Feel free to ask me to delete one or the other if you know where this question should go.

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