RuleML2015: Compact representation of conditional probability for rule-based mobile context-aware systems

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Compact representation of conditional probabilityfor rule-based mobile context-aware systems

Szymon Bobek, Grzegorz J. Nalepa

AGH University of Science and Technology

RuleML 20155 August 2015, Berlinhttp://geist.agh.edu.pl

SBK+GJN (AGH-UST) Indect 5 August 2015 1 / 28

http://geist.agh.edu.pl

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Outline I

1 Introduction

2 Previous works

3 Proposed solution

4 Probabilistic interpretation of XTT2 rules

5 Probabilistic reasoning in XTT2 models

6 Implementation

7 Summary and future work


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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Mobile context-aware systems (mCAS)

• Where you are, who you are with, what resources are nearby (Schillit)

• Any informaiton that can be used to characterize the situation of an entity (Dey)

• Individuality, activity, location, time, relations (Zimmerman)

• Set of variables that may be of interest for an agent and that influence its actions (Bolchini)

Context

• Artificial intelligence methods Aware

• Intelligent homes, intelligent cars, robotics

• Ambient intelligence, pervasive environments, ubiquitous computing

• Mobile computing (location aware mobile applicaitons)

• Intelligent software (contextual advertising, etc.)

Systems


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Mobile environment and uncertainty


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Different types of uncertainty

High-level classification1 Uncertainty due to lack of knowledge – that comes from incomplete

information both at the model level or if the information is not provided bythe sensors,

2 Uncertainty due to lack of semantic precision – that may appear due tosemantic mismatch in the notion of the information,

3 Uncertainty due to lack of machine precision – which covers machine sensorsimprecision and ambiguity.


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Different uncertainty modelling and handlingmechanisms

Uncertainty sourceLack ofknowledge

Semanticimprecision

Machineimprecision

Implementationeffort

Probabilistic w m l HighFuzzy Logic m w w MediumCertainty Factors w m l LowMachine learning l m l High

Table : Comparison of uncertainty handling mechanisms. Full circles represent fullsupport, whereas empty circles represent low or no support.


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Mobile environment and uncertainty

Nature of mCAS

The uncertainty of data is inevitable and it is dynamic

mCAS are build usually as a user centric systems

Intelligibility is very important as it may improve users trust to the system

Mediation may help resolve ambiguity


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF

HeaRTDroid


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CF approach

Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF

HeaRTDroid

XTT2 rule representation


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CF was not enough

Assumed system state

Weather forecast: sunny weather with certainty 0.3, cloudy with 0.1, andrainy with 0.6.

How much user is interested inn particular POIs: places for eating – 60%,culture – 20%, entertainment – 80%, sightseeing – 20%.

the user have been recently walking with certainty 0.8, running with 0.1certainty and driving with certainty 0.1.


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Uncertainties

(?) weather (?) user profile (?) activity cf(conditions) cf(rule) cf(conclusion)0.3 0.6 0.8 0.3 1 0.30.6 0.6 0.8 0.6 1 0.60.6 0.6 0.1 0.1 1 0.10.6 0.84 0.8 0.6 1 0.60.6 0.36 0.8 0.36 1 0.360.3 0.36 0.8 0.3 1 0.3

Assumed system state with zero certainty

Weather forecast: sunny weather with certainty 0.3, cloudy with 0.1, andrainy with 0.6.




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CF was not enough

Assumed system state

Weather forecast: sunny weather with certainty 0.0, cloudy with 0.0,and rainy with 0.0.




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Uncertainties

(?) weather (?) user profile (?) activity cf(conditions) cf(rule) cf(conclusion)0.0 0.6 0.8 0.0 1 0.00.0 0.6 0.8 0.0 1 0.00.0 0.6 0.1 0.0 1 0.00.0 0.84 0.8 0.0 1 0.00.0 0.36 0.8 0.0 1 0.00.0 0.36 0.8 0.0 1 0.0

Assumed system state with zero certainty

Weather forecast: sunny weather with certainty 0.0, cloudy with 0.0,and rainy with 0.0.




