All convergence scores per package:algorithm sored by minimum RMSE

Input parameter
RMSE Score
Other score
Package Algorithm Input format Maxit Learn.rate median D51 MAE WAE
nlsr
  1. NashLM
full fmla & data 200 N/A 3 16 3 6
rminer
  1. nnet_optim(BFGS)
fmla & data 200 N/A 1 6 1 1
nnet
  1. optim (BFGS)
x & y 200 N/A 2 17 2 3
validann
  1. optim(BFGS)
x & y 200 N/A 4 10 4 5
  1. optim(CG)
x & y 1000 N/A 6 10 5 4
  1. optim(L-BFGS-B)
x & y 200 N/A 13 30 14 13
  1. optim(Nelder-Mead)
x & y 10000 N/A 44 45 46 42
  1. optim(SANN)
x & y 1000 N/A 53 51 56 55
MachineShop
  1. nnet_optim(BFGS)
fmla & data 200 N/A 9 22 9 7
traineR
  1. nnet_optim(BFGS)
fmla & data 200 N/A 5 15 6 2
radiant.model
  1. nnet_optim(BFGS)
“y” & data 200 N/A 8 32 12 10
monmlp
  1. optimx(BFGS)
x & y 200 N/A 10 18 9 11
  1. optimx(Nelder-Mead)
x & y 10000 N/A 47 45 44 47
CaDENCE
  1. optim(BFGS)
x & y 200 N/A 28 48 21 40
  1. Rprop
x & y 1000 0.01 54 60 52 58
  1. pso_psoptim
x & y 1000 N/A 56 56 54 56
h2o
  1. first-order
“y” & data 10000 0.01 7 7 8 8
EnsembleBase
  1. nnet_optim(BFGS)
x & y 200 N/A 15 34 15 15
caret
  1. avNNet_nnet_optim(BFGS)
x & y 200 N/A 10 21 11 9
brnn
  1. Gauss-Newton
x & y 200 N/A 12 9 13 12
qrnn
  1. nlm()
x & y 200 N/A 14 25 7 36
RSNNS
  1. Rprop
x & y 1000 N/A 23 52 25 28
  1. SCG
x & y 1000 N/A 17 26 18 19
  1. Std_Backpropagation
x & y 1000 0.1 32 31 31 36
  1. BackpropChunk
x & y 1000 N/A 34 41 32 34
  1. BackpropMomentum
x & y 1000 N/A 35 39 35 30
  1. BackpropWeightDecay
x & y 1000 N/A 30 43 33 31
  1. BackpropBatch
x & y 10000 0.1 48 27 50 48
  1. Quickprop
x & y 10000 N/A 58 36 58 57
automl
  1. trainwgrad_adam
x & y 1000 0.01 20 35 16 20
  1. trainwgrad_RMSprop
x & y 1000 0.01 31 50 29 39
  1. trainwpso
x & y 1000 N/A 41 49 41 38
deepnet
  1. BP
x & y 1000 0.8 18 38 24 17
neuralnet
  1. rprop+
fmla & data 100000 N/A 23 40 23 24
  1. rprop-
fmla & data 100000 N/A 21 42 21 18
  1. slr
fmla & data 100000 N/A 39 37 39 46
  1. sag
fmla & data 100000 N/A 49 59 47 52
  1. backprop
fmla & data 100000 0.001 51 10 49 45
keras
  1. adamax
x & y 10000 0.1 18 20 20 16
  1. adam
x & y 10000 0.1 28 44 30 25
  1. nadam
x & y 10000 0.1 39 58 40 41
  1. adagrad
x & y 10000 0.1 43 53 42 35
  1. adadelta
x & y 10000 0.1 35 19 34 33
  1. sgd
x & y 10000 0.1 45 47 45 43
  1. rmsprop
x & y 10000 0.1 55 57 55 54
AMORE
  1. ADAPTgdwm
x & y 1000 0.01 22 29 16 26
  1. ADAPTgd
x & y 1000 0.01 25 8 26 21
  1. BATCHgdwm
x & y 10000 0.1 33 14 37 27
  1. BATCHgd
x & y 10000 0.1 38 24 42 31
minpack.lm
  1. Levenberg-Marquardt
full fmla & data 200 N/A 16 5 19 14
ANN2
  1. rmsprop
x & y 1000 0.01 25 33 27 23
  1. adam
x & y 1000 0.01 27 27 28 21
  1. sgd
x & y 1000 0.01 37 22 36 29
deepdive
  1. adam
x & y 10000 0.4 42 1 38 44
  1. rmsProp
x & y 1000 0.8 46 4 48 50
  1. momentum
x & y 1000 0.8 52 3 53 51
  1. gradientDescent
x & y 10000 0.8 57 2 57 53
snnR
  1. SemiSmoothNewton
x & y 200 N/A 49 13 50 48
elmNNRcpp
  1. ELM
x & y
N/A 59 55 59 59
ELMR
  1. ELM
fmla & data
N/A 60 53 60 60



Packages Tested per Multivariate Dataset

mDette

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.128 0.4391 0.4564 0.0173 0.3246 2.0005 1
train_ADAPTgdwm 0.184 0.3972 0.4012 0.0040 0.3084 1.7312 2
train_BATCHgd 1.870 1.8688 1.8999 0.0311 1.5158 8.6487 3
train_BATCHgdwm 1.862 1.8586 1.9806 0.1220 1.4990 11.2445 4
ANN2 neuralnetwork_adam 0.218 1.7980 2.0396 0.2416 1.5178 11.5812 5
neuralnetwork_rmsprop 0.206 1.9463 2.0761 0.1298 1.5240 12.6858 6
neuralnetwork_sgd 0.204 1.2208 2.0228 0.8020 1.4953 8.6218 7
automl automl_train_manual_trainwgrad_adam 9.584 0.4255 0.6160 0.1905 0.4710 3.2585 8
automl_train_manual_trainwgrad_RMSprop 8.632 0.4821 0.6996 0.2175 0.5006 3.8172 9
automl_train_manual_trainwpso 13.696 2.7275 4.9634 2.2359 3.7904 24.2831 10
brnn brnn_Gauss-Newton 0.216 0.4578 1.9537 1.4959 1.4572 11.8945 11
CaDENCE cadence.fit_optim 7.072 0.3277 2.5664 2.2387 1.2936 17.3208 12
cadence.fit_psoptim 11.258 3.1663 3.6338 0.4675 2.1362 22.3798 13
cadence.fit_Rprop 17.178 4.6664 5.7488 1.0824 3.4794 31.0108 14
caret avNNet_none 0.252 0.3175 0.3514 0.0339 0.2681 1.8536 15
deepdive deepnet_adam 0.738 3.0971 3.0971 0.0000 2.0640 18.6373 16
deepnet_gradientDescent 7.266 4.4310 4.4310 0.0000 3.2628 20.7622 17
deepnet_momentum 7.434 4.1990 4.1990 0.0000 3.1011 18.5512 18
deepnet_rmsProp 0.758 2.7205 2.7205 0.0000 1.8705 16.1780 19
deepnet nn.train_BP 0.648 0.5308 0.6403 0.1095 0.5135 2.7237 20
elmNNRcpp elm_train_extremeML 0.004 7.3193 7.6899 0.3706 5.9574 32.3344 21
ELMR OSelm_train.formula_extremeML 0.018 6.3469 7.2310 0.8841 5.5344 32.0052 22
EnsembleBase Regression.Batch.Fit_none 0.026 0.8770 13.9426 13.0656 11.3013 47.5398 23
h2o h2o.deeplearning_first-order 6.274 0.3696 0.3789 0.0093 0.2948 1.3228 24
keras fit_adadelta 29.372 2.0733 2.3080 0.2347 1.5890 13.7080 25
fit_adagrad 18.384 1.5412 2.2114 0.6702 1.5982 12.7204 26
fit_adam 2.068 0.7615 1.0487 0.2872 0.7949 6.3699 27
fit_adamax 4.386 0.6492 0.6952 0.0460 0.5462 4.1959 28
fit_nadam 3.422 1.0271 1.2485 0.2214 0.9787 4.9790 29
fit_rmsprop 1.836 2.6780 3.2516 0.5736 2.3382 16.3052 30
fit_sgd 8.816 0.5726 2.3026 1.7300 1.6878 10.2998 31
MachineShop fit_none 0.076 0.2570 1.2314 0.9744 0.9854 8.0327 32
minpack.lm nlsLM_none 0.242 0.6081 0.6081 0.0000 0.4989 1.9776 33
monmlp monmlp.fit_BFGS 0.298 0.3732 0.4512 0.0780 0.3380 1.8359 34
monmlp.fit_Nelder-Mead 1.100 3.0247 3.4557 0.4310 2.5277 18.0917 35
neuralnet neuralnet_backprop 14.200 8.1656 8.1656 0.0000 6.5262 36.2385 36
neuralnet_rprop- 6.318 0.5338 2.0473 1.5135 1.4437 12.5391 37
neuralnet_rprop+ 3.836 0.4859 0.5467 0.0608 0.4149 2.3410 38
neuralnet_sag 12.916 2.1196 8.1656 6.0460 6.5262 36.2385 39
neuralnet_slr 6.914 0.5494 0.5688 0.0194 0.4293 2.4012 40
nlsr nlxb_none 0.522 0.1400 0.4500 0.3100 0.3497 2.7841 41
nnet nnet_none 0.078 0.2650 0.4735 0.2085 0.3557 2.0121 42
qrnn qrnn.fit_none 0.518 0.3632 0.7514 0.3882 0.4482 6.6249 43
radiant.model nn_none 0.112 0.2621 0.5412 0.2791 0.4096 2.1475 44
rminer fit_none 0.248 0.2335 0.3147 0.0812 0.2456 1.2905 45
RSNNS mlp_BackpropBatch 6.752 1.9746 2.0170 0.0424 1.5451 10.0256 46
mlp_BackpropChunk 0.702 0.5892 0.7126 0.1234 0.5252 2.8993 47
mlp_BackpropMomentum 0.688 0.6547 0.7744 0.1197 0.5909 3.1612 48
mlp_BackpropWeightDecay 0.654 0.6328 0.7698 0.1370 0.5856 3.0364 49
mlp_Quickprop 7.460 7.1667 7.3190 0.1523 6.0055 29.6111 50
mlp_Rprop 0.692 0.7757 1.2553 0.4796 0.9246 7.6985 51
mlp_SCG 1.156 0.4652 1.7312 1.2660 1.2784 7.8765 52
mlp_Std_Backpropagation 0.638 0.4789 0.5588 0.0799 0.4219 2.0582 53
snnR snnR_none 0.140 1.9864 1.9864 0.0000 1.5889 8.8501 54
traineR train.nnet_none 0.078 0.4539 0.5799 0.1260 0.4649 2.6448 55
validann ann_BFGS 1.712 0.2730 0.4266 0.1536 0.3155 1.9320 56
ann_CG 11.228 0.3813 0.4231 0.0418 0.3165 1.8043 57
ann_L-BFGS-B 1.828 0.4455 1.5927 1.1472 1.1539 8.9132 58
ann_Nelder-Mead 2.126 3.1073 3.5453 0.4380 2.7197 17.3854 59
ann_SANN 0.172 3.3417 4.0522 0.7105 2.9633 19.6574 60

