Bayesian network

BAYESIAN NETWORKS
BY-
KRUTIKA SHRIVASTAVA

• DNA hybridization arrays simultaneously measure the expression level for
thousands of genes.
• These measurements provide a “snapshot” of transcription levels within the cell.
• A major challenge in computational biology is to uncover, from such measurements,
gene/protein interactions and key biological features of cellular systems.
• Bayesian network helps to solve these.
• A Bayesian network is a graph-based model for conditional independence
assertions and hence for compact specification of full joint distributions.
• Such models are attractive,for their ability to describe complex processes, and since
they provide clear methodologies for learning from (noisy)observations.

• A Bayesian network B is defined as a pair B = (G, P), where G = (V (G),A(G)) is an
acyclic directed graph with a set of vertices (or nodes) V (G) = {X1,X2, . . . ,Xn}
• And a set of arcs A(G) ⊆ V (G) × V (G), and where P is a joint probability distribution
defined on the variables corresponding to the vertices V (G).
• The basic property of a Bayesian network is that the joint probability distribution
P(X1,X2, . . . ,Xn) is equivalent to the product of the(conditional) probabilities which
are specified for the network; formally:
P (X1, … ,Xn) = πi = 1 P (Xi | Parents(Xi))
where (Xi) is the set of parents of the vertex corresponding to the variable Xi.
Thus, P(Xi |(Xi)) are the (conditional) probability distributions which are specified
for the variable Xi,for i = 1, . . . , n, in creating a Bayesian network.

p(A,B,C) = p(C|A,B)p(A)p(B)
A B
C
FORMS OF THE BAYESIAN NETWORKS
A CB Marginal Independence:
p(A,B,C) = p(A) p(B) p(C)
A CB
Markov dependence:
p(A,B,C) = p(C|B) p(B|A)p(A)

A
CB
Conditionally independent effects:
p(A,B,C) = p(B|A)p(C|A)p(A)
B and C are conditionally independent
Given A

• Syntax:
o a set of nodes, one per variable
o a directed, acyclic graph (link ≈ "directly influences")
o a conditional distribution for each node given its parents:
P (Xi | Parents (Xi))
Constructing Bayesian networks
1. Choose an ordering of variables X1, … ,Xn
2. For i = 1 to n
add Xi to the network
select parents from X1, … ,Xi-1 such that
P (Xi | Parents(Xi)) = P (Xi | X1, ... Xi-1)
This choice of parents guarantees:
P (X1, … ,Xn) = πi =1 P (Xi | X1, … , Xi-1)
(chain rule)
= πi =1P (Xi | Parents(Xi))
(by construction)

SOFTWARES USED
o SamIam
o Genie
 SamIam is java-based and runs on all operating systems.
 An alternative package is Genie,a Windows-based system, which,
however, also runs on Linux ; it contains much more functionality
than SamIam.
 However, as a consequence of this, Genie it is less easy to use than
SamIam.

REAL LIFE EXAMPLE
Since the beginning of the 1990s researchers have been developing Bayesian networks
for many different problems.
Treatment of non-Hodgkin lymphoma of the stomach
• The problem
Non-Hodgkin lymphoma of the stomach, gastric NHL for short, is a relatively
uncommon malignant disorder, accounting for about 5% of tumours of the stomach.
Until recently, the cause of gastric NHL was unknown; it is now generally believed that
the main factor in the development of this disease is a chronic infection with the
bacterium Helicobacter pylori.
It was hoped that a Bayesian network of gastric NHL might help doctors in
the prescription of optimal treatment of a patient. The network discussed here is still
in prototype stage; further development needs to take place in order to introduce it in
actual clinical practice.

• Structure of the network
First, the information used in the clinical management of primary
gastric NHL was sub-divided in pre-treatment information, i.e. information that is
required for treatment selection,treatment information, i.e. the various treatment
alternatives, and post-treatment information,i.e. side effects, and early and long-term
treatment results for the disease.
The most important pre-treatment variables in the table are the
variable ‘clinical stage’, which expresses severity of the disease according to a
common clinical classification, and histological classification, which stands for the
assessment by a pathologist of tumour tissue obtained from a biopsy.
Various treatments are in use for gastric NHL such as
chemotherapy, radiotherapy, and a combination of these two, which has been
represented as the single variable ‘ct&rtschedule’ with possible values: chemotherapy
(CT), radiotherapy (RT), chemotherapy followed by radiotherapy (CT-next-RT), and
neither chemotherapy nor radiotherapy (none).

Furthermore, surgery is a therapy with is modelled by the
variable ‘surgery’ with possible values: ‘curative’, ‘palliative’ or ‘none’, where curative
surgery means total or partial resection of the stomach with the complete removal of
tumour mass.
Finally, prescription of antibiotics is also possible.
The most important post-treatment variables are the variable ‘early result’, being the
endoscopically verified result of the treatment, six to eight weeks after treatment
(possible outcomes are: complete remission – i.e. tumour cells are no longer
detectable –, partial remission – some tumour cells are detectable –, no change or
progressive disease),
And the variable ‘5-year result’, which represents the
patient either or not surviving five years following treatment.

CONCLUSION
• Bayesian nets are a network-based framework for representing and analyzing
models involving uncertainty
• Used for the cross fertilization of ideas between the artificial intelligence, decision
analysis, and statistic communities
• People are using this nowadays because of the development of propagation
algorithms followed by availability of easy to use commercial software.
• And growing number of creative applications.

REFERENCES :-
 Bayesian Networks by : Padhraic Smyth, UCIrvine.
 Probabilistic Reasoning in Intelligent Systems_ Networks of Plausible
Inference-Morgan Kaufmann (1988) , Judea Pearl
 Bayesian Networks 2011-2012 Practical Assignment I

Bayesian network

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