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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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Use Bayesian Networks as ”backup” representation

Solution

XTT2 models can be immediately translated into Bayesian networks

HeaRTDroid stores historical states, which can be used to train Bayesiannetworks

(?) location (?) daytime (?) today (->) action

= home

= outside

= work

= work

= outside

= home

= home

= home

= outside

= outside

= morning

= morning

= dayatime

= afternoon

= afternoon

= evening

= night

= any

= evening

= night

= workday

= workday

= workday

= workday

= workday

= any

= any

= weekend

= any

= any

:= leaving_home

:= travelling_work

:= working

:= leaving_work

:= travelling_home

:= resting

:= sleeping

:= resting

:= entertaining

:= travelling_home

Table id: tab_4 - Actions

(?) action (?) transportation (->) {application}

= leaving_home

∈ {leaving_work,leaving_home}

∈ {travelling_home,travelling_work}


∈ {resting,entertaining}

= working

= sleeping


= idle

∈ {walking,running}

∈ {driving,cycling}

∈ {bus,train}

∈ {running,cycling}

= any

= idle

∈ {driving,bus,train}

:= {news,weather}

:= {clock,navigation}

:= navigation

:= {news,clock}

:= {sport_tracker,weather}

:= {calendar,mail}

:= clock

:= trip_advisor

Table id: tab_5 - Applications

(?) action (->) profile

∈ {travelling_home,travelling_work,leaving_home,leaving_work}

∈ {working,resting,entertaining}

= sleeping

:= loud

:= vibrations

:= offline

Table id: tab_6 - Profile

12345678

123

12

34

56

789

10


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Solution




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Solution



XTT2 Model Manager

Reasoning Engine

Working Memory

-n

-n+1

-1

0

.

.

.

Contex Providers

HeaRTDroid

States


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Solution



Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF

HeaRTDroid

XTT2 rule representation


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Solution



Intelligibility

Mediation

Uncertainty

Dynamics

Rules

CF

Dynamic CF

HeaRTDroid

Dual representation


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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ALSV(FD) logic

XTT2 rule in ALSV(FD) logic

(Ai ∝ di ) ∧ (Aj ∝ dj) ∧ . . . (Am ∝ Vm) ∧ (An ∝ Vn) −→ RHS

Syntax Interpretation Relation

Ai = di value of Ai is pre-cisely defined as di

eq

Ai ∈ Vi value of Ai is in Vi inAi 6= di shorthand for Ai ∈

(Di \ {di})neq

Ai 6∈ Vi shorthand for Ai ∈(Di \ Vi )

notin

Table : Formula for simple attributes

Syntax Interpretation Relation

Ai = Vi Ai equal Vi eqAi 6= Vi Ai does not equal

Vineq

Ai ⊆ Vi Ai is a subset Vi subsetAi ⊇ Vi Ai is a superset Vi supsetAi ∼ Vi Ai has non-empty

intersection withVi

sim

Ai 6∼ Vi Ai has empty in-tersection with Vi

notsim

Table : Formula for generalizedattributes


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Probabilistic interpretation of ALSV(FD) rule

XTT2 rule as conditional probability

(Ai ∝ di ) ∧ (Aj ∝ dj) ∧ . . . (An ∝ dn) −→ (Ad = dd)

(Ai ∝ di ) ∧ (Aj ∝ dj) ∧ . . . (An ∝ dn) −→ Ag = {v1, v2, . . . vn}P(DEC | COND)

Interpretation

Every rule is represented by a pair 〈r , p〉, where r is an XTT2 rule and p ∈ [0; 1]defines a certainty of a rule given its preconditions.

simple attributes p : P (Ad | Ai ,Aj . . . ,An)generalised attributes

P(Ag = {v1, v2, . . . vn} | Ai ,Aj , . . . ,An) = P(v1 | Ai ,Aj , . . . ,An)·P(v2 | Ai ,Aj , . . . ,An)·. . .P(vn | Ai ,Aj , . . . ,An)


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Probabilistic interpretation of XTT2 models

