Ies are processed. Six inducing points are applied to each FITC and VFE. Experiment two:

Ies are processed. Six inducing points are applied to each FITC and VFE. Experiment two: Impacts of s f on prediction accuracy and uncertainty. l is set towards the 2 optimised worth. s f varies from 0.1 by means of to 30.0. n is set to 0.five and 1.five, respectively. NO information from each cities are processed. Six inducing points are applied to both FITC and VFE. Experiment 3: Impacts of l on prediction accuracy and uncertainty. s f is set for the two optimised value. l varies from 0.1 by means of to 30.0. n is set to 0.5 and 1.five, respectively. NO data from each cities are processed. Six inducing points are applied to both FITC and VFE.RMSE =iNum (yi – yi )two =1 , Num(34)exactly where yi would be the ground truth worth and yi represents predicted meant. Num would be the sample number in testing set. Figures five and six show the results from Experiment 1. To make the results far more two distinguishable, the horizontal axes of the figures are set to log(n ). We can see from 2 is smaller, GPs carry out the best in general, when the functionality Hexythiazox supplier Figure 5 that when n 2 of FITC and VFE varies. We can also observe that as n keeps rising, the RMSE becomes incredibly important for all methods/pollutants. Equivalent benefits might be observed from Figure six at the same time. Both comply with our theoretical conclusions, regardless of the truth that the two Neumann series is applied to approximate the matrix inverse. We also notice that n includes a two ) reaches more SID 7969543 Data Sheet considerable impact on Sheffield data as RMSE increases ealier just after log(nAtmosphere 2021, 12,11 ofzero. From Figure 6b,c, we also see that the uncertainty bounds of Sheffield information are 2 higher immediately after log(n ) reaches zero. We assume the reason is the fact that Sheffield information are normally much less periodical than Pershawar data (see Figure 2), which influences the efficiency of the models.Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITCPesh-NO -GPPesh-NO 2 -VFE2.2.Pesh-NO -FITCShef-NO2 -GP Shef-NO -VFEShef-NO2 -FITC1.1.0.0.—-(a)3Pesh-SO -GP2 2(b)Pesh-PM2.five 2.five two.-GP -VFE -FITCPesh-SO -VFE2.Pesh-SO -FITC Shef-SO -GP2 22.Pesh-PM Pesh-PM Shef-PMShef-SO -VFE2.five 2.five 2.-GP -VFE -FITCShef-SO -FITCShef-PM Shef-PM1.1.0.0.—-(c)(d)2 Figure 5. Partnership of n with four pollutants prediction RMSE: (a) NO, (b) NO2 , (c) SO2 , (d) PM2.five .eight six 4 2 0 -2 -2 -1 0 1 two 3Pesh_NO_GP Pesh_NO_VFE Pesh_NO_FITC Shef_NO_GP Shef_NO_VFE Shef_NO_FITC8 7 six five 4 3 2 1 0 -1 -2 -2 -1 0 1 2 3Pesh-NO two -GP Pesh-NO two -VFE Pesh-NO two -FITC Shef-NO2 -GP Shef-NO2 -VFE Shef-NO2 -FITC(a)8 7 6 5 4 4 3Pesh-SO2 -GP(b)eight 7 6Pesh-PM two.five -GP Pesh-PM 2.five -VFE Pesh-PM two.five -FITC Shef-PM 2.5 -GP Shef-PM two.5 -VFE Shef-PM two.five -FITCPesh-SO2 -VFE Pesh-SO2 -FITC Shef-SO 2 -GP Shef-SO 2 -VFE Shef-SO two -FITC1 0 -1 -2 -2 -1 0 12 1 0 -1 4 -2 -1 0 1 2 3(c)(d)2 Figure 6. Relationship of n with pollutants prediction uncertainty bound: (a) NO, (b) NO2 , (c) SO2 , (d) PM2.5 .Atmosphere 2021, 12,12 of4.three. Impacts of Noise Level on ELBO and UBML Figure 7 shows the outcomes from Experiment 2. In accordance with our theoretical benefits, the impact of s f around the uncertainty should develop into higher as s f increases. This really is verified by the results shown in Figure 7b,d. Our theoretical results also recommend that the variation of s f would not impact the prediction accuracy. We are able to see from Figure 7a,c that when s f is smaller, it does have an effect on the prediction accuracy, but when it exceeds a specific worth, the impacts come to be negligible. Thinking of the Neumann series approximation, we would say that the experimental results comply with all the theoretical.