1. Bayesian Networks II: Dynamic Networks and Markov Chains By Peter Woolf (pwoolf@umich.edu) University of Michigan Michigan Chemical Process Dynamics and Controls Open Textbook version 1.0 Creative commons

2. Existing plant measurements 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

3. From http://www.norsys.com/netlib/car_diagnosis_2.htm Static Bayesian Network Example 1: Car failure diagnosis network

4. 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.

5. weight  ALT survival RBC procedure Yesterday (t i-1 ) Today (t i ) weight  ALT survival RBC procedure Unrolled Network Dynamic Bayesian Networks weight  ALT survival RBCprocedure These are both examples of Dynamic Bayesian Networks (DBNs) OR Collapsed Network

6. Predicts future responses weight  weight  ALT survival RBC procedure ALT survival RBC procedure ALT survival RBC procedure weight  ALT survival RBC procedure weight  weight  ALT survival RBC procedure ALT survival RBC procedure ALT survival RBC procedure weight  ALT survival RBC procedure t i-1 titi t i-2 t i-3 t i+1 t i+2 Model derived from past data weight  weight  ALT survival RBC procedure ALT survival RBC procedure ALT survival RBC procedure weight  ALT survival RBC procedure

7. Today (t i ) Tomorrow (t i+1 ) weight  ALT survival RBC procedure weight  ALT survival RBC procedure Dynamic Bayesian Networks: Predict to explore alternatives DBNs provide a suitable environment for MPC!

8. DBN: Thermostat example From http://www.norsys.com/networklibrary.html# N: fluctuations Time(t) titi+1 H: Heater T: Temperature G: Temp Set Pt. S: Switch V: Value/Cost N: fluctuations H: Heater T: Temperature G: Temp Set Pt. S: Switch V: Value/Cost Unrolled network Collapsed network

9. N: fluctuations Time(t) titi+1 H: Heater T: Temperature N: fluctuations H: Heater T: Temperature Simplified DBN A Dynamic Bayesian Network can be recast as a Markov Network 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 Markov network describes how a system will transition from system state to state {000} {001} {010} {110} {011} {111} {101} {100}

10. 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} {001} {010} {110} {011} {111} {101} {100} Each edge has a probability associated with it. Note: All rows must sum to 1 P1+P2=1 P5=1 etc.

11. 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

12. Case Study 1: Synthetic Study GFP Gene A Gene B Gene C Idealized Data

13. Case Study 1: Synthetic Study GFP Gene A Gene B Gene C Noisy data

14. 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

15. Case Study 1: Synthetic Study Google “miniTUBA” or go to http://ncibi.minituba.org

16. 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

17. 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