(?) location (?) daytime (?) today (->) action

= home

= outside

= work

= work

= outside

= home

= home

= home

= outside

= outside

= morning

= morning

= dayatime

= afternoon

= afternoon

= evening

= night

= any

= evening

= night

= workday

= workday

= workday

= workday

= workday

= any

= any

= weekend

= any

= any

:= leaving_home

:= travelling_work

:= working

:= leaving_work

:= travelling_home

:= resting

:= sleeping

:= resting

:= entertaining

:= travelling_home

Table id: tab_4 - Actions

(?) action (?) transportation (->) {application}

= leaving_home

∈ {leaving_work,leaving_home}




= working

= sleeping


= idle

∈ {walking,running}

∈ {driving,cycling}

∈ {bus,train}

∈ {running,cycling}

= any

= idle

∈ {driving,bus,train}

:= {news,weather}

:= {clock,navigation}

:= navigation

:= {news,clock}

:= {sport_tracker,weather}

:= {calendar,mail}

:= clock

:= trip_advisor

Table id: tab_5 - Applications

(?) action (->) profile

∈ {travelling_home,travelling_work,leaving_home,leaving_work}

∈ {working,resting,entertaining}

= sleeping

:= loud

:= vibrations

:= offline

Table id: tab_6 - Profile

12345678

123

12

34

56

789

10


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Probabilistic interpretation of XTT2 models


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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Hybrid reasoning

Data: E – the set of all known attributes valuesA – the set of attributes which values are to be found

Result: V – values for attributes from the set A1 Create a stack of tables T that needs to be processed to obtain V ;2 while not empty T do3 t = pop(T );4 Identify schema (COND,DEC) of table t;5 if ∀c ∈ COND,Val(c) ∈ E then6 Execute table t;7 ∀a ∈ DEC ∩ A : add Val(a) to E and V ;8 else9 Run probabilistic reasoning to obtain P(a)∀a ∈ DEC;

10 Select rule 〈rmax , pmax〉 such that: ∀ 〈r , p〉 ∈ t : p ≤ pmax ;11 if pmax ≥ ε then12 execute rule r ;13 ∀a ∈ DEC ∩ A : add Val(a) to E and V ;14 else15 ∀a ∈ DEC ∩ A : add P(a) to E and V ;16 t = pop(T );17 Identify schema (COND,DEC) of table t;18 goto 919 end20 end21 end22 return V ;

Inference modes1 Deterministic

inference2 Probabilistic

inference3 Hybrid

inference


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Hybrid reasoning

Assumptions

Value of attribute G is needed

Only value of attribute C is known

Attribute F is set to be in/out

A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




(->) B

1

2

3

4

5

No. (?) A

B = a

B = b

B = c

B = d

B = e

P(B=d | evidence) = 0.2

P(B=c | evidence) = 0.2

P(B=b | evidence) = 0.2

P(B=a | evidence) = 0.2

P(B=e | evidence) = 0.2


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




(->) E(?) B

1

2

3

4

5

No. (?) D

E = a

E = b

E = c

E = d

E = e

P(E=d | evidence) = 0.6

P(E=c | evidence) = 0.1

P(E=b | evidence) = 0.0

P(E=a | evidence) = 0.1

P(E=e | evidence) = 0.2


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Hybrid reasoning

Assumptions




A B

C D

B D E

E F

E G


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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Prototype Implementation

Components

HeaRTDroid for deterministic reasoning and training set preparation

Translator XTT2 to BN

WEKA

Prototype reasoner that combines HeaRTDroid and WEKA

HeaRTDroidWeka

XTT2 Model

Translator XTT2 to BN

Hybrid Reasoner

States


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Outline

1 Introduction

2 Previous works

3 Proposed solution



6 Implementation



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Summary and future work

Summary

We provided probabilistic interpretation of XTT2 knowledge representation

We proposed a hybrid inference algorithm

We implemented prototype reasoner that binds HeaRTDroid, XTT2 andBayesian network representation of XTT2 into one hybrid reasoner

Future works

Make the reasoner part of HeaRTDroid

Evaluate the hybrid reasoning on the real-life use case


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Thank you for your attention!

Do you have any questions?

RuleML 2015




RuleML2015: Compact representation of conditional probability for rule-based mobile context-aware systems

Science

lack of machine precision

lack of semantic precision

systems sbk gjn aghust

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machine sensors imprecision

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incomplete information

semantic mismatch