# Switching regression

## In words...

Switching regression problems are particular in that the data is assumed to be generated by a collection of processes and a switching mechanism activating one and only one of these processes at a time. This occurs for instance when modeling a system with different operating modes.

In this case, the problem is twofod: we must classify the data points to different modes *and* estimate a model for each one of these modes. All the difficulty comes from the intrinsic inseparability of these two subproblems: the classification influences the model estimation (since the local data set assigned to a mode changes with the classification) while the classification itself also depends on the model.

A simple approach to this problem is taken by the $K$-LinReg algorithm.

## In pictures...

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## In maths...