A Richer Understanding - PowerPoint Presentation

Slide1

A

Richer Understanding

of Bayesian Network Diagrams

Dr.

Kamaran

Fathulla

University of Essex

International Academy

kamaran@essex.ac.uk

June 2011

Clay Tablet map from Ga-Sur, Kirkuk, 2,500 B.C.

Some 2500 years ago people have used clay tablets to express boundaries, groupings, and routes

Diagrams are everywhere

Applied psychology

Cognitive scienceLinguisticsVisual programmingData visualisationGraphic designEducationHistory and philosophy of scienceArchitecture

Blackwell and Engelhardt (1999)

Eppler, 2003

But.... Diagrams continue to be

difficult

to understand and work withThere has been a substantial growth in the use of diagrams in earlier stages of the research process to collect data. Despite this growth, guidance on this technique is often isolated within disciplines.Numerous references

are cited on people expressing difficulty or discomfort with diagramming.

Muriah J Umoquit, et al (2011) A multidisciplinary systematic review of the use of diagrams as a means of collecting data from research subjects: application, benefits and recommendations

Sources of the difficulties

1.

Diversity of types of diagramsBoxes and linesContour mapsBar charts etc..

2. Diversity of types of change (dynamics)Different types of diagrams require different editing operationsDifferent diagram types have different rules of well formedness

Need to relax these rules but maintain well formedness3.

All of the above in semantically mixed diagrams

Even single type diagrams have mixed semantics

Next..... Bayesian type diagrams

Influence Diagrams ID

First introduced in the mid 70s.

ID’s have become a de facto standard for representation of Bayesian decision problems.There is not too much feedback from analysts and experts about their experiences using IDs for building decision-making models.Constructing ID is considered as an art.

Concha Bielza, Manuel Gómez, Prakash P. Shenoy (2009)

Modeling Challenges with Influence Diagrams: Representation IssuesSCHOOL OF BUSINESS WORKING PAPER NO. 319

An Influence Diagram

James E. Corter et al (2009) Bugs and Biases: Diagnosing Misconceptions in the Understanding of Diagrams. Proceedings of the 31st Annual Conference of the Cognitive Science Society

Misconceptions:

No order misconception

: Failure to understand that pathsare ordered (e. g., commits CYB).LAN-as-path misconception: Failure to see that a path

through a LAN visits intervening nodes in sequence, likea physical path (e.g., commits YRBMC)Omit bridge misconception/error

: Failure to recognize or

list a true bridge node (e.g., commits BC or omits BMC)

Commit bridge misconception/error

: Inferring a

nonexistent bridge node, or selectively committing the

LAN-as-path error (e.g., commits YRB)

Reading-order misconception/bias

: Listing only forward

paths (misconception); or omitting backwards paths more

often (bias)

Generate

all possible shortest paths of information flow for Network

1 and Network 2

On the difficulty of Bayesian Network

Diagrams BND

Where to go from here?

It has been argued that Bayesian reasoning is

counterintuitive

. People do not employ Bayesian reasoning intuitively, find it very difficult to learn Bayesian reasoning when tutored, and rapidly forget Bayesian methods once the tutoring is over. This limitation seems to hold equally true for novices and highly trained professionals in a field .

Yudkowsky (2009) An Intuitive Explanation of Baye's Theorem

Pointers for a better understanding diagrams

“Knowledge Representation for people”

Brachman (1985)

“Making Bayesian networks more accessible to the probabilistically unsophisticated”

Eugene

Charniak

(1991) Bayesian Networks without Tears. IA Magazine

Towards a new approach

1 - Pointers

Central role of human functioning D. Watson, Nobel prize winner (1968) (who discovered the structure of DNA): "drawing and thinking are frequently so simultaneous that the graphic image appears almost an organic extension of the thinking process".

