Re: Unexpected results while comparing CMI estimators

[Joseph Lizier]

Hi Valentin,

A few points here:

1. "which are normalised and therefore jointly Gaussian" - I assume you mean you've normalised them to have mean 0 and standard deviation 1? This does not make the individual time series Gaussian however, just their mean and standard deviation are now consistent with a normal Gaussian. It also does nothing to change the relationship between the variables to being only a linear relationship under a Gaussian model. Indeed, it's an established result that scaling or translation of either variable does not change their mutual information, so scaling them isn't going to change the nature of a non-linear relationship between them.

2. Anyway, in comparing the Gaussian and KSG estimators: in short, the KSG is capable of finding both linear and non-linear relationships, however because of its generality it requires more samples in order to be able to do so.

Where the underlying relationships (or a component of them) are a good fit for a linear-Gaussian model, the Gaussian estimator will reliably detect the relationship with substantially less data because it is tuned specifically for such relationships. (And so, given your statement that the series were jointly Gaussian, it's not clear why you expect better results from KSG given that you thought the time series were jointly Gaussian?)

Where KSG is detecting a significant relationship but the Gaussian estimator is not, this would usually indicate that the relationship is non linear.

I hope that addresses your queries?

--joe
+61 408 186 901 (Au mobile)

On Sat, 24 Apr 2021 at 03:24, Valentin RINEAU <valenti...@gmail.com> wrote:

Hi there,
I compared my results (paleontological time series which are normalised and therefore jointly Gaussian) using the Gaussian and the Kraskov estimator, expecting better results with the second one.

However, I am surprised to see that the Gaussian estimator finds many more significant links and with significantly higher TE values in general (with some exceptions of significant links in kraskov but not in Gaussian). Moreover, results are completely different between the estimators (the gaussian does not give the same results with higher TE).
Finally, as I expected, the longer my time series, the higher the TE values obtained. However, this effect of time series size is only seen in Gaussian, not in Kraskov.

Have you tested these two estimators on linear systems? Can these differences be interpreted as the result of the analysis of a system with linear behaviour? Are they any other possible explanations?

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