Learning causal theories Josh Tenenbaum MIT Department of Brain and Cognitive Sciences

1. Learning causal theories Josh Tenenbaum MIT Department of Brain and Cognitive Sciences Computer Science and AI Lab (CSAIL)

2. Collaborators Charles Kemp Noah Goodman Tom Griffiths Vikash Mansinghka

3. How do people learn causal relations from data? A standard answer: infer the network structure that best fits the statistics of the observed data. Structure Data

4. What’s missing from this account? The background knowledge that makes causal learning possible. • Causal schemata: domain-specific theories that constrain “natural” causal hypotheses • Abstract classes of variables and mechanisms • Causal laws defined over these classes • Causal variables: substrate of causal hypotheses • Which variables are relevant • How variables ground out in perceptual and motor experience The puzzle: This background knowledge must itself be learned, and learned together with specific causal relations. How? A possible answer: hierarchical Bayesian models

5. Learning causal schemata Behaviors Diseases Symptoms Causal schema high-fat diet working in factory … heart disease lung cancer … coughing chest pain … Causal model Event data (Griffiths & Tenenbaum; Kemp, Goodman, Tenenbaum)

6. TO ADD • # of Bayes nets on 12 variables: 521939651343829405020504063 • # of Bayes nets on 12 variables that fit this schema: 131072 • Maybe put the bayes net learning slide next.

7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Towards more schema-based machine learning 20 80 1000 # samples recovered model Causal model Data 1 2 3 4 5 6 … “blessing of abstraction” 7 8 9 10 11 12 13 14 15 16 … 0.4 c1 Causal schema … c2 recovered model Causal model Data (Mansinghka, Kemp, Tenenbaum, Griffiths)

8. Learning causal schemata almond walnut macadamia ? cashew chestnut (Kemp, Goodman, Tenenbaum)

9. Learning causal schemata macadamia Causal model ? rash EventData (Kemp, Goodman, Tenenbaum)

10. Learning causal schemata almond chestnut walnut cashew macadamia Causal model ? +0.54 +0.47 rash rash rash rash rash EventData … … … … (Kemp, Goodman, Tenenbaum)

11. Learning causal schemata T1 T2 almond chestnut walnut cashew macadamia Causal schema T1 T2 +0.5 rash rash almond chestnut walnut cashew macadamia Causal model +0.54 +0.47 +0.5? rash rash rash rash rash EventData … … … …

12. + + + + GO

13. One-shot learning: Design Type 2 Type 1 o1 o5 o2 o6 1) o4 o8 o3 o7 • (g,n) condition: • (G,g) condition: • (n) condition: +0.5 e e 3) 4) 2) o1 o3 o1 o3 o2 o2 o1 o5 o2 o6 o5 o5 o4 o6 o4 o6 o4 o8 o3 o7 +0.1 +0.9 +0.1 e e e e • Training phase: 1 of 4 conditions shown above. • Test phase: new object activates the machine once. new object fails on the machine once.

14. One-shot learning: Results o1 o3 o1 o3 o2 o2 o1 o5 o2 o6 o1 o5 o2 o6 o5 o5 o4 o6 o4 o6 o4 o8 o3 o7 o4 o8 o3 o7 Condition +0.5 +0.1 +0.9 +0.1 e e e e e e Question: what is the causal strength of ? Model likelihood likelihood People strength strength strength strength

15. What’s missing from this account? • Causal schemas: domain-specific theories that constrain “natural” causal hypotheses • Abstract classes of variables and mechanisms • Causal laws defined over these classes • Causal variables: constituents of causal hypotheses • Which variables are relevant • How variables ground out in perceptual and motor experience A possible answer: hierarchical Bayesian models (Kemp, Goodman, Griffiths, Tenenbaum).

16. The problem ? • Option 1: Variables are innate. • Option 2 (“clusters than causes”): Variables are learned first, independent of causal relations, through a kind of bottom-up perceptual clustering. • Option 3: Variables are learned together with causal relations. A child learns that petting the cat leads to purring, while pounding leads to growling. But what are the origins of these symbolic event concepts (“variables”) over which causal links are defined?

17. Learning grounded causal models(Goodman, Mansinghka & Tenenbaum) Hypotheses: Data: … Time t Time t’

18. “Alien control panel” experiment “blessing of abstraction” A B C A B C A B C A Blue bar: human Red bar: model B C A B C A B C A B C A B C A B C

19. Testing joint model vs. bottom-up model Humans Blue bars: 3 variables Red bars: 4 variables How many variables are discovered? A B C Bottom-up Model Joint Model

20. Conclusions • Hierarchical Bayesian models (HBMs) explain how the background knowledge that supports causal learning may itself be learned from data through rational inferential means. • Domain-specific schemas constraining candidate causal networks • Causal variables grounded in sensorimotor experience • These issues are more general than just causal learning, relevant to learning associations, symbolic rules, … • Contrast with traditional approaches to knowledge acquisition: • Classical empiricism: variables are innate, schemata learned slowly by accretion and superposition. • Classical nativism: variables are innate, schemata are innate. • Hierarchical Bayes: variables and schemata could be learned; abstract knowledge may be learned from surprisingly little data. • Ongoing and future work: Applying HBMs to many different aspects of cognitive development – categories and properties, word learning, syntax in language, social relations, theory of mind, …

22. “Alien control panel” experiment A B C A B C A B C A B C

23. Modeling learning curves a b c Blue bar: human Red bar: model