MSM lag time cannot be used for variational model selection

TL;DR

This paper explains why the lag time parameter must remain fixed when using the variational principle to construct Markov state models for conformational dynamics, highlighting a key methodological constraint.

Contribution

It clarifies a fundamental limitation in variational model selection, emphasizing the importance of constant lag time during optimization.

Findings

Lag time must be held constant in variational approaches

Variational principle relies on fixed lag time for accurate operator approximation

Changing lag time invalidates the variational optimization process

Abstract

The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note we discuss why lag time of the operator being approximated must be held constant in the variational approach.