mFriedman

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.128 0.0264 0.0296 0.0032 0.0235 0.1101 1
train_ADAPTgdwm 0.178 0.0439 0.0450 0.0011 0.0321 0.1788 2
train_BATCHgd 1.876 0.0177 0.0816 0.0639 0.0748 0.1692 3
train_BATCHgdwm 1.882 0.0173 0.0176 0.0003 0.0138 0.0586 4
ANN2 neuralnetwork_adam 0.234 0.0183 0.0201 0.0018 0.0166 0.0579 5
neuralnetwork_rmsprop 0.226 0.0250 0.0314 0.0064 0.0251 0.0945 6
neuralnetwork_sgd 0.222 0.0178 0.0185 0.0007 0.0147 0.0603 7
automl automl_train_manual_trainwgrad_adam 9.568 0.0277 0.0323 0.0046 0.0250 0.1346 8
automl_train_manual_trainwgrad_RMSprop 8.550 0.0397 0.0504 0.0107 0.0399 0.2019 9
automl_train_manual_trainwpso 14.836 0.1029 0.1228 0.0199 0.0976 0.3922 10
brnn brnn_Gauss-Newton 0.238 0.0046 0.0052 0.0006 0.0043 0.0154 11
CaDENCE cadence.fit_optim 9.226 0.0160 0.0863 0.0703 0.0442 0.3640 12
cadence.fit_psoptim 12.056 0.0950 0.1148 0.0198 0.0739 0.4058 13
cadence.fit_Rprop 22.516 0.0850 0.1295 0.0445 0.0858 0.5842 14
caret avNNet_none 0.288 0.0123 0.0197 0.0074 0.0162 0.0727 15
deepdive deepnet_adam 0.768 0.0875 0.0875 0.0000 0.0764 0.2699 16
deepnet_gradientDescent 7.642 0.1474 0.1474 0.0000 0.1154 0.4581 17
deepnet_momentum 7.848 0.1363 0.1363 0.0000 0.1061 0.4860 18
deepnet_rmsProp 0.772 0.1287 0.1287 0.0000 0.0990 0.4133 19
deepnet nn.train_BP 0.664 0.0396 0.0967 0.0571 0.0838 0.2139 20
elmNNRcpp elm_train_extremeML 0.000 0.1516 0.1734 0.0218 0.1379 0.5055 21
ELMR OSelm_train.formula_extremeML 0.008 0.1677 0.1924 0.0247 0.1538 0.5716 22
EnsembleBase Regression.Batch.Fit_none 0.092 0.0245 0.0262 0.0017 0.0181 0.1321 23
h2o h2o.deeplearning_first-order 6.046 0.0225 0.0261 0.0036 0.0204 0.0902 24
keras fit_adadelta 29.424 0.0257 0.0267 0.0010 0.0211 0.0948 25
fit_adagrad 14.836 0.0296 0.0842 0.0546 0.0747 0.2012 26
fit_adam 2.160 0.0636 0.0774 0.0138 0.0612 0.2686 27
fit_adamax 4.326 0.0326 0.0395 0.0069 0.0319 0.1140 28
fit_nadam 2.482 0.0732 0.0992 0.0260 0.0817 0.3144 29
fit_rmsprop 2.240 0.1010 0.1147 0.0137 0.0860 0.3822 30
fit_sgd 4.136 0.0365 0.0527 0.0162 0.0403 0.1922 31
MachineShop fit_none 0.106 0.0085 0.0116 0.0031 0.0092 0.0360 32
minpack.lm nlsLM_none 0.380 0.1269 0.1269 0.0000 0.1009 0.3714 33
monmlp monmlp.fit_BFGS 0.308 0.0132 0.0139 0.0007 0.0110 0.0465 34
monmlp.fit_Nelder-Mead 1.084 0.1155 0.1219 0.0064 0.0960 0.3777 35
neuralnet neuralnet_backprop 14.676 0.2348 0.2348 0.0000 0.1880 0.6346 36
neuralnet_rprop- 5.058 0.0095 0.0110 0.0015 0.0085 0.0412 37
neuralnet_rprop+ 5.862 0.0102 0.0106 0.0004 0.0083 0.0356 38
neuralnet_sag 13.202 0.0806 0.2348 0.1542 0.1880 0.6346 39
neuralnet_slr 12.928 0.0690 0.2348 0.1658 0.1880 0.6346 40
nlsr nlxb_none 0.762 0.0045 0.0061 0.0016 0.0048 0.0196 41
nnet nnet_none 0.102 0.0091 0.0120 0.0029 0.0094 0.0404 42
qrnn qrnn.fit_none 0.578 0.0105 0.0296 0.0191 0.0190 0.1330 43
radiant.model nn_none 0.122 0.0084 0.0150 0.0066 0.0106 0.0664 44
rminer fit_none 0.286 0.0095 0.0112 0.0017 0.0088 0.0373 45
RSNNS mlp_BackpropBatch 6.886 0.0434 0.0851 0.0417 0.0754 0.2084 46
mlp_BackpropChunk 0.732 0.0541 0.0657 0.0116 0.0532 0.2284 47
mlp_BackpropMomentum 0.706 0.0558 0.0789 0.0231 0.0582 0.2590 48
mlp_BackpropWeightDecay 0.726 0.0429 0.0595 0.0166 0.0488 0.1832 49
mlp_Quickprop 7.502 0.1664 0.1722 0.0058 0.1384 0.5541 50
mlp_Rprop 0.706 0.0307 0.0452 0.0145 0.0374 0.1660 51
mlp_SCG 1.140 0.0202 0.0218 0.0016 0.0170 0.0747 52
mlp_Std_Backpropagation 0.694 0.0420 0.0900 0.0480 0.0761 0.2168 53
snnR snnR_none 0.102 0.0457 0.0839 0.0382 0.0747 0.2113 54
traineR train.nnet_none 0.094 0.0112 0.0263 0.0151 0.0209 0.0954 55
validann ann_BFGS 2.500 0.0096 0.0688 0.0592 0.0500 0.1513 56
ann_CG 25.592 0.0163 0.0184 0.0021 0.0145 0.0580 57
ann_L-BFGS-B 2.702 0.0211 0.0256 0.0045 0.0208 0.0865 58
ann_Nelder-Mead 6.334 0.0991 0.1082 0.0091 0.0820 0.3701 59
ann_SANN 0.204 0.1414 0.1485 0.0071 0.1149 0.5629 60

