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 independentGiven A

• Syntax:• 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, … ,Xn2. For i = 1 to nadd Xi to the network

select parents from X1, … ,Xi-1 such thatP (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)

EXAMPLE

Learning phase

Testing phase (inference)

SOFTWARES USED

o SamIamo 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 theendoscopically 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

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