I am interested in detecting changepoints in a signal using the fused lasso (as implemented here for example). I am in particular interested in getting estimates of changepoints which are close to the real changepoints (as opposed to being interested in prediction).
Is anything known about the optimal value of the fused lasso penalty? Any such result would of course be conditional on some model. But assuming some simple model, for example a signal with a single changepoint and i.i.d. Gaussian noise, you should be able to derive the optimal penalty, it seems to me.
Best would be a formula.