mIshigami

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.222 0.7690 0.8135 0.0445 0.6083 2.9968 1
train_ADAPTgdwm 0.330 0.8636 0.9950 0.1314 0.7280 3.8394 2
train_BATCHgd 2.624 2.5215 2.5544 0.0329 2.1768 6.3018 3
train_BATCHgdwm 2.678 2.4805 2.5259 0.0454 2.1518 6.4536 4
ANN2 neuralnetwork_adam 1.058 0.7560 0.8062 0.0502 0.6130 3.5492 5
neuralnetwork_rmsprop 1.048 0.7045 0.8590 0.1545 0.6409 2.9940 6
neuralnetwork_sgd 1.048 0.7787 0.9097 0.1310 0.6798 3.8085 7
automl automl_train_manual_trainwgrad_adam 9.932 0.7511 0.7995 0.0484 0.6120 2.9212 8
automl_train_manual_trainwgrad_RMSprop 8.882 1.8225 2.5662 0.7437 2.1749 6.0520 9
automl_train_manual_trainwpso 25.376 1.8381 2.4317 0.5936 1.9867 7.8872 10
brnn brnn_Gauss-Newton 0.204 0.6588 0.6635 0.0047 0.5100 2.9395 11
CaDENCE cadence.fit_optim 14.912 1.0465 1.6993 0.6528 0.8815 5.3208 12
cadence.fit_psoptim 14.936 2.6775 2.7432 0.0657 2.3281 8.8488 13
cadence.fit_Rprop 36.926 1.3422 2.3133 0.9711 1.3927 8.8022 14
caret avNNet_none 0.418 1.0310 1.6339 0.6029 1.3615 4.7983 15
deepdive deepnet_adam 0.902 2.5913 2.5913 0.0000 2.0819 10.0604 16
deepnet_gradientDescent 9.062 3.0218 3.0218 0.0000 2.4940 10.2360 17
deepnet_momentum 9.220 2.5791 2.5791 0.0000 2.0107 8.7569 18
deepnet_rmsProp 0.892 2.6728 2.6728 0.0000 2.3060 7.1452 19
deepnet nn.train_BP 0.770 1.0536 1.4687 0.4151 1.0190 6.8677 20
elmNNRcpp elm_train_extremeML 0.000 3.0949 3.2590 0.1641 2.6511 11.3823 21
ELMR OSelm_train.formula_extremeML 0.008 3.2348 3.2840 0.0492 2.6674 12.0160 22
EnsembleBase Regression.Batch.Fit_none 0.132 0.6342 0.8141 0.1799 0.5735 3.9523 23
h2o h2o.deeplearning_first-order 6.462 0.8347 0.8467 0.0120 0.6295 3.6234 24
keras fit_adadelta 31.676 2.4074 2.6007 0.1933 2.2281 6.9184 25
fit_adagrad 31.856 0.8522 2.5746 1.7224 2.1958 6.9534 26
fit_adam 2.796 0.9777 1.0728 0.0951 0.7886 4.0357 27
fit_adamax 5.302 0.8307 0.8615 0.0308 0.6388 3.6379 28
fit_nadam 3.264 1.0800 2.7592 1.6792 2.3587 8.0273 29
fit_rmsprop 1.924 2.8335 3.0118 0.1783 2.4550 9.4367 30
fit_sgd 2.788 2.7076 2.7302 0.0226 2.3252 7.5362 31
MachineShop fit_none 0.152 0.6685 2.1956 1.5271 1.7857 5.3089 32
minpack.lm nlsLM_none 0.940 2.5379 2.5379 0.0000 2.0524 7.6035 33
monmlp monmlp.fit_BFGS 0.460 0.8185 0.9739 0.1554 0.7577 3.6164 34
monmlp.fit_Nelder-Mead 1.600 2.7368 2.8463 0.1095 2.3257 8.7509 35
neuralnet neuralnet_backprop 23.958 3.6898 3.6898 0.0000 2.9776 13.1137 36
neuralnet_rprop- 1.954 0.6728 0.7126 0.0398 0.5316 2.8674 37
neuralnet_rprop+ 4.596 0.5788 0.6650 0.0862 0.5052 2.7746 38
neuralnet_sag 25.218 3.6898 3.6898 0.0000 2.9776 13.1137 39
neuralnet_slr 24.586 0.6816 3.6898 3.0082 2.9776 13.1137 40
nlsr nlxb_none 1.470 0.6602 2.2311 1.5709 1.8053 5.7864 41
nnet nnet_none 0.152 0.5462 0.6959 0.1497 0.5147 3.0034 42
qrnn qrnn.fit_none 1.122 0.7656 0.7907 0.0251 0.4951 4.0838 43
radiant.model nn_none 0.172 0.4934 0.7868 0.2934 0.5896 3.1250 44
rminer fit_none 0.446 0.6490 0.6668 0.0178 0.5016 3.0019 45
RSNNS mlp_BackpropBatch 8.542 2.6668 2.6742 0.0074 2.3004 7.1688 46
mlp_BackpropChunk 0.816 1.3784 2.6226 1.2442 2.0664 8.9928 47
mlp_BackpropMomentum 0.822 2.6138 2.6595 0.0457 2.1268 10.0368 48
mlp_BackpropWeightDecay 0.854 1.2711 2.0728 0.8017 1.5275 7.9148 49
mlp_Quickprop 9.656 3.4245 3.5389 0.1144 2.8752 13.1137 50
mlp_Rprop 0.840 1.3146 2.3451 1.0305 1.8953 6.5010 51
mlp_SCG 1.456 0.6980 0.7363 0.0383 0.5439 3.0529 52
mlp_Std_Backpropagation 0.814 2.7659 2.8040 0.0381 2.1912 11.0805 53
snnR snnR_none 0.430 0.7757 0.8621 0.0864 0.6030 3.4730 54
traineR train.nnet_none 0.152 0.6846 0.7400 0.0554 0.5453 3.2851 55
validann ann_BFGS 5.086 0.6342 0.7284 0.0942 0.5216 3.3533 56
ann_CG 58.524 0.6427 0.7212 0.0785 0.5352 3.3323 57
ann_L-BFGS-B 5.418 0.8502 1.1103 0.2601 0.8812 3.5016 58
ann_Nelder-Mead 16.114 2.6029 2.6812 0.0783 2.2886 7.2908 59
ann_SANN 0.270 2.9199 2.9986 0.0787 2.4922 10.0706 60

mRef153

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.038 3.3184 3.3402 0.0218 2.3679 13.7131 1
train_ADAPTgdwm 0.050 3.3209 3.5541 0.2332 2.5492 14.1047 2
train_BATCHgd 1.436 3.3610 3.5412 0.1802 2.5557 13.2065 3
train_BATCHgdwm 1.438 3.3094 3.4478 0.1384 2.4907 13.6270 4
ANN2 neuralnetwork_adam 0.042 3.4586 3.4861 0.0275 2.5495 13.6835 5
neuralnetwork_rmsprop 0.050 3.2991 3.3581 0.0590 2.4231 13.0278 6
neuralnetwork_sgd 0.046 3.5190 3.6375 0.1185 2.6189 13.4490 7
automl automl_train_manual_trainwgrad_adam 2.760 3.4616 3.7944 0.3328 2.7431 15.5607 8
automl_train_manual_trainwgrad_RMSprop 2.792 3.5937 3.9015 0.3078 2.7453 14.5783 9
automl_train_manual_trainwpso 6.730 3.7011 3.9237 0.2226 2.8771 13.9777 10
brnn brnn_Gauss-Newton 0.020 3.4791 3.4796 0.0005 2.5068 13.7382 11
CaDENCE cadence.fit_optim 3.666 3.2677 3.7049 0.4372 2.6819 15.6761 12
cadence.fit_psoptim 7.650 3.7348 3.8749 0.1401 2.7851 15.8749 13
cadence.fit_Rprop 9.946 3.7332 4.3519 0.6187 3.0787 16.5513 14
caret avNNet_none 0.042 3.2329 3.3749 0.1420 2.3825 12.7439 15
deepdive deepnet_adam 0.638 3.7605 3.7605 0.0000 2.6651 15.3279 16
deepnet_gradientDescent 5.964 4.1805 4.1805 0.0000 3.1843 14.4946 17
deepnet_momentum 6.090 3.8424 3.8424 0.0000 2.7879 15.0474 18
deepnet_rmsProp 0.638 4.0384 4.0384 0.0000 3.0290 15.7099 19
deepnet nn.train_BP 0.206 3.4561 3.8740 0.4179 2.9819 15.8992 20
elmNNRcpp elm_train_extremeML 0.000 16.4917 18.7626 2.2709 15.3993 53.2953 21
ELMR OSelm_train.formula_extremeML 0.000 9.4764 15.5973 6.1209 12.5855 41.9893 22
EnsembleBase Regression.Batch.Fit_none 0.016 3.0740 3.4380 0.3640 2.4557 13.5954 23
h2o h2o.deeplearning_first-order 4.408 3.2514 3.5349 0.2835 2.5500 14.8677 24
keras fit_adadelta 7.872 3.8172 3.9063 0.0891 2.9028 14.4159 25
fit_adagrad 3.186 3.8952 3.9503 0.0551 2.9457 13.8555 26
fit_adam 1.430 3.9276 4.1763 0.2487 3.1624 14.4220 27
fit_adamax 2.194 3.7083 3.9479 0.2396 2.9160 15.5093 28
fit_nadam 1.434 4.1342 4.5026 0.3684 3.4678 16.1957 29
fit_rmsprop 0.996 4.5931 6.6007 2.0076 5.4044 17.1610 30
fit_sgd 2.398 3.7419 4.2292 0.4873 3.1633 15.5181 31
MachineShop fit_none 0.014 3.1772 3.4737 0.2965 2.4888 13.8862 32
minpack.lm nlsLM_none 0.068 3.4318 3.4318 0.0000 2.4646 13.2825 33
monmlp monmlp.fit_BFGS 0.224 3.2360 3.2363 0.0003 2.2071 14.2052 34
monmlp.fit_Nelder-Mead 0.544 3.7710 4.1087 0.3377 3.0462 15.0511 35
neuralnet neuralnet_backprop 0.104 3.8593 4.2101 0.3508 3.1568 14.3890 36
neuralnet_rprop- 0.010 3.4657 3.9379 0.4722 2.8577 15.5126 37
neuralnet_rprop+ 0.018 3.4475 3.9946 0.5471 2.8060 16.5481 38
neuralnet_sag 0.874 3.3829 3.7868 0.4039 2.6065 16.3454 39
neuralnet_slr 0.026 3.8201 3.9883 0.1682 2.9187 15.3885 40
nlsr nlxb_none 0.116 3.1128 3.4349 0.3221 2.4566 14.5501 41
nnet nnet_none 0.012 3.0865 3.2253 0.1388 2.2336 13.9974 42
qrnn qrnn.fit_none 0.180 3.2636 3.4540 0.1904 2.1362 15.2840 43
radiant.model nn_none 0.050 3.1803 3.3593 0.1790 2.4590 13.9894 44
rminer fit_none 0.048 3.1128 3.1819 0.0691 2.1870 13.5191 45
RSNNS mlp_BackpropBatch 2.068 3.5172 3.6890 0.1718 2.7410 14.2974 46
mlp_BackpropChunk 0.212 3.5933 3.8022 0.2089 2.7830 14.4056 47
mlp_BackpropMomentum 0.210 3.4853 4.0633 0.5780 3.1325 14.3828 48
mlp_BackpropWeightDecay 0.246 3.4319 3.7632 0.3313 2.8900 14.3467 49
mlp_Quickprop 2.094 6.3871 8.1528 1.7657 6.2517 24.5588 50
mlp_Rprop 0.202 3.1838 3.5905 0.4067 2.5733 14.7429 51
mlp_SCG 0.326 3.2498 3.2841 0.0343 2.2854 14.4231 52
mlp_Std_Backpropagation 0.234 3.5707 3.6319 0.0612 2.6701 14.8068 53
snnR snnR_none 0.020 4.3529 4.3529 0.0000 3.2423 15.2576 54
traineR train.nnet_none 0.014 3.1128 3.3913 0.2785 2.4098 13.3731 55
validann ann_BFGS 0.904 3.2262 3.3341 0.1079 2.3356 14.3369 56
ann_CG 30.460 3.1175 3.2299 0.1124 2.1865 13.2863 57
ann_L-BFGS-B 1.038 3.2380 3.5703 0.3323 2.6699 14.7850 58
ann_Nelder-Mead 22.952 3.9234 4.1325 0.2091 3.1924 14.4615 59
ann_SANN 0.140 5.7592 7.3556 1.5964 5.9016 19.8265 60


