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Old 09-17-2012, 03:05 AM
mareram mareram is offline
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Join Date: Jul 2012
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Default Regression on hidden variables

I'm thinking about...

Imagine that I've got a set of variables x_i I want to make regression on. But I can only observe other different set of variables y_j = f_j(x_i). With f_j not known and the x_i being hidden variables.

I guess that I can make assumptions (which can be tested using validation later with different sets of f_j) about the form of the functions f and then derive certain nonlinear transformations that correspond to those f and which relate the x's and the y's.

Then I can make nonlinear regression to the x's. But it seems a bit twisted since I'm applying nonlinear transformations twice.

does anyone know about a particular theory on machine learning that copes with this kind of problems? Or simply what I should do is considering a set of nonlinear transformations big enough so that it contains the transformations needed for adjusting to x_i and to transform them later to the y_j?

Thanks a lot
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