Table 7: Performance of the best two CP methods (HopCPT and SPCI) and state-of-the-art non-CP methods for the different datasets and levels of  $\alpha$ . All approaches build upon an LSTM model. Bold numbers correspond to the best result for the respective metric in the experiment (PI-Width and Winkler score), given that  $\Delta \mathrm{Cov} \geq -0.25\alpha$ , i.e., the specific algorithm reached at least approximate coverage (the result is grayed out otherwise). The error term represents the standard deviation over repeated runs with different seeds (results without an error term are from deterministic models).
α	HopCPT	SPCI	MCD	Gauss	MDN
Solar 3Y	0.05	Δ CovPI-WidthWinkler	-0.003±0.00522.7±0.80.38±0.01	0.004±0.00047.7±0.000	-0.058±0.00417.5±0.10.75±0.01	-0.331±0.24325.9±4.10.46±0.10	-0.005±0.01316.2±1.00.33±0.06
0.10	Δ CovPI-WidthWinkler	0.001±0.00617.9±0.60.30±0.01	0.014±0.00027.8±0.000	-0.030±0.00614.8±0.10.49±0.00	-0.310±0.23821.8±3.50.37±0.06	-0.013±0.04713.2±0.80.26±0.03
0.15	Δ CovPI-WidthWinkler	0.002±0.00715.0±0.40.26±0.00	0.024±0.00018.1±0.000	0.001±0.00712.9±0.10.38±0.00	-0.320±0.16619.1±3.00.32±0.04	-0.053±0.1411.4±0.80.23±0.02
Solar 1Y	0.05	Δ CovPI-WidthWinkler	0.019±0.00321.4±0.70.27±0.01	0.006±0.00037.0±0.000	-0.041±0.00420.5±0.30.58±0.01	-0.109±0.19114.6±0.80.22±0.01	-0.055±0.10413.2±1.40.20±0.03
0.10	Δ CovPI-WidthWinkler	0.028±0.01016.0±0.60.22±0.01	0.018±0.00022.5±0.000	-0.011±0.00517.3±0.20.40±0.01	-0.134±0.25312.3±0.70.18±0.01	-0.130±0.18210.8±1.20.17±0.02
0.15	Δ CovPI-WidthWinkler	0.029±0.01713.1±0.50.19±0.00	0.032±0.00015.3±0.000	0.022±0.00615.2±0.20.32±0.00	-0.148±0.23610.8±0.60.16±0.01	-0.185±0.2249.3±1.10.15±0.02
Air 10 PM	0.05	Δ CovPI-WidthWinkler	-0.001±0.00190.7±1.91.83±0.03	0.003±0.00086.1±0.01.63±0.00	-0.202±0.00842.3±0.82.36±0.03	-0.191±0.02445.8±2.22.08±0.12	-0.218±0.11543.9±9.52.22±0.59
0.10	Δ CovPI-WidthWinkler	-0.002±0.00562.7±1.51.33±0.01	0.010±0.00062.2±0.01.21±0.00	-0.201±0.00935.7±0.71.49±0.01	-0.211±0.02638.6±1.91.42±0.06	-0.243±0.12235.3±7.31.48±0.30
0.15	Δ CovPI-WidthWinkler	-0.002±0.01049.4±1.71.09±0.01	0.017±0.00050.2±0.01.01±0.00	-0.192±0.00931.4±0.61.16±0.01	-0.218±0.02733.8±1.71.15±0.04	-0.252±0.12230.2±6.01.17±0.20
Air 25 PM	0.05	Δ CovPI-WidthWinkler	0.005±0.00557.1±5.61.19±0.08	-0.015±0.00044.9±0.011.29±0.00	-0.100±0.02231.7±3.51.41±0.05	-0.227±0.01827.1±1.41.58±0.08	-0.209±0.11926.9±6.11.57±0.47
0.10	Δ CovPI-WidthWinkler	0.007±0.00840.7±4.30.88±0.05	-0.017±0.00032.4±0.0000.93±0.00	-0.095±0.02726.6±3.00.95±0.03	-0.247±0.02022.8±1.21.06±0.04	-0.234±0.12921.6±4.91.05±0.24
0.15	Δ CovPI-WidthWinkler	0.005±0.01132.5±3.70.74±0.04	-0.016±0.00026.1±0.0000.76±0.00	-0.086±0.03023.2±2.60.76±0.02	-0.253±0.02020.0±1.00.85±0.02	-0.243±0.13118.4±4.20.84±0.16
Sap flow	0.05	Δ CovPI-WidthWinkler	0.001±0.002783.5±9.20.25±0.01	0.000±0.000897.7±0.90.33±0.00	-0.150±0.007421.6±5.20.49±0.01	-0.072±0.018494.7±26.00.29±0.02	-0.059±0.035494.6±41.20.27±0.06
0.10	Δ CovPI-WidthWinkler	0.004±0.004594.3±7.70.19±0.01	0.004±0.000628.2±0.90.24±0.00	-0.139±0.007355.2±4.30.30±0.01	-0.067±0.022416.5±21.90.20±0.01	-0.067±0.037391.7±31.40.19±0.03
0.15	Δ CovPI-WidthWinkler	0.005±0.005489.9±7.00.17±0.01	0.006±0.000493.2±0.50.20±0.00	-0.122±0.007311.4±3.80.23±0.01	-0.059±0.024364.9±19.20.17±0.01	-0.068±0.039331.5±25.80.16±0.02