Re: [AMBER] [cpptraj] Kullback Leibler Divergence cutoff choice

From: Daniel Roe <>
Date: Wed, 5 Aug 2015 11:31:31 -0600


On Wed, Aug 5, 2015 at 10:01 AM, Eiros Zamora, Juan
<> wrote:
> I’ve replicated the KLD analysis of this paper on my system and I have a couple of questions.
> A cutoff of convergence of KLD < 0.02 is chosen because the slope of the KLD plot vs time no longer changes once its below this number. For my system, this appears to be happening as well, but for a KLD < 2.5.

Note that since KL divergence is a logarithmic, a value of 2.5
signifies that the overlap is orders of magnitude worse than 0.02.
From personal experience I consider any value over 1.0 extremely poor
overlap. You will really want to look at the distributions themselves
- it's pretty easy to see whether the overlap is "good" or not. If you
look at figure 3 of that publication showing the final distributions
of projections of PC1 and compare them to the final values of KLD
(figure 4), you can start to get an idea of how the value of KLD
relates to actual overlap. Also note that a low value does not always
mean "well converged". From the discussion of those figures:

"Note that, in the case of the DFC-HREMD runs, the initial KLD values
for PCs 1 and 2 drop rapidly to ∼0.021 at around 48 ns before rising
back up to ∼0.269. This illustrates a potential pitfall of using KLD
as a metric of convergence when sampling is limited, such as at the
beginning of an MD simulation: if two otherwise independent runs begin
in the same conformational space of a certain PC, they may both
initially explore the same limited subspace along that PC and the
overlap of their PC projection histograms may actually be quite good.
Once sampling increases and one or both of the runs can explore
outside of their initial regions, the KLD better reflects the
convergence between the two simulations. Therefore, the KLD of PC
projection histograms is a good measure of convergence between two
simulations only if at least one simulation has explored along most or
all of a given PC. In other words, there is a minimum sampling time
required before this metric can be considered viable."

In our case since we were using enhanced sampling (HREMD and MREMD) as
well as other measures of convergence (like combined clustering) we
were confident that we had enough sampling to start to claim the
distributions are well-converged. So KLD is a useful metric for
quantifying overlap, but by itself does not necessarily indicate

> 1) Are the KLD values expected to be higher the more complex a system is?

No - it's purely a measure of overlap between distributions and has
nothing to do with system size.

> 2) Is there a reason to not do all the pairwise KLD comparisons between the independent runs?

You certainly can. In our case we only wanted to look at overlap
between the 2 independent runs for each enhanced sampling method

Hope this helps answer some of your questions. Let me know if you have any more,


Daniel R. Roe, PhD
Department of Medicinal Chemistry
University of Utah
30 South 2000 East, Room 307
Salt Lake City, UT 84112-5820
(801) 587-9652
(801) 585-6208 (Fax)
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Received on Wed Aug 05 2015 - 11:00:03 PDT
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