Information Inference

1. Information Inference Mimicking human text-based reasoning P.D. Bruza & D. Song Information Ecology Project Distributed Systems Technology Centre

2. Penguin Books U.K Why Linus chose a penguin Surfing the Himalayas

3. Introductory remarks • Information inference is a common and real phenomenom • It can be modelled by symbolic inference, but this isn’t satisfying • The inferences are often latent associations triggered by seeing a word(s) in the context of other words- so inference is not deductive, but about producing appropriate implicit associations appropriate to the context • We need to look at the problem from a cognitive perspective….

4. Since last time…. • (Philosophical) positioning of the work is clearer • Some encouraging experimental results using information inference to derive query models • Some initial ideas about how information inference fits into an abductive logic for text-based knowledge discovery

5. Dretske’s Information Content To a person with prior knowledge K, r being F carries the information that s is G if and only if the conditional probability of s being G given r is F is 1 (and less than one given K alone) We can say that s being G is inferred (informationally) from r is F and K

6. T= “Why Linus chose a penguin” So Dretske’s definition does not permit the inference “Linus” is “Linus Torvalds”, though a human being may proceed under this “hasty” judgment. Dretske’s information content “sets too high a standard” (Barwise & Seligman)

7. Inferential information content (Barwise &Seligman) To a person with prior knowledge K, r being F carries the information that s is G, if the person could legitimately infer that s is G from r being F together with K (but could not from K alone)

8. T= “Why Linus chose a penguin” “Linus” being with “penguin” in T, together with K, carries the information that “Linus” is “Linus Torvalds”

9. Barwise & Seligman (con’t) “… by relativizing information flow to human inference, this definition makes room for different standards in what sorts of inferences the person is able and willing to make” Remarks: - Psychologistic stance taken - Onerous from an engineering standpoint: “different standards” implies “nonmonotonicity”. Consider, “Linux Online: Why Linus chose a penguin” (willing) v.s. “Why Linus chose a penguin” (not willing)

10. Consequences of psychologism • Representations of information need not be propositional • Semantics is not a model-theoretic issue, but a cognitive one - the “meanings” stored and manipulated by the system should accord with what we have in our heads.

11. Propositional representation symbolic conceptual Geometric representation associationist (sub-conceptual) Connectionist representation Gärdenfors’ cognitive model

12. Conceptual spaces: the property “red” hue red(x) chromaticity brightness Properties and concepts are dimensional (geometric) objects. Dimensions may be integral - the value in a dimension(s) determines the value in another.

13. Barwise & Seligman’s real valued state spaces Observation function

14. Gärdenfors’ cognitive model: how we realize it Propositional representation symbolic keywords LSA conceptual Geometric representation HAL associationist (sub-conceptual) Connectionist representation

15. Geometric representations of words via Hyperspace Analogue to Language (HAL) reagan = < administration: 0.45, bill: 0.05, budget: 0.07, house: 0.06, president: 0.83, reagan: 0.21, trade: 0.05, veto: 0.06, … > This example demonstrates how a word is represented as a weighted vector Whose dimensions comprise other words. The weights represent the strengths of association between “reagan” and other words seen in the same context(s)

16. How HAL vectors are constructed …….Kemp urges Reagan to oppose stock tax….. Slide a window of width n across corpus Per word: Compute weight of association with other words within window the weight is inversely proportional to distance HAL space: each word in the corpus represented by a multi-dimensional vector - a weighted sum of the contexts the word appeared in. (Burgess et al refer to it as a “high dimensional context space”, or a “high dimensional semantic space”)

17. Remarks about HAL • A HAL space is easy to construct • Cognitive compatibility with human information processing • “word representations learned by HAL account for a variety of semantic phenomena” (Burgess et al) • Therefore a good candidate for represented “meanings” in accord with our psychologistic stance • A HAL space is a real-valued state space, thus opening the door to driving information inference according to Barwise & Seligman’s definition • A HAL vector represents a word’s “state” in the context of the text corpus it was derived from

18. Differences with Burgess et al. • We (often) normalize the weights • Pre- and post- vectors are added into a single vector • HAL vectors derived from small text corpora (e.g., Reuters-21758) seem to be OK • HAL vectors are “summed” representations- similar in spirit to “prototypical concepts” (which are averaged representations

19. Reagan traces President Reagan was ignorant about much of the Iran arms scandal Reagan says U.S. to offer missile treaty REAGAN SEEKS MORE AID FOR CENTRAL AMERICA Kemp urges Reagan to oppose stock tax

20. Prototypical concepts * * * * * *

21. Prototypical “Reagan” = average of vectors from traces president: 3.23, administration: 1.82, trade: 0.40, budget: 0.37, veto: 0.34, bill: 0.31, congress: 0.31, tax: 0.29, : :

