
#1




Regression on hidden variables
I'm thinking about...
Imagine that I've got a set of variables I want to make regression on. But I can only observe other different set of variables . With not known and the being hidden variables. I guess that I can make assumptions (which can be tested using validation later with different sets of ) 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 and to transform them later to the ? Thanks a lot 
#2




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 statespace models or linear dynamical systems.

Tags 
hidden variables, nonlinear transformations, regression, unknown variables 
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