# Segmentation in the mean of heteroscedastic data via resampling

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

m

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

m

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

m

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

m

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

m

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## Complexity measure in the homoscedastic setup

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 2

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## Heteroscedastic data

0 5 10 15 20 25 30 35 40 45 50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Average estimated loss for Reg= 1, S= 5

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u∈Sm

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(Xi,Yi)

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(Xi,Yi)

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(Xi,Yi)

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(Xi,Yi)

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## BM, VFCV: performance (number of breakpoints)

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2 0.25 0.3

0.35 Average estimated loss for Reg= 1, S= 2 Ideal VFCV BM

### Homoscedastic

0 10 20 30 40 50

0 0.05 0.1 0.15 0.2

0.25 Average estimated loss for Reg= 2, S= 5 Ideal VFCV BM

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## Quality of the segmentations: Homoscedastic

5 10 15 20 25 30 35 40 45 50

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Average estimated loss for r= 3, b= 2

ERM LOO

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## Quality of the segmentations: Heteroscedastic

5 10 15 20 25 30 35 40 45 50

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10−5 Average estimated loss for r= 3, b= 12

ERM LOO

5 10 15 20 25 30 35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Average estimated loss for r= 3, b= 7

ERM LOO

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## Overfitting with ERM: dimension 6

0 10 20 30 40 50 60 70 80 90 100

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−1.5

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−0.5 0 0.5 1 1.5

ERM LOO Oracle

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## Overfitting with ERM: dimension 7

0 10 20 30 40 50 60 70 80 90 100

−2

−1.5

−1

−0.5 0 0.5 1 1.5

ERM LOO Oracle

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## Overfitting with ERM: dimension 8

0 10 20 30 40 50 60 70 80 90 100

−2

−1.5

−1

−0.5 0 0.5 1 1.5

ERM LOO Oracle

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## Overfitting with ERM: dimension 9

0 10 20 30 40 50 60 70 80 90 100

−2

−1.5

−1

−0.5 0 0.5 1 1.5

ERM LOO Oracle

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## Overfitting with ERM: dimension 10

0 10 20 30 40 50 60 70 80 90 100

−2

−1.5

−1

−0.5 0 0.5 1 1.5

ERM LOO Oracle

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## Results: Chromosome 9

Homoscedastic model (Picardet al.(05))

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## Results: Chromosome 1

Homoscedastic model (Picardet al.(05))

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## References

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