22. Concept combination: “Pink Elephant” Elephant = < , , …… >

23. Heuristic concept combination: “Star wars” Observation: “star” dominates “wars” star = <trek: 0.2, episode: 0.05, soviet: 0.3, bush: 0.4, missile: 0.25> wars = <soviet: 0.1, missile:0.2, iran: 0.33, iraq: 0.28, gulf: 0.4> starwars = < trek: 0.3, episode: 0.15, soviet: 0.6, bush: 0.53, missile: 0.65, iran: 0.2, iraq: 0.18, gulf: 0.25> How to weight dimensions appropriately according to context? Weights are affected by how one concept appears in the light of another concept: Intersecting dimensions are emphasized, weights are adjusted according to degree of dominance. (NB moving prototypical concepts in the HAL space is a cleaner way of dealing with context)

24. Theoretical background: Information inference via HAL-based information flow computations Barwise&Seligman: state-based “information flow” HAL-based “information flow” symbolic conceptual 

25. Degree of inclusion (flow) computation source target Consider the “quality properties” above mean weight in the source concept. (Intuition: how much of the salient aspects of the source are contained in the target) Compute the ratio of intersecting dimensions between source and target concept to the dimensions in the source concept

26. Visualizing degree of inclusion between HAL vectors A . F . K . . Q A B C D F G K L M Many of the above avg. “quality properties” of the source concept are present in the target, so the degree of inclusion will be high source target

28. Information Inference in practice: deriving query models • Construct HAL vectors for all vocabulary terms from the document collection • Given a query such as “space program”, compute the information flows from it and use these to expand the query, e.g. Query expansion term derived via information flow computation (We used the top 80 information flows for expansion without feedback, 65 with feedback)

29. The experiments • Associated Press 88/89 collections • TREC topics 1 – 50, 100-150, 151-200 (titles only). • Models for comparison: Baseline, Composition, Relevance Model, Markov chain model

30. Baseline Model • BM-25 term weighting (terms were stemmed) • Replication of Lafferty & Zhai’s baseline (SIGIR 2001) • Dot product matching function

31. Composition model • Combine the HAL vectors of individual query terms by recursively applying the concept combination heuristic; query terms ranked according to idf (dominance ranking) starwars = < trek: 0.3, episode: 0.15, soviet: 0.6, bush: 0.53, missile: 0.65, iran: 0.2, iraq: 0.18, gulf: 0.25>

32. Results

33. The effect of information inference 26% of the 35% improvement in precision of the HAL-based information flow model is due to information inference For example, the query “space program”. The information flow model infers query expansion terms such as “Reagan”, “satellites”,”scientists”, “pentagon”, “mars”, “moon”. These are real inferences with respect “space program”, as these terms do not appear as dimensions in HAL vectors of the concept combination: spaceprogram

34. Comparison with probabilistic query language models • MC: Markov chain model (Lafferty & Zhai, SIGIR 2001) Scores are average precision

35. Comparison with probabilistic query language models (con’t) • RM: Relevance model (Lavrenko & Croft, SIGIR 2001) Scores are average precision

36. Text-based scientific discovery B1 Blood viscosity Raynaud C A Fish Oil B2 Platelet Aggregation B3 Vascular Reactivity “.., he made the connection between these literatures and formulated the hypothesis that fish oil may be used for treating Raynaud’s disease..” Weeber et al “Using Concepts in Literature-Based Discovery JASIST 52(7):548-557

37. Logic of Abduction (Gabbay & Woods) Abductive logic Logic of discovery Logic of justification Hypothesis testing ? ? HAL-based info flow

38. Raw material for abduction? Information flows from “Raynaud” Raynaud: 1.0 myocardial: 0.56 coronary: 0.54 renal: 0.52 ventricular: 0.52 . . . oil: 0.23 . fish: 0.20 . . . . Raynaud Some promise, but lack of representation of integral dimensions a problem

39. Index expressions “Beneficial effects of fish oil on blood viscosity” beneficial effects of on fish blood oil viscosity

40. Power index expressions for representing integral dimensions eff of fish oil eff on blood viscosity fish effects blood viscosity oil Information flows are single terms, power index expressions determine how they may be combined into higher order syntactic structures

41. Initial results from using information flow computations as a logic of discovery 27 ventricular (0.52) infarction (0.46) 27 thromboplastin (0.17) 27 pulmonary (0.51) arteries (0.25) 27 placental (0.19) protein (0.42) 27 monoamine (0.17) oxidase (0.18) 27 lupus (0.37) nephritis (0.17) 27 instruments (0.17) 27 coagulant (0.21) 27 blood (0.63) coagulation (0.29) 26 umbilical (0.24) vein (0.32) 25 fish (0.20) 23 viscosity (0.21) 23 cigarette (0.26) smokers (0.22) 4 fish (0.20) oil (0.23)

42. Summary • (Barwise & Seligman) and Gärdenfors have very stance wrt “human stance” (Gabbay and Woods also)… psychologism is alive…. • An integration of a primitive approximation of a conceptual space with an information inference mechanism driven by information flow computations • An initial attempt towards realizing Gärdenfors’ conceptual spaces • A HAL space is only a primitive approximation • We are looking at Voronoi tessellations • A tiny contribution to Barwise & Seligman’s call for a “distinctively different model of human reasoning” • (We are looking beyond IR)