Hidden Markov Model for Bad Data Detection. Semester: Spring 2019 Presentation 1 Date: Feb 8, 2019

1. Department of Electrical Engineering
University of Arkansas
Hidden Markov Model for
Bad Data Detection
Md Abul Hayat
mahayat@uark.edu
Feb 8, 2019

2. Contents
• Markov Assumption
• State Space Models
– Properties
– Dynamic Linear Model
• Hidden Markov Model
– Introduction
• Problem Formulations
– Mathematical Proofs
• Experimental Results

3. Markov Assumption

4. Markov Assumption

5. State Space Model

6. Dynamic Linear Models
• Dynamic Linear Models

7. Hidden Markov Model

8. Hidden Markov Model

9. Three Problems in HMM

10. Overview of Data
• 6 Patients, each having 2 signals or time series data
– We denote them as PAT# 33, 34, 35, 36, 37, 39
• Each patient has two signals
– PVP: Peripheral Venous Pressure (Blood Pressure Collected from Vein)
• Weak Periodic Component
– PZO: Peizo-electric Signal (Corresponds to Heart Rate)
• Strong Periodic Component
• Both these signals were sampled at 1000 samples/ second
• I am using data with sampling rate of 100 samples/ second
– 100 samples or data points correspond to 1 second.

11. Hidden Markov Model
• Hidden States (Discrete)
For each sample i, there is a hidden state
– θi = 0, which corresponds to good data and Yi ~ N(μ0, σ0
2)
– Similarly θi = 1, corresponds to bad data with Yi ~ N(μ1, σ1
2)
• Estimating Parameters: Baum-Welch (EM for HMM)
• Estimating States: Viterbi Algorithm

12. Evaluation Problem (Forward Algorithm)

13. Evaluation Problem (Forward Algorithm)

14. Evaluation Problem (Forward Algorithm)

15. Decoding Problem (Forward - Backward)

16. Decoding Problem (Forward - Backward)

17. Decoding Problem (Forward - Backward)

18. Decoding Problem

19. Decoding Problem (Viterbi Algorithm)

20. Decoding Problem (Viterbi Algorithm)

21. Decoding Problem (Viterbi Algorithm)

22. Learning Problem (Baum-Welch)

23. Learning Problem (Baum-Welch)

24. Learning Problem (Baum-Welch)

25. Hidden Markov Model - Summary

26. Experimental Results
• Hidden States (Discrete)
For each sample i, there is a hidden state
– θi = 0, which corresponds to good data and Yi ~ N(μ0, σ0
2)
– Similarly θi = 1, corresponds to bad data with Yi ~ N(μ1, σ1
2)
• Estimating Parameters: Baum-Welch (EM for HMM)
• Estimating States: Viterbi Algorithm

27. HMM Results (PAT# 34)
$pm$mean $pm$sd
[1] 37.94871 51.65487 [1] 1.372279 13.391213

28. HMM Results (PAT# 35)
$pm$mean $pm$sd
[1] 7.637553 12.593328 [1] 0.8133069 5.4323029

29. HMM Results (PAT# 36)
$pm$mean $pm$sd
[1] 13.24376 17.34136 [1] 1.120354 1.735898

30. HMM Results (PAT# 37)
$pm$mean $pm$sd
[1] 25.48785 27.44577 [1] 0.4980413 1.8101689

31. HMM Results (PAT# 39)
$pm$mean $pm$sd
[1] -3.167427 9.069818 [1] 1.574438 12.219896

32. HMM Results (PAT# 33)
$pm$mean $pm$sd
[1] -24.62568 -11.19702 [1] 1.423284 9.781044

33. Comments on PVP Data Model Assumptions
• Two distributions should have different mean which are far apart.
• Bad part of data should have significantly large variance.
• The distribution changes after a big noise spike in some cases.
• HMM with Gaussian Distribution is good at removing sudden
spikes from time series data.
• Non-stationary assumption should also be taken care of.

34. HMM Results (PAT# 33 Continued)

35. HMM Results (PAT# 33 Continued)
– Using HMM for PZO can be used for more granular cleaning of both PVP
and PZO signals
– The distribution is not normal, other distributions can also be used.
– Can be modelled using 3 states.
PZO Signal

36. Thanks for your patience !
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