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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