Packages Tested per Univariate Dataset

uDmod1

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.036 0.3082 0.3271 0.0189 0.2829 0.7263 1
train_ADAPTgdwm 0.054 0.2197 0.2765 0.0568 0.2204 0.6575 2
train_BATCHgd 1.780 0.2023 0.2922 0.0899 0.2393 0.6802 3
train_BATCHgdwm 1.804 0.3265 0.3274 0.0009 0.2853 0.7289 4
ANN2 neuralnetwork_adam 0.012 0.2198 0.2274 0.0076 0.1806 0.5242 5
neuralnetwork_rmsprop 0.016 0.2345 0.2495 0.0150 0.1926 0.6040 6
neuralnetwork_sgd 0.014 0.2581 0.3342 0.0761 0.2899 0.6824 7
automl automl_train_manual_trainwgrad_adam 1.262 0.0596 0.1157 0.0561 0.0741 0.5060 8
automl_train_manual_trainwgrad_RMSprop 1.128 0.1052 0.1595 0.0543 0.1323 0.3299 9
automl_train_manual_trainwpso 6.964 0.2424 0.2517 0.0093 0.1929 0.6461 10
brnn brnn_Gauss-Newton 0.010 0.0451 0.5884 0.5433 0.5069 1.0104 11
CaDENCE cadence.fit_optim 2.442 0.0564 0.2112 0.1548 0.1061 0.6888 12
cadence.fit_psoptim 5.378 0.3096 0.3190 0.0094 0.2672 0.7427 13
cadence.fit_Rprop 6.654 0.2005 0.4116 0.2111 0.3162 0.8665 14
caret avNNet_none 0.030 0.0535 0.0948 0.0413 0.0602 0.3176 15
deepdive deepnet_adam 0.568 0.1178 0.1178 0.0000 0.0797 0.4868 16
deepnet_gradientDescent 5.340 0.3353 0.3353 0.0000 0.2912 0.7067 17
deepnet_momentum 5.524 0.3320 0.3320 0.0000 0.2891 0.7441 18
deepnet_rmsProp 0.584 0.1728 0.1728 0.0000 0.1257 0.4478 19
deepnet nn.train_BP 0.094 0.0582 0.1173 0.0591 0.0845 0.3896 20
elmNNRcpp elm_train_extremeML 0.000 0.3320 0.3623 0.0303 0.3038 0.8727 21
ELMR OSelm_train.formula_extremeML 0.000 0.3003 0.3082 0.0079 0.2529 0.7867 22
EnsembleBase Regression.Batch.Fit_none 0.004 0.0733 0.1033 0.0300 0.0759 0.4193 23
h2o h2o.deeplearning_first-order 3.346 0.0480 0.0494 0.0014 0.0402 0.1185 24
keras fit_adadelta 23.966 0.2314 0.2333 0.0019 0.1843 0.5698 25
fit_adagrad 8.322 0.2252 0.3529 0.1277 0.3037 0.8099 26
fit_adam 2.576 0.1376 0.1811 0.0435 0.1461 0.4721 27
fit_adamax 4.566 0.0883 0.2240 0.1357 0.1782 0.5854 28
fit_nadam 2.242 0.1786 0.2607 0.0821 0.2055 0.6971 29
fit_rmsprop 1.326 0.2375 0.3800 0.1425 0.2964 0.8503 30
fit_sgd 2.644 0.2044 0.3548 0.1504 0.2992 0.8224 31
MachineShop fit_none 0.012 0.0442 0.0456 0.0014 0.0365 0.1181 32
minpack.lm nlsLM_none 0.038 0.0445 0.0445 0.0000 0.0362 0.1153 33
monmlp monmlp.fit_BFGS 0.208 0.0919 0.0983 0.0064 0.0750 0.3693 34
monmlp.fit_Nelder-Mead 0.428 0.1381 0.2639 0.1258 0.2153 0.6177 35
neuralnet neuralnet_backprop 0.490 0.1521 0.1699 0.0178 0.1280 0.5924 36
neuralnet_rprop- 0.030 0.1634 0.1750 0.0116 0.1370 0.5212 37
neuralnet_rprop+ 0.042 0.1086 0.1639 0.0553 0.1319 0.5153 38
neuralnet_sag 1.430 0.0583 0.1315 0.0732 0.1061 0.3669 39
neuralnet_slr 0.100 0.0839 0.1213 0.0374 0.0922 0.3196 40
nlsr nlxb_none 0.088 0.0433 0.0433 0.0000 0.0349 0.1063 41
nnet nnet_none 0.008 0.0437 0.0865 0.0428 0.0636 0.3435 42
qrnn qrnn.fit_none 0.230 0.1162 0.1349 0.0187 0.0830 0.6014 43
radiant.model nn_none 0.026 0.0800 0.1088 0.0288 0.0817 0.3346 44
rminer fit_none 0.030 0.0449 0.0495 0.0046 0.0418 0.1258 45
RSNNS mlp_BackpropBatch 0.874 0.2568 0.3344 0.0776 0.2870 0.7691 46
mlp_BackpropChunk 0.140 0.1298 0.1448 0.0150 0.1073 0.5245 47
mlp_BackpropMomentum 0.088 0.1445 0.1647 0.0202 0.1252 0.5800 48
mlp_BackpropWeightDecay 0.090 0.1314 0.1656 0.0342 0.1218 0.5395 49
mlp_Quickprop 0.938 0.5775 0.5884 0.0109 0.5068 1.0104 50
mlp_Rprop 0.090 0.1232 0.1401 0.0169 0.1048 0.4453 51
mlp_SCG 0.140 0.0970 0.1118 0.0148 0.0916 0.4280 52
mlp_Std_Backpropagation 0.094 0.1215 0.2226 0.1011 0.1736 0.5618 53
snnR snnR_none 0.040 0.2927 0.2927 0.0000 0.2512 0.6561 54
traineR train.nnet_none 0.004 0.0410 0.0470 0.0060 0.0393 0.1293 55
validann ann_BFGS 0.790 0.0435 0.0725 0.0290 0.0540 0.1810 56
ann_CG 29.066 0.0506 0.0679 0.0173 0.0544 0.1577 57
ann_L-BFGS-B 0.880 0.0489 0.1090 0.0601 0.0759 0.4093 58
ann_Nelder-Mead 28.208 0.1034 0.1810 0.0776 0.1538 0.4017 59
ann_SANN 0.128 0.2296 0.3046 0.0750 0.2441 0.6614 60

