Tag: Emergence

(Note: Another publication out of my Zettelblogging Tinderbox File. This comes from notes on reading a paper in the scientific literature. I’m seeing that my notes need to be cleaned up a bit for publication even when they are written to be understood by future me, since current you may need a bit more help understanding terms and logic. Plus I have links in Tinderbox to  files like PDFs in other apps. Those links need to be taken out or redirected to web sources. Publishing notes takes a few extra steps)

See: Granger Causality

This is a summary of a nice review of Granger Causality: “Wiener-Granger causality: a well established methodology by Bressler and Seth, 2011

Even though Granger Causality is quite limited in its utility, it’s a good starting point for understanding how to view cause and effect in complex systems. As a method, it only works with linear models- where any input causes a proportional effect. We’ve know that most of the world isn’t linear and exponential, non-linear effects are the rule in the real world rather than the exception.

Granger Causality also requires the time series to be stationary, that is not changing over time. Now over shorter intervals, some complex systems may be stable, but again, the nature of complex systems is to change and be unpredictable over time. It’s what makes prediction hard, so it’s not surprising that assigning causal effect would also be hard.

And finally, this kind of analysis can’t account for hidden variables. We might measure Y and see whether it predicts future states of X, but it’s entirely possible that Z is the real driving factor, loosely connected to X, so we mistakenly say the Y causes X because we were entirely ignorant of the real significance of Z.

The more general approach is called “Transfer Entropy” based on time-asymmetric information flow. This is nonparametric and based on Shannon entropy based on the amount of information measured between two processes. Can be used when the Granger assumptions (linearity, stability) don’t hold as it is a generalization of the Granger autocorrelation method.

But if you have time series and want a description of effective connectivity, then Granger Causality may be a good method.

There are lots of time series in neuroscience like EEG, neural spike trains, and fMRI.
We can look at causal interaction between brain areas or between different types of data. For example, we might want to predict behavior from spike train recordings of individual neurons. If the data contains predictive information in addition to past events plus everything else, then is causal in this G-causality sense.

If a neural activity precedes and predicts an event, like reporting of conscious perception, it shows “Granger Causality”. This is a bottom up, weak emergence where we can say that the neural activity caused the behavior even though we know that the pure physical causal change was at a lower level, but with a courser grained analysis brain activity causes behavior, subjective experience.

This is a first step in linking causality to emergence.

(Note: What follows is an example of a topic note in my Zettelblogging Tinderbox file). I was able to drop it into the revision of the ODB manuscript pretty much as is. I’m posting it here as an example, pending building out a way to more directly publish these notes on a dedicated Zettelblogging site).

Clive Granger won 2003 Nobel prize in Economics for the idea we know as Granger Causality. Causality seems intuitively obvious when a system can be explicitly understood. But in complex systems or systems that appear to us as a black box (like the brain) how do you define cause and effect?

In the early 1960’s, Granger was looking at how two time de processes could seem to be related over time. Did one cause the other? Norbert Wiener had suggested had suggested that a causal relationship could be defined simply by seeing whether series Y together with series X predicts the future series X’ better than X alone, then Y causes X.

This is causality defined purely on the basis of predictive information, with the predictor a possible explanatory variable coming before it in time. Granger expanded it to say that:

If you have Xt, Yt and Wt and try to forecast Xt+1 from Xt and Wt, if Xt, Wt and Yt proves a better prediction than Xt and Wt alone, then we can say that Yt provides some predictive information. Think of W as what you know about the world in general, (which should be really large to reflect everything you know) then if you add Yt to be really specific and it is better that X plus W alone, then Yt is passing a stringent test of containing information that we can call “causal”

Granger had created analysis methods for time series analysis using earlier events to predict later events. He had created a systems definition of causality based on information. It’s a weak causality, as it is not understood mechanistically, so we like to refer to it specifically as Granger Causality, sometimes G-Causality.