Everyday diagramming

Composed of visual elements which each have some symbolic meaning

Expressing several different types of symbolic information

Contain a number

of

mixed visual styles

to express these different types respectively

Growing rather than finished

Having parts already drawn being replaced by others

Part of the thinking is inherent in communication

The diagramming process is fluid

Need a meta approach

Existing frameworks of understanding diagrams

Indexing

Synopsie

Free rides Useful awkwardnessUnevenness Lability

PermissivenessProgramming Salience Provisionality Story Content

Modifiability

Controllability

Referencability

Focus

Coordination

Documentation

Consistency

Accountability

Traceability

Visual immediacy

Visual impetus

Visual impedance

Plastic-robust

Weakly-strongly structured

Abstract-concrete

Different meaning - common structure

General-specific

Conventionalizedcustomized

Abstraction

Hidden dependencies Premature commitment Secondary notation

Viscosity Visibility Closeness of mapping Consistency Diffuseness Error-proneness Hard mental operations

Progressive evaluation Provisionality Role-expressiveness Creative Ambiguity Specificity

Detail in context

Too fine grained

Too broad/general

Bertin, Peirce, etc

Eppler et al (2008)

Reductionist

Spatial, visual, cognitive, etc..

Dooyeweerd's Meaning-Oriented Approach

Dooyeweerd said (

1955), "Meaning is the being of all that has been created and the nature even of our selfhood. It has a religious root and a divine origin."

This led him to presuppose that Meaning is the primary property of that is, and that Existence emerges from Meaning. Meaning is better grasped intuitively, not theoretically.

The ordinary person can understand it in the full, holistic sense of the word

Towards a new approach

2 – Philosophy

Meaning is given to the cosmos (by its Creator) as a framework.

The framework is a framework of law which provides guidance for how all entities function.

Diversity of types of existing based on a diversity of

types of meaningThis leads into the notion of

Aspects

Towards a new approach

3 – Aspectual Philosophy

Aspects

What do they mean

Numeric

Discrete quantity

Spatial

Continuous extension

Kinematic

Motion

Physical

Energy and matter

Biotic

Life and vitality

Sensitive

Seeing and feeling

Analytic

Distinction

Formative

Formative power

Lingual

Symbolic representation

Social

Social interaction and institutions

Economic

Frugality

Aesthetic

Harmony

Juridical

What is due

Ethical

Self-giving love, generosity

Pistic

Faith, vision, commitment

Aspects are irreducible

Aspects are related

Aspects are not absolute

Aspects are independent of things or entities

Aspects are rich

Numeric

Concerned with the number of shapes, etc.

Spatial

Concerned with things like shapes in the diagram, spatial arrangement, connectivity, etc.

Kinematic

This concerns the activity of diagramming itself when conveying symbolic meaning

Physical

This concerns the specific physical medium or substrate used to display the diagram

Biotic

This aspect concerns life functions that are a necessary precondition for the sensory and nervous systems to function well

enough for diagram creation or reading.

Sensitive

This concerns perceiving color, texture, etc.. and also emotions

Analytic

This aspect concerns the activity of distinguishing what is meaningful in a diagram from its background

Formative

The laws of this aspect govern the creation or formation of the symbol structure being expressed, and also of the method by which the drawing is composed.

Lingual /

Symbolic

This concerns conveyance of meaning

Social

This concerns social impact and norms used when diagramming

Economic

This concerns the cost of producing the diagram

Aesthetic

This concerns how well a diagram is presented

Juridical

This concerns issues such as copyrights

Ethical

Diagrams should not be offensive

Pistic

Diagrams could express faith

Qualifying Aspects of Diagrams

Multi Aspectual nature of diagrams

What is a SySpM?

A distinct collection of Sy elements, or as

A distinct collection of Sp elements, or asA distinct collection of M

No.

The SySpM

Mapping

1

Boxes and Arrows

Item mapped onto Box,

Relationship mapped onto Arrow

2

Communicating Similarity

A collection of items mapped onto a collection of shapes

3

Map of Objects

Item location mapped onto Icon position

4

Set Membership

A shape inside a loop mapped onto Member of a set

5

Bar Charts

Magnitude mapped onto Length of a bar

6

Route Maps

Route mapped onto Curvilinear Line

7

Contour Maps

The set of location with the same quantitative value mapped onto Closed continuous curve

8

Surface Coverage

Region mapped onto Area

Symbolic Aspect

Primary

Sy1. Items, entities: meaning deliberate intention of creator to symbolize a distinct concept2. Relationship: deliberate intention of creator to symbolize the idea that two items are related in a meaningful

way Secondary Sy

3. Direction of relationship4. Relationships can be treated as items

5. Types of items

6. Types of relationship

7. Names to identify the items or relationships

Box and Arrow type of diagram

Spatial Aspect

Primary Sp

1. Boxes: as being present rather than absent.2. A line which is straight, curved, or bent. Secondary Sp3. Boxes shape: this could be a pictogram, a diamond, a square, etc. Box shapes are considered as a spatial sub type of a thing and in this case it is a visual characteristics which may also include color, texture, etc.

