A Richer Understanding of Bayesian Network Diagrams

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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 science

Linguistics

Visual programming

Data visualisation

Graphic design

Education

History and philosophy of science

Architecture

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 diagrams

Boxes and lines

Contour maps

Bar charts

etc..



2.

Diversity of types of change (dynamics)

Different types of diagrams require different editing operations

Different 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 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 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 paths

are ordered (e. g., commits CYB).


LAN
-
as
-
path misconception
: Failure to see that a path

through a LAN visits intervening nodes in sequence, like

a 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 awkwardness

Unevenness

Lability

Permissiveness

Programming 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 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 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 as

A 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
Sy

1. 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
Sy

3. Direction of
relationship

4. 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 Sp

3. Boxes shape: this could be a pictogram, a diamond, a square, etc. Box shapes are considered as a spatial sub type of a thi
ng
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

wh
ere 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 t
he
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