uDmod2

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.022 0.2579 0.2632 0.0053 0.2333 0.5307 1
train_ADAPTgdwm 0.034 0.1145 0.1924 0.0779 0.1573 0.4195 2
train_BATCHgd 1.650 0.2228 0.2644 0.0416 0.2347 0.4989 3
train_BATCHgdwm 1.650 0.1585 0.2621 0.1036 0.2341 0.4898 4
ANN2 neuralnetwork_adam 0.014 0.1702 0.2126 0.0424 0.1747 0.4630 5
neuralnetwork_rmsprop 0.012 0.1831 0.2585 0.0754 0.2227 0.5514 6
neuralnetwork_sgd 0.012 0.2518 0.2732 0.0214 0.2401 0.5272 7
automl automl_train_manual_trainwgrad_adam 1.260 0.0511 0.0867 0.0356 0.0707 0.1976 8
automl_train_manual_trainwgrad_RMSprop 1.104 0.1245 0.2296 0.1051 0.1669 0.5276 9
automl_train_manual_trainwpso 10.432 0.2032 0.2573 0.0541 0.2232 0.5240 10
brnn brnn_Gauss-Newton 0.020 0.0435 0.0673 0.0238 0.0522 0.1838 11
CaDENCE cadence.fit_optim 2.310 0.0688 0.0805 0.0117 0.0582 0.2385 12
cadence.fit_psoptim 5.052 0.2114 0.3238 0.1124 0.2711 0.6808 13
cadence.fit_Rprop 5.784 0.1820 0.2615 0.0795 0.2061 0.6887 14
caret avNNet_none 0.024 0.0512 0.0558 0.0046 0.0454 0.1561 15
deepdive deepnet_adam 0.572 0.3189 0.3189 0.0000 0.2113 0.7209 16
deepnet_gradientDescent 5.326 0.2699 0.2699 0.0000 0.2369 0.5509 17
deepnet_momentum 5.460 0.2656 0.2656 0.0000 0.2355 0.5269 18
deepnet_rmsProp 0.558 0.2252 0.2252 0.0000 0.1580 0.5513 19
deepnet nn.train_BP 0.092 0.0563 0.0608 0.0045 0.0490 0.1446 20
elmNNRcpp elm_train_extremeML 0.000 0.2589 0.2648 0.0059 0.2308 0.5419 21
ELMR OSelm_train.formula_extremeML 0.000 0.2613 0.2735 0.0122 0.2358 0.5366 22
EnsembleBase Regression.Batch.Fit_none 0.006 0.0618 0.0638 0.0020 0.0504 0.1716 23
h2o h2o.deeplearning_first-order 3.342 0.0474 0.0482 0.0008 0.0394 0.1126 24
keras fit_adadelta 26.680 0.1746 0.1792 0.0046 0.1379 0.4116 25
fit_adagrad 13.616 0.1597 0.1792 0.0195 0.1379 0.4143 26
fit_adam 2.338 0.0963 0.1767 0.0804 0.1397 0.4913 27
fit_adamax 3.696 0.1082 0.1728 0.0646 0.1393 0.3885 28
fit_nadam 2.460 0.1201 0.1884 0.0683 0.1486 0.5214 29
fit_rmsprop 1.744 0.1629 0.2166 0.0537 0.1697 0.5175 30
fit_sgd 1.868 0.2431 0.3056 0.0625 0.2606 0.6923 31
MachineShop fit_none 0.012 0.0406 0.0494 0.0088 0.0374 0.1288 32
minpack.lm nlsLM_none 0.024 0.0427 0.0427 0.0000 0.0333 0.1058 33
monmlp monmlp.fit_BFGS 0.210 0.0522 0.0796 0.0274 0.0625 0.2280 34
monmlp.fit_Nelder-Mead 0.370 0.1342 0.1780 0.0438 0.1371 0.4534 35
neuralnet neuralnet_backprop 0.372 0.1091 0.1355 0.0264 0.1084 0.3411 36
neuralnet_rprop- 0.062 0.0955 0.1186 0.0231 0.0920 0.2812 37
neuralnet_rprop+ 0.036 0.1077 0.1207 0.0130 0.0926 0.2648 38
neuralnet_sag 0.950 0.0811 0.1160 0.0349 0.0943 0.2960 39
neuralnet_slr 0.092 0.0840 0.1039 0.0199 0.0866 0.2554 40
nlsr nlxb_none 0.036 0.0427 0.0427 0.0000 0.0333 0.1058 41
nnet nnet_none 0.008 0.0602 0.0615 0.0013 0.0489 0.1408 42
qrnn qrnn.fit_none 0.214 0.0511 0.0821 0.0310 0.0598 0.2411 43
radiant.model nn_none 0.022 0.0647 0.0771 0.0124 0.0602 0.2202 44
rminer fit_none 0.016 0.0405 0.0579 0.0174 0.0479 0.1065 45
RSNNS mlp_BackpropBatch 0.870 0.2601 0.2736 0.0135 0.2371 0.6099 46
mlp_BackpropChunk 0.090 0.0829 0.0892 0.0063 0.0732 0.2035 47
mlp_BackpropMomentum 0.092 0.0752 0.0964 0.0212 0.0786 0.2134 48
mlp_BackpropWeightDecay 0.094 0.0799 0.0888 0.0089 0.0704 0.2063 49
mlp_Quickprop 0.906 0.2570 0.4804 0.2234 0.4177 1.0187 50
mlp_Rprop 0.090 0.0447 0.0959 0.0512 0.0717 0.2622 51
mlp_SCG 0.132 0.0555 0.0788 0.0233 0.0618 0.2070 52
mlp_Std_Backpropagation 0.086 0.0788 0.1292 0.0504 0.0999 0.3342 53
snnR snnR_none 0.020 0.2585 0.2984 0.0399 0.2556 0.6651 54
traineR train.nnet_none 0.016 0.0505 0.0649 0.0144 0.0529 0.1392 55
validann ann_BFGS 0.676 0.0405 0.0437 0.0032 0.0342 0.1131 56
ann_CG 31.616 0.0536 0.0610 0.0074 0.0476 0.1415 57
ann_L-BFGS-B 0.784 0.0691 0.0778 0.0087 0.0617 0.2019 58
ann_Nelder-Mead 30.686 0.0633 0.1987 0.1354 0.1673 0.4305 59
ann_SANN 0.148 0.2274 0.2546 0.0272 0.1990 0.5099 60

