Cause and Effect: How a Revolutionary New Statistical Test Can Tease Them Apart

KentuckyFC writes Statisticians have long thought it impossible to tell cause and effect apart using observational data. The problem is to take two sets of measurements that are correlated, say X and Y, and to find out if X caused Y or Y caused X. That's straightforward with a controlled experiment in which one variable can be held constant to see how this influences the other. Take for example, a correlation between wind speed and the rotation speed of a wind turbine. Observational data gives no clue about cause and effect but an experiment that holds the wind speed constant while measuring the speed of the turbine, and vice versa, would soon give an answer. But in the last couple of years, statisticians have developed a technique that can tease apart cause and effect from the observational data alone. It is based on the idea that any set of measurements always contain noise. However, the noise in the cause variable can influence the effect but not the other way round. So the noise in the effect dataset is always more complex than the noise in the cause dataset. The new statistical test, known as the additive noise model, is designed to find this asymmetry. Now statisticians have tested the model on 88 sets of cause-and-effect data, ranging from altitude and temperature measurements at German weather stations to the correlation between rent and apartment size in student accommodation.The results suggest that the additive noise model can tease apart cause and effect correctly in up to 80 per cent of the cases (provided there are no confounding factors or selection effects). That's a useful new trick in a statistician's armoury, particularly in areas of science where controlled experiments are expensive, unethical or practically impossible.

Comments

Other causality tests exist

[Anonymous Coward]

Many other attempts at detecting causality exist. There's one based on dynamical systems theory (Takens' theorem): in a multidimensional, causally linked dynamical system, all the information in the high-dimensional system can be recovered from a multiple values of a single dimension over time.

The method works by reconstructing values of X from lagged vectors of Y(t) nearest-neighbor lagged vectors of Y in a training set. As the training set gets larger, the predictions get better. If they keep getting better, X probably causes Y. The idea that the noise in X(t) shows up in Y(t) but not the other way around is implicitly captured in that approach, although not in a statistically rigorous way.

Sugihara et al. Science 2012 (sorry about paywall).

Re:Always

[TechyImmigrant]

An algorithm changes its behavior based on the value.

The example I gave is a sneaky algorithm in the FIPS spec that deletes consecutive values when they match.
I.E.
If this_value == last_value:
    don't output this_value
else
    do output this_value.

This is on the output of an RNG and so it reduces the entropy in the random numbers because there are no matching consecutive numbers, whereas in a full entropy stream, all pairs would be equally likely.

In the context of noise in statistical analysis, it can confound the additive noise models.

Algorithms that do things to data, but don't look at the values of the data when deciding what to do are not data dependent and so that limits the scope various bad things to happen.