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Bayesian Networks II: Dynamic Networks and Markov Chains By Peter Woolf ([email protected])

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Dynamic Networks and

Markov Chains

By Peter Woolf ([email protected])

University of MichiganMichigan Chemical Process Dynamics and Controls Open Textbookversion 1.0

Creative commons

Physics, chemistry, and chemical engineering knowledge & intuition

Bayesian network models to establish connections

Patterns of likely causes & influences

Efficient experimental design to test combinations of causes

ANOVA & probabilistic models to eliminate irrelevant or uninteresting relationships

Process optimization (e.g. controllers, architecture, unit optimization, sequencing, and utilization)

Dynamical process modeling

Static Bayesian Network Example 1:

Car failure diagnosis network

From http://www.norsys.com/netlib/car_diagnosis_2.htm

Static Bayesian Network Example 2:

ALARM network: A Logical Alarm Reduction Mechanism

A medical diagnostic system for patient monitoring with 8 diagnoses, 16 findings, and 13 intermediate values

From Beinlich, Ingo, H. J. Suermondt, R. M. Chavez, and G. F. Cooper (1989) "The ALARM monitoring system: A case study with two probabilistic inference techniques for belief networks" in Proc. of the Second European Conf. on Artificial Intelligence in Medicine (London, Aug.), 38, 247-256. Also Tech. Report KSL-88-84, Knowledge Systems Laboratory, Medical Computer Science, Stanford Univ., CA.

RBC

ALT

procedure

OR

weight

survival

These are both examples of

Dynamic Bayesian Networks

(DBNs)

Dynamic Bayesian NetworksUnrolled Network

Yesterday

(ti-1)

Today

(ti)

ALT

ALT

RBC

RBC

procedure

procedure

survival

survival

weight

weight

Model derived from past data

ti+2

ti

ti+1

ti-1

ti-2

ti-3

ALT

ALT

ALT

ALT

ALT

ALT

ALT

ALT

ALT

ALT

ALT

ALT

RBC

RBC

RBC

RBC

RBC

RBC

RBC

RBC

RBC

RBC

RBC

RBC

procedure

procedure

procedure

procedure

procedure

procedure

procedure

procedure

procedure

procedure

procedure

procedure

survival

survival

survival

survival

survival

survival

survival

survival

survival

survival

survival

survival

weight

weight

weight

weight

weight

weight

weight

weight

weight

ALT

RBC

RBC

procedure

procedure

survival

survival

weight

weight

Dynamic Bayesian Networks:Predict to explore alternativesToday

(ti)

Tomorrow

(ti+1)

DBNs provide a suitable environment for MPC!

ti ti+1

N: fluctuations

N: fluctuations

H: Heater

H: Heater

T: Temperature

T: Temperature

G: Temp Set Pt.

G: Temp Set Pt.

S: Switch

S: Switch

V: Value/Cost

V: Value/Cost

Unrolled network

DBN: Thermostat example

Collapsed network

From http://www.norsys.com/networklibrary.html#

{110}

{001}

{100}

{011}

{111}

{101}

{010}

Time(t)

ti ti+1

A Dynamic Bayesian Network can be recast as a Markov Network

A Markov network describes how a system will transition from system state to state

N: fluctuations

N: fluctuations

H: Heater

H: Heater

T: Temperature

T: Temperature

Simplified DBN

Assume each variable is binary (has states 1 or 0), thus any configuration could be written as {010} meaning N=0, H=1, T=0

A Dynamic Bayesian Network can be recast as a Markov Network

A Markov network describes how a system will transition from system state to state

{000}

{110}

{001}

{100}

Note: All rows must sum to 1

P1+P2=1

P5=1 etc.

{011}

{111}

{101}

{010}

Each edge has a probability associated with it.

Case Study: Synthetic Study

Situation: Imagine that we are exploring the effect of a DNA damaging drug and UV light on the expression of 4 genes.

GFP

Gene A

Gene B

Gene C

Case Study 1: Synthetic Study

Noisy data

Idealized Data

Given idealized or noisy data, can we find any relationships

between the drug, UV exposure, GFP, and the gene

expression profiles?

See miniTUBA.demodata.xls

Case Study 1: Synthetic Study

Google “miniTUBA” or go to http://ncibi.minituba.org

Case study 1: synthetic data

- Observations:
- Stronger relationships require fewer observations to identify
- Noise in measurements are okay
- Moderate binning errors are forgivable
- Uncontrolled experiments can be your friend in model learning

Take Home Messages

- Noisy, time varying processes can be modeled as a Dynamic Bayesian Network (DBN)
- A DBN can be recast as a Markov model of a stochastic system
- DBNs can be learned directly from data using tools such as miniTUBA

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