uDreyfus1

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.020 0.3308 0.3475 0.0167 0.2718 0.7716 1
train_ADAPTgdwm 0.030 0.1804 0.2112 0.0308 0.1476 0.4856 2
train_BATCHgd 1.382 0.3160 0.3346 0.0186 0.2740 0.7087 3
train_BATCHgdwm 1.376 0.3346 0.3370 0.0024 0.2785 0.7142 4
ANN2 neuralnetwork_adam 0.006 0.2762 0.3201 0.0439 0.2542 0.7372 5
neuralnetwork_rmsprop 0.006 0.2467 0.3428 0.0961 0.2715 0.7616 6
neuralnetwork_sgd 0.008 0.3493 0.3546 0.0053 0.2689 0.8481 7
automl automl_train_manual_trainwgrad_adam 0.906 0.0087 0.0725 0.0638 0.0481 0.2070 8
automl_train_manual_trainwgrad_RMSprop 1.114 0.0479 0.0727 0.0248 0.0498 0.2335 9
automl_train_manual_trainwpso 5.358 0.1052 0.1154 0.0102 0.0854 0.3281 10
brnn brnn_Gauss-Newton 0.000 0.0026 0.0034 0.0008 0.0029 0.0115 11
CaDENCE cadence.fit_optim 1.030 0.0032 0.6701 0.6669 0.3727 1.9004 12
cadence.fit_psoptim 4.512 0.4218 0.5720 0.1502 0.3001 1.6829 13
cadence.fit_Rprop 3.762 0.3995 1.1290 0.7295 0.8219 2.2557 14
caret avNNet_none 0.018 0.0262 0.0359 0.0097 0.0282 0.1115 15
deepdive deepnet_adam 0.564 0.0304 0.0304 0.0000 0.0265 0.0644 16
deepnet_gradientDescent 5.162 0.3429 0.3429 0.0000 0.2801 0.7346 17
deepnet_momentum 5.460 0.3429 0.3429 0.0000 0.2801 0.7341 18
deepnet_rmsProp 0.566 0.1184 0.1184 0.0000 0.0878 0.3446 19
deepnet nn.train_BP 0.084 0.0139 0.0704 0.0565 0.0451 0.2219 20
elmNNRcpp elm_train_extremeML 0.000 0.3407 0.4066 0.0659 0.2973 1.0342 21
ELMR OSelm_train.formula_extremeML 0.000 0.3987 0.4505 0.0518 0.3027 1.1845 22
EnsembleBase Regression.Batch.Fit_none 0.002 0.0922 0.1151 0.0229 0.0834 0.3335 23
h2o h2o.deeplearning_first-order 3.334 0.0131 0.0146 0.0015 0.0112 0.0432 24
keras fit_adadelta 10.958 0.2178 0.3498 0.1320 0.2655 0.8040 25
fit_adagrad 5.918 0.1630 0.3528 0.1898 0.2697 0.8045 26
fit_adam 2.808 0.0706 0.0897 0.0191 0.0690 0.2075 27
fit_adamax 5.074 0.0365 0.0487 0.0122 0.0404 0.1489 28
fit_nadam 2.082 0.0648 0.1550 0.0902 0.1179 0.3970 29
fit_rmsprop 0.942 0.3101 0.3622 0.0521 0.2798 0.9265 30
fit_sgd 2.312 0.3373 0.3450 0.0077 0.2698 0.7744 31
MachineShop fit_none 0.010 0.0023 0.0034 0.0011 0.0028 0.0102 32
minpack.lm nlsLM_none 0.000 0.0000 0.0000 0.0000 0.0000 0.0001 33
monmlp monmlp.fit_BFGS 0.190 0.0323 0.0541 0.0218 0.0434 0.1524 34
monmlp.fit_Nelder-Mead 0.270 0.1425 0.2017 0.0592 0.1653 0.4572 35
neuralnet neuralnet_backprop 0.040 0.3201 0.3503 0.0302 0.2743 0.7831 36
neuralnet_rprop- 0.008 0.1014 0.2856 0.1842 0.2227 0.7157 37
neuralnet_rprop+ 0.004 0.2119 0.3475 0.1356 0.2662 0.7910 38
neuralnet_sag 0.048 0.1963 0.3371 0.1408 0.2652 0.7510 39
neuralnet_slr 0.012 0.2981 0.3450 0.0469 0.2730 0.7821 40
nlsr nlxb_none 0.014 0.0000 0.0000 0.0000 0.0000 0.0001 41
nnet nnet_none 0.004 0.0026 0.0716 0.0690 0.0449 0.2254 42
qrnn qrnn.fit_none 0.128 0.2781 0.2841 0.0060 0.1815 0.9095 43
radiant.model nn_none 0.022 0.0121 0.0682 0.0561 0.0555 0.1546 44
rminer fit_none 0.012 0.0020 0.0023 0.0003 0.0018 0.0057 45
RSNNS mlp_BackpropBatch 0.812 0.3120 0.3387 0.0267 0.2647 0.7662 46
mlp_BackpropChunk 0.088 0.0838 0.1275 0.0437 0.0822 0.3313 47
mlp_BackpropMomentum 0.080 0.0719 0.0795 0.0076 0.0606 0.2070 48
mlp_BackpropWeightDecay 0.090 0.0797 0.0849 0.0052 0.0657 0.2541 49
mlp_Quickprop 0.822 0.2177 0.2408 0.0231 0.2084 0.5154 50
mlp_Rprop 0.080 0.0617 0.0689 0.0072 0.0484 0.2211 51
mlp_SCG 0.122 0.0851 0.1018 0.0167 0.0848 0.2408 52
mlp_Std_Backpropagation 0.078 0.1127 0.1190 0.0063 0.1000 0.2547 53
snnR snnR_none 0.006 0.3691 0.3691 0.0000 0.2756 0.8531 54
traineR train.nnet_none 0.000 0.0019 0.0022 0.0003 0.0019 0.0076 55
validann ann_BFGS 0.350 0.0022 0.0023 0.0001 0.0019 0.0070 56
ann_CG 25.106 0.0035 0.0076 0.0041 0.0061 0.0205 57
ann_L-BFGS-B 0.512 0.0038 0.0084 0.0046 0.0066 0.0207 58
ann_Nelder-Mead 17.878 0.0833 0.1951 0.1118 0.1633 0.3615 59
ann_SANN 0.142 0.2692 0.3271 0.0579 0.2707 0.6914 60

uDreyfus2

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.020 0.3555 0.3612 0.0057 0.2824 0.9010 1
train_ADAPTgdwm 0.030 0.1675 0.2519 0.0844 0.1964 0.6689 2
train_BATCHgd 1.378 0.1778 0.2708 0.0930 0.2148 0.6304 3
train_BATCHgdwm 1.380 0.2097 0.3405 0.1308 0.2704 0.8640 4
ANN2 neuralnetwork_adam 0.010 0.3222 0.3836 0.0614 0.2918 0.8958 5
neuralnetwork_rmsprop 0.014 0.2338 0.2845 0.0507 0.2093 0.8061 6
neuralnetwork_sgd 0.008 0.3581 0.3717 0.0136 0.2806 0.9555 7
automl automl_train_manual_trainwgrad_adam 1.244 0.0933 0.1579 0.0646 0.1212 0.4579 8
automl_train_manual_trainwgrad_RMSprop 1.096 0.1179 0.1615 0.0436 0.1223 0.4550 9
automl_train_manual_trainwpso 5.164 0.1180 0.1616 0.0436 0.1233 0.4403 10
brnn brnn_Gauss-Newton 0.000 0.0913 0.0913 0.0000 0.0730 0.2241 11
CaDENCE cadence.fit_optim 1.046 0.0924 0.3856 0.2932 0.2560 1.1222 12
cadence.fit_psoptim 4.500 0.3210 0.3814 0.0604 0.2825 1.0638 13
cadence.fit_Rprop 4.272 0.1684 0.2586 0.0902 0.1963 0.7853 14
caret avNNet_none 0.022 0.0926 0.1039 0.0113 0.0811 0.2375 15
deepdive deepnet_adam 0.566 0.1149 0.1149 0.0000 0.0907 0.2749 16
deepnet_gradientDescent 5.222 0.3570 0.3570 0.0000 0.2905 0.8478 17
deepnet_momentum 5.390 0.3570 0.3570 0.0000 0.2907 0.8468 18
deepnet_rmsProp 0.552 0.1625 0.1625 0.0000 0.1232 0.4839 19
deepnet nn.train_BP 0.080 0.0928 0.1049 0.0121 0.0824 0.2577 20
elmNNRcpp elm_train_extremeML 0.000 0.4534 0.6226 0.1692 0.5077 1.4031 21
ELMR OSelm_train.formula_extremeML 0.002 0.4554 0.5844 0.1290 0.4293 1.3727 22
EnsembleBase Regression.Batch.Fit_none 0.008 0.1196 0.1272 0.0076 0.1022 0.3102 23
h2o h2o.deeplearning_first-order 3.356 0.0926 0.0933 0.0007 0.0740 0.2242 24
keras fit_adadelta 7.248 0.3605 0.3726 0.0121 0.2763 0.9935 25
fit_adagrad 14.992 0.1847 0.1979 0.0132 0.1420 0.6153 26
fit_adam 2.354 0.1105 0.1345 0.0240 0.1062 0.3156 27
fit_adamax 4.740 0.1118 0.1154 0.0036 0.0935 0.3048 28
fit_nadam 2.366 0.1341 0.1957 0.0616 0.1530 0.5132 29
fit_rmsprop 1.096 0.2221 0.3598 0.1377 0.2805 0.8788 30
fit_sgd 2.546 0.3523 0.3548 0.0025 0.2760 0.9224 31
MachineShop fit_none 0.012 0.0906 0.1415 0.0509 0.1045 0.4507 32
minpack.lm nlsLM_none 0.022 0.0906 0.0906 0.0000 0.0723 0.2197 33
monmlp monmlp.fit_BFGS 0.210 0.0917 0.0951 0.0034 0.0746 0.2363 34
monmlp.fit_Nelder-Mead 0.248 0.1762 0.2448 0.0686 0.1940 0.6268 35
neuralnet neuralnet_backprop 0.042 0.3205 0.3655 0.0450 0.2776 0.9575 36
neuralnet_rprop- 0.014 0.1632 0.3537 0.1905 0.2756 0.9038 37
neuralnet_rprop+ 0.008 0.2846 0.3562 0.0716 0.2762 0.8861 38
neuralnet_sag 0.098 0.1663 0.2521 0.0858 0.1997 0.7213 39
neuralnet_slr 0.012 0.3374 0.3435 0.0061 0.2714 0.9130 40
nlsr nlxb_none 0.064 0.0906 0.0906 0.0000 0.0723 0.2197 41
nnet nnet_none 0.000 0.0906 0.0906 0.0000 0.0725 0.2202 42
qrnn qrnn.fit_none 0.170 0.1601 0.2693 0.1092 0.1983 0.6891 43
radiant.model nn_none 0.026 0.0907 0.0917 0.0010 0.0732 0.2275 44
rminer fit_none 0.018 0.0906 0.0906 0.0000 0.0724 0.2202 45
RSNNS mlp_BackpropBatch 0.820 0.3063 0.3491 0.0428 0.2736 0.8922 46
mlp_BackpropChunk 0.084 0.1199 0.1689 0.0490 0.1245 0.5094 47
mlp_BackpropMomentum 0.086 0.1209 0.1297 0.0088 0.1042 0.3327 48
mlp_BackpropWeightDecay 0.082 0.1186 0.1214 0.0028 0.0950 0.2751 49
mlp_Quickprop 0.826 0.2122 0.2993 0.0871 0.2338 0.8131 50
mlp_Rprop 0.082 0.1145 0.1252 0.0107 0.1009 0.3338 51
mlp_SCG 0.114 0.1238 0.2542 0.1304 0.1876 0.7205 52
mlp_Std_Backpropagation 0.080 0.1298 0.1325 0.0027 0.1025 0.3352 53
snnR snnR_none 0.012 0.3837 0.3837 0.0000 0.2773 1.0352 54
traineR train.nnet_none 0.004 0.0906 0.1123 0.0217 0.0901 0.2736 55
validann ann_BFGS 0.442 0.0906 0.0906 0.0000 0.0724 0.2200 56
ann_CG 26.808 0.0910 0.0913 0.0003 0.0730 0.2244 57
ann_L-BFGS-B 0.504 0.0907 0.1123 0.0216 0.0897 0.2733 58
ann_Nelder-Mead 16.024 0.1300 0.1604 0.0304 0.1224 0.4798 59
ann_SANN 0.152 0.2712 0.2972 0.0260 0.2354 0.7465 60

