Data analysis Piecewise-constant linear regression Hidden Markov - - PowerPoint PPT Presentation

data analysis piecewise constant linear regression hidden
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Data analysis Piecewise-constant linear regression Hidden Markov - - PowerPoint PPT Presentation

Data analysis Piecewise-constant linear regression Hidden Markov Models Let x t denote the log-transformed data and u t the underlying signal. A transition kernel accounting for shift and drift Hidden state space: grid with Algorithmic


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Data analysis

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Piecewise-constant linear regression

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Hidden Markov Models

Let xt denote the log-transformed data and ut the underlying signal.

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A transition kernel accounting for shift and drift

Hidden state space: grid with

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Algorithmic complexity O(nK 2)

Take the example of Forward-Backward.

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Impact of the grid step h = UG

BT /1]TJ111110Tf 125.754

  • 90996d

[( UGmaxBT /1]53.9701 Tf 12.1.79 90996d [( UG TJ/F48 7.9701 Tf 1252287 Td [( =)

  • BT

/1]TJ111110Tf 125.754

  • 1.514d

[( UGminBT / ET 1 1 141.5156.275 cm []0 d 1 J 90436 w 1 m 40.013 1 [ 362 Td [( =)

  • g7Tf

12.711 4.8955 T88m 05 T000TJ/FK.9701 Tf 12.1.79 906 1 9 BT /1]T48 7.9701 Tf 1252287 Td [( =)

  • BT

/1]T11 0g G g G g G g G g G g G BT /F24 10 1 141.515628.346 75UG 4d 1 835.3535241.515.3535241.51 1 83249.449 cm51 1 /Im10 Do [( 8 G =) ]T.) ]T.25 rg =) ]T.) ]T.25 RG3249.449

  • 28.346
  • 75UG

4d 1 .9091 Tf8.96647 Td28.346 575 000TJ/FLL

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Model comparison

Cross-Validated Log-Likelihood for robust assessment of model fitness.

Model d

  • s
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Correlation between breakpoints and biological features

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