Conditional Linear Regression

Linear regression is the task of modeling the relationship between a result variable and some explanatory variables by a linear rule. Linear regression is a standard tool of statistical analysis, with widespread applications spanning essentially all of the sciences. While the standard linear regression task seeks to model the majority of the data, we consider problems where a regression fit could exist for some subset or portion of the data, that does not necessarily model the majority of the data. We will consider cases in which the subset with a linear model is described by some simple condition; in other words, we desire to perform linear regression on this conditional distribution. Note that neither the condition nor the model is known in advance.