4. Box visibility: distinction between 1 and 3 becomes important in software generated diagrams. A box could be present but hidden. Software should be able to understand that an invisible box does not necessarily mean it is not present.

5. Edges of boxes6. Position of box

7. Size of box

8. Boundary: outside rather than inside. This refers to the spatially defined vicinity of a thing. This is important in cases where a line ends in the vicinity of a box rather than on one of its edges.

9. Route of line.

10. Line texture: this refers to the use of dotted, dashed, thick/narrow features of lines.

11. Connect/Attach: this is about the attachment of a line end to a box in an unambiguous way as opposed to a line being in the vicinity of one box rather than another.

12. Arrow head. These may be of various kinds. They indicate direction of a line.

13. Text. These are used to identify boxes.

14. Empty background (white space): this may actually be decorated as in backdrop.

15. Width of a line.

Sy

Sp

M

Item

Box

Presence of a box

Relationship

Line

Presence of a line

The potential for creating new items

Background space (backdrop)

Empty = Non present

Item type

Shape of a box

Changing the shape of a box results in changing its item type

Relationship type

Texture

Changing the shape of a line results in changing its line type

Direction

Arrow head or other directionally specific visual effect or target

Redirecting the direction of an arrow results in redirection of its relationship

Name

Text

Text express name. Proximity of text to box/line links name to item/relationship

1. Sp Mapped to Sy

Sp

Size of a boxes (if not seen as different from shape)

Exact route of a line

Position of boxes

Relative alignment/proximity of boxes

Boxes/lines crossing

Thickness of a line does not map to anything in this

SySpM

except where thickness is treated as texture.

3. Sp Not Mapped to Sy

Sy reason

Sp constraint

Relationships must always be between items

Both ends of a line must always be connected to a box.

Items and its relationships move together

When a box moves all lines connected to it move with it

Items are self contained things

A box is a closed shape

2. Constraints

Putting it all together Continued

Sy

Sp

M

Create item

Box appears in empty space

Empty space indicate no items created thus far

Delete an item

Erase box

The space of a box becomes empty

Hide an item

Make box invisible

Removal of a box’s visual properties expresses hiding an item

an item

Divide a box into two boxes of similar size and shape to original box

Divide a box into two, ensure all lines remain joined to the two created boxes

Merge two items

Combine two boxes into one box of similar size and shape to original boxes

Bringing together two boxes indicates intention to combine

Create a relationship

Draw a line between two boxes

Growth of line indicates intention to relate and direction suggests which item will eventually relate

Detach a relationship

Erase a line

Detachment of both ends of a line indicates intention to erase

Delete an item with all of its relationships

Erase a box and lines connected to it

The space of the deleted item and its relationship becomes empty

Redirect a relationship

Disconnect a line from the edge of a box and change its position

Detachment of line end from box indicates intention to redirect, direction of movement of line can suggest which item, attachment o item indicates fulfillment of intention to redirect

Split a relationship to form two parallel relationships

Thicken the line, then split the line, then bend them apart, but ensure both lines continue to touch the original two boxes

Delete a line and create two other lines relating the same items

4. Handling Change

What does

this mean

for BND’s ?

Bayesian networks are complex diagrams

A definition of BND: “Bayesian networks are directed acyclic graphs whose:

nodes

represent

variables

, and whose

edges

represent

conditional relationships

between two variables”

Consider the use of the Box and Arrows diagram type and modify its constraints to reflect BND

Develop BND

a

s a new diagram type.

OR

1

2

A typical BND

Box and Arrows diagram

Tabular display