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Table 3 A comprehensive comparison of our method with previous methods on real world datasets, COVID-19 Air and Khan Academy. We use the same abbreviations as in Table 1. For COVID-19, the measure of \(t_{0}\) is number of days since 01/01/2020. For Khan Academy, the measure of \(t_{0}\) is Unix timestamp, namely, number of seconds since midnight 01/01/1970. Correct values are roughly 80 days for COVID-19 air data, and \(1.365 \times 10^{9}\) seconds for Khan Academy data. Bold values indicate change points that are closest to the correct value

From: Leveraging change point detection to discover natural experiments in data

  

COVID Air

Khan

  

Time (day)

Time (sec)

MtChD(RF)

\(\mu (t_{0})\)

80.0829

\(\mathbf{1.3703e}{\boldsymbol{+}}\mathbf{09}\)

\(\sigma (t_{0})\)

2.9713

\(\mathbf{2.6992e}{\boldsymbol{+}}\mathbf{05}\)

μ(α)

0.4164

0.2803

σ(α)

0.0392

0.0029

MtChD(MLP)

\(\mu (t_{0})\)

99.5820

\(\mathbf{1.3694e}{\boldsymbol{+}}\mathbf{09}\)

\(\sigma (t_{0})\)

99.5820

\(\mathbf{1.3694e}{\boldsymbol{+}}\mathbf{09}\)

μ(α)

0.4843

0.1491

σ(α)

0.3264

0.0173

DP + Normal

\(\mu (t_{0})\)

71.8333

1.3577e+09

(Normal GLR eq.)

\(\sigma (t_{0})\)

0.3727

2.2059e+07

DP + RBF

\(\mu (t_{0})\)

37.1667

1.3763e+09

\(\sigma (t_{0})\)

25.5761

9.4481e+06

DP + L2

\(\mu (t_{0})\)

70.1667

1.3679e+09

\(\sigma (t_{0})\)

53.8911

1.0014e+07

BinSeg + RBF

\(\mu (t_{0})\)

1.0000

1.3741e+09

\(\sigma (t_{0})\)

0.0000

8.9074e+06

Window + RBF

\(\mu (t_{0})\)

55.0000

1.3587e+09

\(\sigma (t_{0})\)

0.0000

1.2031e+07

BottomUp + RBF

\(\mu (t_{0})\)

54.0000

1.3528e+09

\(\sigma (t_{0})\)

0.8165

1.2960e+06

Uniform + Gaussian

\(\mu (t_{0})\)

96.9167

1.3439e+09

\(\sigma (t_{0})\)

37.5859

4.2047e+06

Uniform + IFM

\(\mu (t_{0})\)

−0.5833

1.3564e+09

\(\sigma (t_{0})\)

0.8858

1.5300e+07

Uniform + FullCov

\(\mu (t_{0})\)

0.0000

1.3591e+09

\(\sigma (t_{0})\)

0.6455

1.6176e+07

Geo + Gaussian

\(\mu (t_{0})\)

8.1667

1.3396e+09

\(\sigma (t_{0})\)

8.9334

2.9504e+05