uGauss1

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.050 12.5180 28.6849 16.1669 23.0898 63.3445 1
train_ADAPTgdwm 0.084 14.8661 28.9286 14.0625 15.0901 75.7312 2
train_BATCHgd 1.694 12.0830 12.6864 0.6034 10.8841 27.5733 3
train_BATCHgdwm 1.724 12.0720 12.5131 0.4411 10.6879 26.8772 4
ANN2 neuralnetwork_adam 0.080 2.7029 9.5851 6.8822 7.9902 22.2599 5
neuralnetwork_rmsprop 0.076 5.5210 8.5210 3.0000 7.0532 20.1249 6
neuralnetwork_sgd 0.080 11.0994 11.9128 0.8134 10.0259 25.8843 7
automl automl_train_manual_trainwgrad_adam 4.982 4.4523 4.9986 0.5463 3.8522 18.0133 8
automl_train_manual_trainwgrad_RMSprop 4.482 4.9906 5.2304 0.2398 4.1778 17.4681 9
automl_train_manual_trainwpso 8.586 9.8111 13.4226 3.6115 9.5187 39.8505 10
brnn brnn_Gauss-Newton 0.042 2.2434 2.4366 0.1932 1.8814 8.7824 11
CaDENCE cadence.fit_optim 2.906 2.3392 2.4124 0.0732 1.9079 7.6898 12
cadence.fit_psoptim 6.144 25.3213 29.0788 3.7575 22.9938 64.9998 13
cadence.fit_Rprop 9.070 17.7666 25.2780 7.5114 17.3441 56.1202 14
caret avNNet_none 0.108 2.3241 2.6365 0.3124 2.0948 7.8111 15
deepdive deepnet_adam 0.634 20.5179 20.5179 0.0000 16.5474 47.6354 16
deepnet_gradientDescent 6.084 23.6597 23.6597 0.0000 19.1988 57.7174 17
deepnet_momentum 6.236 16.2557 16.2557 0.0000 13.0878 49.2409 18
deepnet_rmsProp 0.658 23.5833 23.5833 0.0000 19.1113 57.9958 19
deepnet nn.train_BP 0.304 3.4191 4.2839 0.8648 3.5260 11.8002 20
elmNNRcpp elm_train_extremeML 0.000 17.0430 18.7830 1.7400 15.4373 50.7429 21
ELMR OSelm_train.formula_extremeML 0.010 37.3986 490.0535 452.6549 426.0995 1516.4503 22
EnsembleBase Regression.Batch.Fit_none 0.038 2.5261 2.6857 0.1596 2.0641 8.3968 23
h2o h2o.deeplearning_first-order 4.372 2.2985 2.3587 0.0602 1.8349 7.6990 24
keras fit_adadelta 73.920 4.4960 5.1564 0.6604 3.8748 16.8817 25
fit_adagrad 52.480 6.5047 6.7324 0.2277 5.3578 20.2040 26
fit_adam 3.620 2.8614 3.0075 0.1461 2.3994 8.8657 27
fit_adamax 6.082 2.5783 3.1920 0.6137 2.5827 8.6394 28
fit_nadam 3.166 5.2915 12.2499 6.9584 9.8464 27.3131 29
fit_rmsprop 2.552 6.6698 13.1877 6.5179 10.5806 32.3150 30
fit_sgd 13.988 3.4196 3.9121 0.4925 3.1018 14.8772 31
MachineShop fit_none 0.034 2.2521 2.2681 0.0160 1.7734 7.5718 32
minpack.lm nlsLM_none 0.068 2.2329 2.2329 0.0000 1.7383 6.9429 33
monmlp monmlp.fit_BFGS 0.226 2.7246 5.7229 2.9983 4.8218 14.7964 34
monmlp.fit_Nelder-Mead 0.574 12.1868 12.7777 0.5909 9.8127 35.0537 35
neuralnet neuralnet_backprop 0.622 2.9109 3.4962 0.5853 2.6743 11.9971 36
neuralnet_rprop- 0.308 2.6198 3.8778 1.2580 2.9818 13.8198 37
neuralnet_rprop+ 0.298 2.9603 3.7997 0.8394 2.8334 14.1152 38
neuralnet_sag 7.138 2.2972 41.6253 39.3281 36.1679 91.5205 39
neuralnet_slr 0.440 2.8881 4.3263 1.4382 3.1765 14.4615 40
nlsr nlxb_none 0.156 2.2321 2.6129 0.3808 2.0484 8.2482 41
nnet nnet_none 0.032 2.2380 2.2557 0.0177 1.7541 7.3381 42
qrnn qrnn.fit_none 0.158 2.7155 2.7208 0.0053 2.0888 8.1916 43
radiant.model nn_none 0.054 2.3275 6.3010 3.9735 5.1479 17.4222 44
rminer fit_none 0.084 2.2452 2.2628 0.0176 1.7485 7.3946 45
RSNNS mlp_BackpropBatch 3.478 14.5624 19.9070 5.3446 16.5809 52.1745 46
mlp_BackpropChunk 0.368 2.9425 2.9820 0.0395 2.4160 10.5110 47
mlp_BackpropMomentum 0.334 2.8791 2.9074 0.0283 2.2991 9.6946 48
mlp_BackpropWeightDecay 0.372 2.8682 3.0805 0.2123 2.3657 8.8148 49
mlp_Quickprop 3.696 23.6323 24.1323 0.5000 20.1405 57.6774 50
mlp_Rprop 0.320 2.9859 10.3291 7.3432 7.2486 33.1339 51
mlp_SCG 0.558 2.7001 4.7483 2.0482 3.6042 16.9268 52
mlp_Std_Backpropagation 0.370 3.0594 3.2011 0.1417 2.5444 9.0758 53
snnR snnR_none 0.038 11.6175 11.6175 0.0000 9.5749 25.9147 54
traineR train.nnet_none 0.038 2.2431 2.3022 0.0591 1.7999 7.5122 55
validann ann_BFGS 0.932 2.2606 2.3192 0.0586 1.8215 7.5409 56
ann_CG 41.996 2.3620 2.3962 0.0342 1.9105 8.2206 57
ann_L-BFGS-B 1.060 2.7065 3.4311 0.7246 2.6492 9.8990 58
ann_Nelder-Mead 42.914 9.2009 11.1644 1.9635 9.1979 26.4353 59
ann_SANN 0.204 12.6829 15.2562 2.5733 12.8000 37.0901 60

