Ies are processed. Six inducing points are applied to each FITC and VFE. Experiment 2: Impacts of s f on prediction accuracy and uncertainty. l is set to the 2 optimised worth. s f varies from 0.1 via to 30.0. n is set to 0.5 and 1.5, respectively. NO data from each cities are processed. Six inducing points are applied to each FITC and VFE. Experiment 3: Impacts of l on prediction accuracy and uncertainty. s f is set to the 2 optimised worth. l varies from 0.1 by means of to 30.0. n is set to 0.5 and 1.5, respectively. NO information from both cities are processed. Six inducing points are applied to both FITC and VFE.RMSE =iNum (yi – yi )two =1 , Num(34)where yi is definitely the ground truth value and yi represents predicted meant. Num is the sample number in testing set. figures 5 and six show the outcomes from Experiment 1. To produce the outcomes additional two distinguishable, the horizontal axes of the figures are set to log(n ). We can see from 2 is small, GPs carry out the ideal generally, although the functionality Figure 5 that when n 2 of FITC and VFE varies. We are able to also observe that as n keeps increasing, the RMSE becomes Karrikinolide web really substantial for all methods/pollutants. Related results is often observed from Figure six as well. Both comply with our theoretical conclusions, regardless of the fact that the two Neumann series is used to approximate the matrix inverse. We also notice that n features a two ) reaches a lot more important impact on Sheffield data as RMSE increases ealier right after log(nAtmosphere 2021, 12,11 ofzero. From Figure 6b,c, we also see that the Undecan-2-ol Cancer uncertainty bounds of Sheffield data are two greater right after log(n ) reaches zero. We feel the purpose is the fact that Sheffield data are usually much less periodical than Pershawar data (see Figure two), which influences the performance of your models.Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITCPesh-NO -GPPesh-NO two -VFE2.two.Pesh-NO -FITCShef-NO2 -GP Shef-NO -VFEShef-NO2 -FITC1.1.0.0.—-(a)3Pesh-SO -GP2 2(b)Pesh-PM2.5 two.five two.-GP -VFE -FITCPesh-SO -VFE2.Pesh-SO -FITC Shef-SO -GP2 22.Pesh-PM Pesh-PM Shef-PMShef-SO -VFE2.5 2.5 2.-GP -VFE -FITCShef-SO -FITCShef-PM Shef-PM1.1.0.0.—-(c)(d)2 Figure five. Relationship of n with four pollutants prediction RMSE: (a) NO, (b) NO2 , (c) SO2 , (d) PM2.five .8 6 4 2 0 -2 -2 -1 0 1 2 3Pesh_NO_GP Pesh_NO_VFE Pesh_NO_FITC Shef_NO_GP Shef_NO_VFE Shef_NO_FITC8 7 6 five 4 three two 1 0 -1 -2 -2 -1 0 1 2 3Pesh-NO 2 -GP Pesh-NO 2 -VFE Pesh-NO 2 -FITC Shef-NO2 -GP Shef-NO2 -VFE Shef-NO2 -FITC(a)8 7 6 five 4 4 3Pesh-SO2 -GP(b)8 7 6Pesh-PM 2.five -GP Pesh-PM two.five -VFE Pesh-PM 2.five -FITC Shef-PM 2.five -GP Shef-PM 2.5 -VFE Shef-PM 2.5 -FITCPesh-SO2 -VFE Pesh-SO2 -FITC Shef-SO 2 -GP Shef-SO 2 -VFE Shef-SO 2 -FITC1 0 -1 -2 -2 -1 0 12 1 0 -1 four -2 -1 0 1 two three(c)(d)two Figure six. Connection of n with pollutants prediction uncertainty bound: (a) NO, (b) NO2 , (c) SO2 , (d) PM2.5 .Atmosphere 2021, 12,12 of4.3. Impacts of Noise Level on ELBO and UBML Figure 7 shows the outcomes from Experiment two. As outlined by our theoretical outcomes, the impact of s f around the uncertainty should really turn into higher as s f increases. This is verified by the results shown in Figure 7b,d. Our theoretical benefits also recommend that the variation of s f wouldn’t have an effect on the prediction accuracy. We can see from Figure 7a,c that when s f is smaller sized, it does impact the prediction accuracy, but when it exceeds a certain value, the impacts come to be negligible. Contemplating the Neumann series approximation, we would say that the experimental results comply using the theoretical.
