Sugihara ea’s Detecting Causality …
George Sugihara, Robert May, Hao Ye, Chih-hao Hsieh, Ethan Deyle, Michael Fogarty, Stephan Munch Detecting Causality in Complex Ecosystems Science 2012.
Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. Here we introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation.
[S]tate-dependent behavior is a defining hallmark of complex nonlinear systems.
Theoretically, the systems considered are assumed to be stable, but with complex ‘strange attractors’, like Lorenz’s. The approach develops the insights of Takens’ Theorem, that if one plots a time-series against delayed versions of itself one maps out something that topologically resembles the attractor.
Our alternative approach [to Granger causality], convergent cross mapping (CCM), tests for causation by measuring the extent to which the historical record of Y-values can reliably estimate the state of X. This can only happen if X is causally influencing Y. In more detail, CCM looks for the signature of X in Y’s time series by seeing if there is a correspondence between the “library” of points in the attractor manifold built from Y, MY, and points in the X manifold, MX; these two manifolds are constructed from lagged-coordinates of the time series variables Y and X respectively.
Some good brief videos are provided.
[A]ccurate knowledge of the causal network can be essential for avoiding unforeseen consequences of regulatory.
This develops the notion of causality beyond simple ‘linear’ systems, but the appropriate context is still of a fixed system, with fixed attractors. To me the interesting thing is that many ecologies and even human-influenced or driven systems appear, over reasonable time periods, to be fixed in this sense. In otherwords their evolution is simply that of a (fixed) dynamical system. Thus this new type of causality might seem to explain emergence in ‘climate, epidemiology, financial regulation, and much else’.
It does seem to me that the previous notions of causality are much too narrow to support policy-making in such areas, and that CCM could offer a promising insight that could usefully be applied to policy-making, but I am unconvinced that the systems of interest are all – or even typically – stable over periods that one might wish policy-making to be effective for. Even in ecologies, what is the point of the theory unless it is to intervene to change the system?
The work is also of interest from an uncertainty perspective. Attempts to model systems are typically confounded by noise. In systems with simple attractors one can develop representative (Markov) probabilistic models. Takens showed that, in a sense, one can even do this even when their are strange attractors. But the resultant models are atypical, and violate the usual justifications for statistical methods. In evolutionary or man-driven systems it is easy to see why: if the usual control techniques worked, they would be used. Hence systems tend to end up as being ‘unmanageable’. If this is so, then by introducing a way of managing some complexity, we might simply end up with more. In fact, we might even be there.
Clearly, “accurate knowledge of the causal network can be essential for avoiding unforeseen consequences of regulatory actions.” But is the network static? Can emerging elements of the network be determined from the data? It seems to me that faced with a potential crisis the one needs to consider potential causal networks, and that often one needs to significantly modify that network, so that situations don’t continually recur. Is this simply a case of biasing the network, or more substantial?
In terms of finance, for example, the downside of using sophisticated mathematical techniques such as CCM is that their outputs tend to be so very useful in the short run, and so policy makers – foolishly – come to rely on them. But – used with full regard to their strengths and weaknesses, there might be an upside.
I have taken a quick look at KEDS data (about news reports of regional relations), plotting data against delayed versions. This has the following features that are unlike the paper’s ecologies:
- There are a few sudden large-impact events that appear to ‘change the system’.
- Even when the behaviour is relatively stable, the behaviour fails to show clear cycles of behaviour, but rather seems to display continual novelty.
- Periods of apparent stability seem too short compared with the ‘noise’ to be able to conduct useful CCM-type analysis.
- Often, forewarning of the sudden exceptions (‘transformations’) would be much more of use to policy makers than more detailed characterisation of the status quo.
- If there is one system, history has not been long enough to build up an adequate library of its transformations.
- If there are fixed attractors, they seem to exist on multiple time-scales. (As in a fractal system, except that each ‘level’ may have its own character.)
In ecology it may be that the aim is not to change the system, but simply to protect or distort it to avoid, for example, lows in fish-stocks. But in regions like the middle-east the aim, presumably, is to change the system away from its current pathological state. One might argue that finance is more like ecology, in that one wants to avoid excessive lows. But finance is clearly affected by international relations, and often entangled with it. And it is not clear that large crashes and recessions can be avoided without changing the causal nature of the system. So there is a real question as to whether we simply want to tilt the financial table in our favour, or to change the system more radically. Applying CCM to finance would seem to assume the former. It is not clear that this is a good – or even viable – policy stance.
- Noting where the assumptions of the paper fail is in itself providing useful insights for policy-makers.
- One might be able to analyse different challenge domains, such as ecologies and finance, to see which assumptions hold or fail, and perhaps draw lessons on policy-making from different domains.
(None of these domains are simple classical systems, and maybe we can draw some finer distinctions.)
- Even though the assumptions of CCM seem to be false, one can still legitimately use analyses based on it to form hypotheses that could then inform policy-making.
An interesting feature of the CCM analysis is that it is topologically sound. KEDS data is based on news reports, so one has concerns that it may be a poor proxy for whatever is ‘really’ going on. It may be possible to adopt the topological argument to KEDS and finance.
Finally, in my own analysis of the KEDS data I suppose that, for example, changes in the concentrations of interactions between nations (as when one group ‘gangs up’ on another) seem to me to indicate a change of the effective ‘system’ and hence changes in the ‘attractors’. One could thus consider deploying CCM on epochs of the problem, but not more broadly. Something similar seems to be true for finance (at least, according to Keynes and Smuts). But if so, then within-epoch tools, such as CCM, are more appropriate to those concerned with managing the current system to extract value (e.g. fund managers) than to regulators and policy makers, who are concerned with a different type of causality. But the paper does draw our attention to a useful distinction, between policy and regulation that seeks to adjust the working of a system (e.g., by altering transaction costs) and one which seeks to alter the ‘causal network’ (e.g., by splitting retail and ‘casino’ banking). The two require very different intellectual tools.