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 psychologyCognitive scienceLinguisticsVisual programmingData visualisationGraphic designEducationHistory and philosophy of scienceArchitecture

Blackwell and Engelhardt (1999)

Eppler, 2003

But.... Diagrams continue to be difficult to understand and work with

There 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 formedness

3. All of the above in semantically mixed diagramsEven 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 Issues

SCHOOL 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 paththrough a LAN visits intervening nodes in sequence, likea physical path (e.g., commits YRBMC)

Omit bridge misconception/error: Failure to recognize orlist a true bridge node (e.g., commits BC or omits BMC)

Commit bridge misconception/error: Inferring anonexistent bridge node, or selectively committing theLAN-as-path error (e.g., commits YRB)

Reading-order misconception/bias: Listing only forwardpaths (misconception); or omitting backwards paths moreoften (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 ModifiabilityControllability Referencability Focus Coordination Documentation Consistency Accountability Traceability Visual immediacy Visual impetus Visual impedance

Plastic-robust Weakly-strongly structuredAbstract-concrete Different meaning - common structureGeneral-specificConventionalizedcustomizedAbstraction 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 meaning

This 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 wellenough 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 Mapping1 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 concept

2. Relationship: deliberate intention of creator to symbolize the idea that two items are related in a meaningful way

 Secondary Sy3. Direction of relationship4. Relationships can be treated as items5. Types of items6. Types of relationship7. Names to identify the items or relationships

Box and Arrow type of diagram

Spatial Aspect Primary Sp1. 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 boxes

6. 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 MItem Box Presence of a boxRelationship 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

SpSize of a boxes (if not seen as different from shape)Exact route of a linePosition of boxesRelative alignment/proximity of boxesBoxes/lines crossingThickness 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 MCreate item Box appears in empty space Empty space indicate no items

created thus farDelete 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 as a new diagram type.

OR

1 2

A typical BND

Box and Arrows diagram

Tabular display