Variables that are Both Predictors and Response Variables

I have been reading about variable/feature selection algorithms. All of the algorithms that I have seen presume that there is a clear distinction between predictive and response variables. However, I have some variables that could be either. I would like to analyze a large set of variables and determine whether there are some hidden correlations among them but it is not always clear which are predictive and which are response variables. Some are probably a mixture of both. Is there an algorithm for finding hidden associations among variables when the response/predictor classification is unclear?