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### Information Inference

Mimicking human text-based reasoning

P.D. Bruza & D. Song

Information Ecology Project

Distributed Systems Technology Centre

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….

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

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

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)

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)

T= “Why Linus chose a penguin”

“Linus” being with “penguin” in T, together with K, carries the information that

“Linus” is “Linus Torvalds”

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)

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.

representation

symbolic

conceptual

Geometric

representation

associationist

(sub-conceptual)

Connectionist

representation

Gärdenfors’ cognitive modelConceptual 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.

Barwise & Seligman’s real valued state spaces

Observation function

Gärdenfors’ cognitive model: how we realize it

Propositional

representation

symbolic

keywords

LSA

conceptual

Geometric

representation

HAL

associationist

(sub-conceptual)

Connectionist

representation

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)

How HAL vectors are constructed to Language (HAL)

…….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”)

Remarks about HAL to Language (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

Differences with Burgess et al. to Language (HAL)

- 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

Reagan traces to Language (HAL)

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

Prototypical “Reagan” = average of vectors from traces to Language (HAL)

president: 3.23,

administration: 1.82,

trade: 0.40,

budget: 0.37,

veto: 0.34,

bill: 0.31,

congress: 0.31,

tax: 0.29,

:

:

Concept combination: “Pink Elephant” to Language (HAL)

Elephant = < , , …… >

Heuristic concept combination: “Star wars” to Language (HAL)

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>

starwars = < 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)

Theoretical background: Information inference via HAL-based information flow computations

Barwise&Seligman: state-based “information flow”

HAL-based “information flow”

symbolic

conceptual

Degree of inclusion (flow) computation information flow computations

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

Visualizing degree of inclusion between HAL vectors information flow computations

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

Information Inference in practice: deriving query models information flow computations

- 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)

The experiments information flow computations

- 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

Baseline Model information flow computations

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

Composition model information flow computations

- Combine the HAL vectors of individual query terms by recursively applying the concept combination heuristic; query terms ranked according to idf (dominance ranking)

starwars = < trek: 0.3, episode: 0.15, soviet: 0.6, bush: 0.53, missile: 0.65,

iran: 0.2, iraq: 0.18, gulf: 0.25>

Results information flow computations

The effect of information inference information flow computations

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:

spaceprogram

Comparison with probabilistic query language models information flow computations

- MC: Markov chain model (Lafferty & Zhai, SIGIR 2001)

Scores are average precision

Comparison with probabilistic query language models (con’t)

- RM: Relevance model (Lavrenko & Croft, SIGIR 2001)

Scores are average precision

Text-based scientific discovery (con’t)

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

Logic of Abduction (Gabbay & Woods) (con’t)

Abductive logic

Logic of discovery

Logic of

justification

Hypothesis testing

?

?

HAL-based info flow

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

Index expressions “Raynaud”

“Beneficial effects of fish oil on blood viscosity”

beneficial

effects

of

on

fish

blood

oil

viscosity

Power index expressions for representing integral dimensions “Raynaud”

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

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)

Summary a logic of discovery

- (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)

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