Nonmonotonic Abductive – Inductive Learning

1. Nonmonotonic Abductive – Inductive Learning Oliver RayDepartment of Computer ScienceUniversity of BristolAIAI'07, September 15th, 2007 Aix-en-Provence

2. (for temporal process modelling in bioinformatics and AI) Nonmonotonic Abductive – Inductive Learning Oliver RayDepartment of Computer ScienceUniversity of BristolAIAI'07, September 15th, 2007 Aix-en-Provence

3. Motivation: Learning Temporal Theories • Machine Learning: automated methods needed to handle the volume and complexity of data generated by modern experimental and data logging techniques. • Inductive Logic Programming: produces expressive human-understandable hypotheses, exploits prior domain knowledge, and facilitates incremental knowledge update. • Abductive–Inductive Learning: combines explanation and generalisation, allows for non-observation predicate learning, supports non-monotonic inference. • Non-monotonic Learning of Temporal Theories: Infer temporal models of systems or processes from (partial) domain knowledge and (partial) observations.

4. Problem: Induction of Process Models • Given: • temporal logic calculus • partial process model • scenarios/narratives • Find: • (more) complete model • that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

5. Problem: Induction of Process Models • Given: • temporal logic calculus …event calculus • partial process model …events, fluents, time • scenarios/narratives …happens, holds, initially • Find: • (more) complete model …initiates, terminates • that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

6. Problem: Induction of Process Models • Given: • temporal logic calculus …event calculus • partial process model …events, fluents, time • scenarios/narratives …happens, holds, initially • Find: • (more) complete model …initiates, terminates B E NM ILP H • that extends the partial model and explains the given narratives and scenarios wrt. the temporal calculus

7. Example: E. coli Lactose Metabolism ACTIONS (Events) ..…TIME..… (Integers) EFFECTS (Fluents) add_lactose pres_lactose growth medium sub_lactose meta_lactose E. coli add_glucose pres_glucose sub_glucose

8. Transcriptional Regulation of LAC Operon activator polymerase allolactose (low glucose) (high lactose) 5. 1. repressor 4. cAMP 2. 3. CAP Prom Op lac(z) lac(y) (a) Lactose metabolising genes not expressed 7. 8. galactosidase permease 6. CAP Prom Op lac(z) lac(y) (b) Lactose metabolising genes expressed

9. Event Calculus Axioms holdsAt(F,T2)  happens(E,T1), T1<T2, initiates(E,F,T1), not clipped(T1,F,T2). holdsAt(F,T2)  initially(F), not clipped(0,F,T2). clipped(T1,F,T2)  happens(E,T), T1<T, T<T2, terminates(E,F,T).

10. Partial LAC Process Model % ontology time(0..9). event(add_gluc). event(add_lact). event(sub_gluc). event(sub_lact). fluent(pres_lact). fluent(pres_gluc). fluent(meta_lact). % behaviour initiates(add_gluc, pres_gluc, T). initiates(add_lact, pres_lact, T). terminates(sub_gluc, pres_gluc, T). terminates(sub_lact, pres_lact, T).

11. LAC Scenario / Narrative % actions initially(pres(gluc)). happens(add(lact),1). happens(sub(gluc),2). happens(sub(lact),3). happens(add(lact),4). happens(add(gluc),5). happens(sub(lact),6). happens(sub(gluc),7). % observations not holdsAt(meta(lact),1), not holdsAt(meta(lact),2), holdsAt(meta(lact),3), not holdsAt(meta(lact),4), holdsAt(meta(lact),5), not holdsAt(meta(lact),6), not holdsAt(meta(lact),7), not holdsAt(meta(lact),8). n.b. in general, could have partial knowledge of actions and/or observations, many actions per timepoint, etc.,

12. Language and Search Bias % domain specific mode declarations modeh(2 , initiates(#event,#fluent,+time) ). modeh(2, terminates(#event,#fluent,+time) ). modeb(3 , holdsAt(#fluent,+time) ). modeb(3 , not holdsAt(#fluent,+time) ). % built-in preference criterion: Occam’s Razer % (greedily )prefer the simplest (i.e., smallest ) % hypothesis that correctly explains the data n.b. in general, need ways to constrain the search space both syntactically and semantically

13. Abductive–Inductive Learning 1 Abduction head atoms of K are abductive explanation of the examples E: i.e., B |= e . Given: B,E,M a1 : an  = 2 Deduction body atoms of K are deductive consequences of the theory B: i.e., B |= di . IDEA: construct and generalise an initial ground hypothesis K called a Kernel Set 1 1 1 a1 d1 d2 … dm1 : an d1 d2 … dmn K= n n n 3 Induction H is a compressive theory subsuming the theory K: i.e., H  K . 1 1 1 A1 D1 D2 … Dm1 : An D1 D2 … Dmn Return: H H= n n n

14. Abductive Phase

15. Deductive Phase

16. Inductive Phase

17. DEMO CLICK ME!

18. Related Work • Sakama • Baral • Otero & Lorenzo • Muggleton & Moyle • Inoue, Iwanuma & Nabeshima

19. Conclusion • XHAIL provides a (stable model) semantics and proof procedure for NM-ILP • It uses mode declarations in the construction of a Kernel Set to reduce generalisation search space • It is well suited to learning temporal theories in the Event Calculus (which provides a more intuitive event-based formalism than pure first order logic) • But, still need to investigate stability, noise, confidence, …

20. END