The influence of domain priors on intervention strategy

1. The influence of domain priors on intervention strategy Neil Bramley

2. Intro 1. Limitations of Causal Bayes Nets as psychological models. 2. Extension of the approach using the hierarchical Bayesian framework. 3. Philosophical implications of this framework 4. Rational vs. Heuristic models for psychology, future directions. 5. Potential Discussion Points.

3. . Causal Bayes Nets Mean that this: Becomes this:

4. Modelling Interventions Pearl, J. (2000/2009). Causality. New York: CUP (2nd edition).

5. CBNs: Scope and Limits • A useful tool for prediction and diagnosis in applied settings. • AND a plausible model of mental models of causation? • Much stronger than associationist accounts; i.e. can explain blocking effects + provide a structure for counterfactual inference & reasoning. • BUT: Simultaneously too strong and too weak for psychological plausibility.

6. Non statistical cues to causation • Prima facie we identify causation through non-statistical cues most of the time. • Temporal and spatial contiguity. • Ability to identify characteristic domains and mechanisms: Light Switches, Toasters, Magnets, Diseases etc etc... • We usually appear to have very strong priors. • Can we include these in our psychological model?

7. The Hierarchical Bayesian Framework Nest hypotheses about what network generates given events within a hypothesis about the permissable causal structures for different domains. Nest hypotheses about permissable structures (called frameworks or causal grammars) within a hypothesis about the nature of causation. Continue ad abstractum. Kemp, C., Goodman, N. & Tenenbaum, J. (2010). Learning to learn causal models. Cognitive Science, 34, 1185-1243.

8. An Example Diseases, their causes and effects The framework/grammar: Sample of possible causal networks: Adated from Griffiths, T. L. & Tenenbaum, J. B. (2007). Two proposals for causal grammars. In Gopnik, A., & Schulz, L. (eds.), Causal learning: Psychology, philosophy, and computation. Oxford: OUP.

9. Bottom-Up Learning • Can be shown computationally that a theory of causality can be derived by hierarchical Bayesian updating from causally generated data. • Works generally for categorisation, language aquisition, potentially generative of entire ontology.. No need for a priori knowledge. • “Blessing of abstraction” – The highest level of the hierarchy pop out first then constrain/direct inferences at lower levels. Goodman, N. D., Ullman, T. D. and Tenenbaum J. B. (in press). Learning a theory of causality.Psychological Review.

10. Top-Down Inferences • Higher levels provide prior probabilities for lower levels. • E.g. perceptual (temporal/spatial) cues bootstrap inference to most likely causal network by constraining hypothesis space. • Explains one-shot / zero-shot causal inference. • Supported by evidence for ‘theory change’ during development. • Compatible with CBNs as mental models.

11. Philosophical Implications? • Anti-humean?: We need an overriding theory of causation to make sense of cause-effect relations. • Quasi-Kantian?: The theory appears prior causal ascription (although not prior to the world). • Instrumentalist: A theory of causality is useful in making sense of incoming sensory information. • May gel with Cartwright’s ‘nomological machines’: e.g. Knowledge of the normal mechanism for a causal domain (identified perceptually) important, can override some covariational cues.

12. Intractability • PROBLEM: Updating in a hierarchical Bayesian framework becomes intractable for realistically complex data. • Part of more general debate in cognitive science: Rational Models vs. heuristic or process orientated models. • An answer: Rational models formulated at Marr’s “Computational” level of explanation, others at the algorithmic. • Search is on for heuristic/stochastic algorithims which can approximate the outputs of the rational model. • Need for process tracing and models which work within plausible computational constraints i.e. Working memory and decision time limitations.

13. Future Directions • I would like to: test the influence of domain priors on interventional strategy. I.e. Test when, and to what degree, the ‘domain’ of presentation of an inference problem influences what causal hypotheses subjects’ test while trying to learn it. • Test the extent to which we are able to learn to use framework level cues to boost performance in subsequent learning problems (e.g. Tenenbaum et al). • More work in identifying ‘theory shifts’ in development (e.g. Gopnik et al). • My current thesis: looking at model fitting interventional/observational strategy in recovering increasingly complex networks – testing the fit of Bayesian vs. Constraint based (Sprites & Pearl) vs. various other heuristic models.

14. Possible Discussion Points • Opinion of CBNs as psychological models and in general? Alternatives? • If a domain general Bayesian learning framework can derive theory of causality from scratch, how does this impact on the philosophical debate? • Opinions on the status of ‘rational’ models in cognitive science/psychology?