Open mjhajharia opened 2 years ago
Yes, I was suggesting we report fraction of negative-definite Hessians (sorry---I can never keep signs straight---it's the negative inverse Hessian that looks like covariance). But then I also suggested reporting condition number. So that could be a histogram. So maybe histogram plus fraction negative definite?
Also, RMSE is computed w.r.t. known true answers gathered heavily thinned HMC runs yielding 10K draws.
Yes, I was suggesting we report fraction of negative-definite Hessians (sorry---I can never keep signs straight---it's the negative inverse Hessian that looks like covariance). But then I also suggested reporting condition number. So that could be a histogram. So maybe histogram plus fraction negative definite?
sounds good i'll make a PR
- I think it makes sense to compute ESS for both bulk and tail. If the tail reveals nothing useful it can go in the appendix.
- I commented this on the paper, but by CDF, do you mean empirical CDF (ECDF) or CDF of the KDE?
- How is RMSE computed?
- @bob-carpenter suggested in Geometry of transforms #9 computing the fraction of transitions where the Hessian is negative (I think) definite. This could be computed on a per-chain basis or for the combination of all draws across all chains. Is that something we still would like to do? Not sure if this should be a plot or just a table. I wonder if there are other properties of the Hessian that would be worth looking at and might inform whether the transform would make it hard for HMC to adapt a metric, like the condition number mentioned after Eq 9 of https://arxiv.org/pdf/1905.11916.pdf. (try as I might, I haven't been able to grok that paper)
cdf of kde
but i can get ecdf too (statsmodels.api.ecdf) if that's preferred i guess
- @bob-carpenter suggested in Geometry of transforms #9 computing the fraction of transitions where the Hessian is negative (I think) definite. This could be computed on a per-chain basis or for the combination of all draws across all chains. Is that something we still would like to do? Not sure if this should be a plot or just a table. I wonder if there are other properties of the Hessian that would be worth looking at and might inform whether the transform would make it hard for HMC to adapt a metric, like the condition number mentioned after Eq 9 of https://arxiv.org/pdf/1905.11916.pdf. (try as I might, I haven't been able to grok that paper)
alright i'll check that out, and yes actually had a conversation with yuling about this - he also suggested using sampler divergences like wasserstein distance. which has quite some connections to convexity as well, trying to write it all down in a coherent way, will get back about this soon
cdf of kde
but i can get ecdf too (statsmodels.api.ecdf) if that's preferred i guess
I think that makes sense. Unlike KDE or a histogram, the ECDF (at sufficiently high resolution) contains all of the information of the original sample. There's no benefit to passing through a KDE first.
list of transforms to sample:
plots currently:
any other transforms or plots we want to add? do we want something with ess bulk/tail separately or anything
cc: @sethaxen @spinkney