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-   -   Regression on hidden variables (http://book.caltech.edu/bookforum/showthread.php?t=1573)

mareram 09-17-2012 04:05 AM

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

palmipede 01-21-2013 11:21 AM

Re: Regression on hidden variables
 
Life is much easier if the f's are known and linear. If they are not known but linear that is an estimation problem. I'd start looking for Gaussian state-space models or linear dynamical systems.


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