The day in conversation for 2026-10-21

The discussion: Tom: I’m still thinking about how robust that recovery method for stochastic generators is when you move away from simple Euler-Maruyama coefficients; specifically, what are the practical implications of needing those strong ergodicity assumptions for real-world simulation? Jane: I see the point there. From a statistical perspective, if we can't guarantee ergodicity in complex systems, even a sparse symbolic recovery might only be providing an approximation whose error bounds become unbounded as the system state evolves. What about the stability selection work—does decorrelating variables truly solve the selection instability issue regardless of whether their correlation is positive or negative? Lu: That depends heavily on the underlying model structure. If we assume a specific dependency structure, like Gaussianity, then decorrelation might indeed stabilize Lasso performance by decoupling predictors from spurious correlations. But if the true relationship is non-linear, just changing the correlation sign doesn't change the fundamental bias introduced by multicollinearity. Meng: Speaking of bias in selection, I wonder if those weighting schemes in A Stable Lasso address the dependency on the regularization parameter lambda differently than a pure penalty approach does when dealing with highly heterogeneous predictor scales? Are we improving stability