Finding the right causal tool for the right complex job

1. Finding the right causal tool for the right complex job Dr Matthew Berryman

2. Inspiration TSI • Total systems intervention (Flood & Jackson): • An umbrella framework for guiding the choice of systems methodologies (system dynamics, soft systems methodology, etc.) • 3 phases: creativity, choice, implementation.

3. Proposed structure • Knowledge-based expert system: • Set of if-then rules. • Easy for humans to read & follow • Natural to break on distinguishing features.

4. Chaining • Forward chaining: • Start with the data available – details of the problem, and system – and work forwards to reach a conclusion – decision as to which method(s) to use. • Backwards chaining: • Start with a method, and work out what the problem & system would look like. • If the expert system can’t identify a method, then pick the one that’s closest and work back.

5. Problems • Only as good as the expert(s). • In terms of rules for distinguishing between the different methods. • In terms of what methods are considered as outcomes. • May be more than one for a completely specified set of data. • Only as good as the user(s). • Has the user correctly identified all the distinguishing characteristics? • There may be multiple reasonable views of the system and hence multiple correct sets of distinguishing characteristics. • Does the user follow it blindly (deliberately, or unknowingly)?

6. Granger causality • Based on whether the past can give an improved forecast of the future (causality can only go forwards). • Stronger than just using correlation (avoids the sea level in Venice / bread price in the UK problem), but not 100% evidence for causality. • Different statistical tests can be used: • Original (regression based on asymptotic distribution theory) – can’t handle non-stationarity. • Vector Error Correction Model (VECM). • Vector AutoRegressive (VAR) model. • Toda-Yamamoto modified Wald test.

7. Bayesian belief networks • Problems: • Represent subjective beliefs. Assume fixed set of variables, and compute the probabilities. Can update the probabilities, but not the structure. • Can’t have cycles (A→B→C→A). Image from: http://cli.vu/pubdirectory/67/huygen50.png

8. Markov random networks • Benefits: • Can handle cycles. • Better training than BBNs. • Problems: • Can’t specify whether it’s A→B or B→A. Image from: http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0809/ORCHARD/

9. Causal State Splitting Reconstruction • Doesn’t presuppose a causal structure, instead it infers one (the maximally predictive, minimal space) one from the data. • Disadvantage: • Applies to an output of a discretised (time and value dimensions) 1D time series data (x[k], x and k discrete). • Some extensions of ideas to 2D CAs but they rely on the specific nature of CAs in constructing causal states.

10. Combing this • if (you want to find causal relationships) { If (1D time series) { CSSR } else { Granger } } else (if you want to analyse a causal system with known relationships) { if (cycles) { Markov } else { BBN } }

11. Adaptive • Adapt the decision tree. • Fine tune the existing (exploitation, level 1) causal methods. • Develop new ones (level 2). • Proxies.

12. Conclusions • Despite limitations, I believe this to be a useful way of organising the set of causal methods we will research. • High-level descriptions. • Be adaptive!