uGauss2

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.054 7.4794 8.1969 0.7175 6.0059 23.9130 1
train_ADAPTgdwm 0.068 4.3864 10.4646 6.0782 6.6054 38.5720 2
train_BATCHgd 1.552 9.1582 9.7638 0.6056 7.1783 28.5231 3
train_BATCHgdwm 1.578 9.2190 9.4697 0.2507 6.9325 27.9676 4
ANN2 neuralnetwork_adam 0.086 3.7310 4.0836 0.3526 3.2330 12.0798 5
neuralnetwork_rmsprop 0.100 3.5637 4.2355 0.6718 3.2536 15.9291 6
neuralnetwork_sgd 0.078 7.4578 8.3914 0.9336 6.3470 25.3806 7
automl automl_train_manual_trainwgrad_adam 4.952 8.1454 8.6420 0.4966 6.1349 30.0687 8
automl_train_manual_trainwgrad_RMSprop 4.436 3.9723 8.4113 4.4390 5.6794 30.3739 9
automl_train_manual_trainwpso 8.702 6.1384 8.6501 2.5117 6.2805 24.3330 10
brnn brnn_Gauss-Newton 0.048 2.3781 3.5508 1.1727 2.9377 10.2283 11
CaDENCE cadence.fit_optim 2.320 2.4041 3.1503 0.7462 2.3988 10.7996 12
cadence.fit_psoptim 5.752 11.1566 15.4210 4.2644 12.0091 37.0326 13
cadence.fit_Rprop 5.810 11.7899 17.6638 5.8739 12.7742 39.4495 14
caret avNNet_none 0.086 2.4240 3.2653 0.8413 2.6499 9.8629 15
deepdive deepnet_adam 0.618 16.8843 16.8843 0.0000 11.6361 46.6218 16
deepnet_gradientDescent 5.934 28.8118 28.8118 0.0000 25.1770 67.7823 17
deepnet_momentum 6.176 28.8104 28.8104 0.0000 25.1756 67.8020 18
deepnet_rmsProp 0.620 18.3426 18.3426 0.0000 12.6957 49.5614 19
deepnet nn.train_BP 0.320 3.4032 6.4830 3.0798 4.8425 17.3581 20
elmNNRcpp elm_train_extremeML 0.000 20.3911 23.5586 3.1675 20.1337 51.5475 21
ELMR OSelm_train.formula_extremeML 0.014 27.8077 31.2976 3.4899 25.2946 82.5683 22
EnsembleBase Regression.Batch.Fit_none 0.030 2.7901 3.8821 1.0920 3.0341 11.9878 23
h2o h2o.deeplearning_first-order 4.394 2.8574 3.4454 0.5880 2.7928 11.6466 24
keras fit_adadelta 51.048 3.8515 3.8918 0.0403 2.8916 15.2710 25
fit_adagrad 31.862 5.0447 8.8810 3.8363 6.5481 25.2992 26
fit_adam 3.046 3.9732 6.7909 2.8177 5.1083 18.9390 27
fit_adamax 6.844 3.8559 4.2292 0.3733 3.3180 12.7852 28
fit_nadam 3.374 4.2819 7.1607 2.8788 5.6164 19.4085 29
fit_rmsprop 2.276 8.1016 10.2651 2.1635 7.5917 28.4689 30
fit_sgd 9.784 5.1907 8.8123 3.6216 6.4800 24.8510 31
MachineShop fit_none 0.024 2.5986 3.1210 0.5224 2.4847 9.3644 32
minpack.lm nlsLM_none 0.050 2.9795 2.9795 0.0000 2.3890 9.0540 33
monmlp monmlp.fit_BFGS 0.224 3.0438 4.6769 1.6331 3.6151 13.7834 34
monmlp.fit_Nelder-Mead 0.412 8.2728 9.5898 1.3170 6.7817 30.1673 35
neuralnet neuralnet_backprop 0.866 4.2479 4.3983 0.1504 3.4494 12.7619 36
neuralnet_rprop- 0.080 3.5904 4.4020 0.8116 3.4777 14.1560 37
neuralnet_rprop+ 0.064 3.6133 8.6404 5.0271 6.1594 25.2448 38
neuralnet_sag 1.916 3.3723 8.6390 5.2667 6.1167 24.7388 39
neuralnet_slr 0.190 3.5678 3.7435 0.1757 2.7163 14.9299 40
nlsr nlxb_none 0.118 2.3327 2.9754 0.6427 2.3838 9.0619 41
nnet nnet_none 0.026 2.3625 3.0894 0.7269 2.4567 9.4881 42
qrnn qrnn.fit_none 0.248 2.6571 3.7782 1.1211 2.6654 16.0998 43
radiant.model nn_none 0.056 2.5784 4.5795 2.0011 3.7498 11.3454 44
rminer fit_none 0.082 2.3604 2.3690 0.0086 1.8630 7.5477 45
RSNNS mlp_BackpropBatch 3.266 12.1638 14.7088 2.5450 11.5655 30.3793 46
mlp_BackpropChunk 0.332 3.2955 4.7181 1.4226 3.6073 15.4886 47
mlp_BackpropMomentum 0.352 3.3532 4.8150 1.4618 3.7195 15.6644 48
mlp_BackpropWeightDecay 0.320 4.5703 6.7390 2.1687 5.5508 19.8255 49
mlp_Quickprop 3.522 24.5455 25.0662 0.5207 19.9234 51.7595 50
mlp_Rprop 0.316 3.5732 6.3892 2.8160 4.6858 19.1326 51
mlp_SCG 0.556 6.2398 6.4892 0.2494 4.8401 20.2438 52
mlp_Std_Backpropagation 0.318 3.4215 4.8320 1.4105 3.8106 15.2518 53
snnR snnR_none 0.044 8.8419 9.4678 0.6259 6.9147 30.1105 54
traineR train.nnet_none 0.018 2.3713 2.6020 0.2307 2.0822 8.0308 55
validann ann_BFGS 0.792 2.3571 2.3654 0.0083 1.8640 7.5013 56
ann_CG 34.308 3.5928 6.3016 2.7088 4.7543 17.8412 57
ann_L-BFGS-B 0.840 3.0632 4.0776 1.0144 3.1853 13.2715 58
ann_Nelder-Mead 29.606 6.7221 7.5819 0.8598 5.9618 22.5839 59
ann_SANN 0.204 9.9162 14.2730 4.3568 11.6041 32.1496 60

uGauss3

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.046 4.7958 4.8043 0.0085 3.9113 12.5672 1
train_ADAPTgdwm 0.080 4.4658 5.1079 0.6421 3.6709 20.0320 2
train_BATCHgd 1.556 5.0863 5.2682 0.1819 4.1337 14.8772 3
train_BATCHgdwm 1.566 5.0868 5.2355 0.1487 4.1127 14.7918 4
ANN2 neuralnetwork_adam 0.082 3.1354 3.6437 0.5083 2.8900 10.5979 5
neuralnetwork_rmsprop 0.082 2.9727 3.2852 0.3125 2.5929 9.6420 6
neuralnetwork_sgd 0.080 4.8318 4.8821 0.0503 3.8567 14.4928 7
automl automl_train_manual_trainwgrad_adam 4.984 3.1214 3.4986 0.3772 2.7250 9.7689 8
automl_train_manual_trainwgrad_RMSprop 4.398 3.5555 3.7519 0.1964 3.0224 11.8905 9
automl_train_manual_trainwpso 6.586 4.8318 6.6613 1.8295 4.7306 20.0899 10
brnn brnn_Gauss-Newton 0.026 2.8273 3.1966 0.3693 2.5109 10.0153 11
CaDENCE cadence.fit_optim 2.334 2.4116 2.8622 0.4506 2.2233 7.8710 12
cadence.fit_psoptim 5.746 10.8502 14.8615 4.0113 11.6021 34.5796 13
cadence.fit_Rprop 5.790 9.1862 21.8896 12.7034 15.2197 62.4249 14
caret avNNet_none 0.080 2.4976 3.1181 0.6205 2.3743 9.6517 15
deepdive deepnet_adam 0.624 10.0466 10.0466 0.0000 7.3484 31.6838 16
deepnet_gradientDescent 5.946 32.2441 32.2441 0.0000 27.7063 70.1972 17
deepnet_momentum 6.146 32.2413 32.2413 0.0000 27.7055 70.2077 18
deepnet_rmsProp 0.622 20.7977 20.7977 0.0000 15.4531 49.0396 19
deepnet nn.train_BP 0.300 3.5001 3.7035 0.2034 2.9180 12.1143 20
elmNNRcpp elm_train_extremeML 0.000 8.4445 19.1869 10.7424 16.8753 35.7678 21
ELMR OSelm_train.formula_extremeML 0.010 31.0706 41.2586 10.1880 33.0051 112.2972 22
EnsembleBase Regression.Batch.Fit_none 0.036 2.3829 3.1571 0.7742 2.4537 9.9903 23
h2o h2o.deeplearning_first-order 4.706 2.9525 3.2931 0.3406 2.5635 9.9032 24
keras fit_adadelta 19.964 3.9293 4.3921 0.4628 3.3906 13.1185 25
fit_adagrad 13.448 3.4760 4.8342 1.3582 3.7910 14.2616 26
fit_adam 2.296 3.2791 4.0840 0.8049 3.1478 11.9057 27
fit_adamax 5.008 2.5583 2.9976 0.4393 2.3357 9.7110 28
fit_nadam 2.708 3.2682 3.4600 0.1918 2.8802 9.8016 29
fit_rmsprop 1.890 5.4568 6.4457 0.9889 5.4036 15.4436 30
fit_sgd 5.274 4.8610 5.1138 0.2528 3.9761 15.1244 31
MachineShop fit_none 0.034 2.3086 3.1576 0.8490 2.4940 9.7409 32
minpack.lm nlsLM_none 0.040 3.1472 3.1472 0.0000 2.4837 9.7293 33
monmlp monmlp.fit_BFGS 0.220 2.9135 3.5782 0.6647 2.8497 10.8707 34
monmlp.fit_Nelder-Mead 0.424 5.8001 7.3161 1.5160 5.7523 20.8098 35
neuralnet neuralnet_backprop 0.302 3.8802 4.2928 0.4126 3.4361 11.4729 36
neuralnet_rprop- 0.036 2.6706 3.6253 0.9547 2.8533 9.9037 37
neuralnet_rprop+ 0.066 2.5491 3.6200 1.0709 2.8585 10.5212 38
neuralnet_sag 1.016 2.7247 3.8181 1.0934 2.8290 11.6167 39
neuralnet_slr 0.102 2.8318 3.7840 0.9522 3.0024 10.4000 40
nlsr nlxb_none 0.110 2.2991 2.8185 0.5194 2.2078 7.5077 41
nnet nnet_none 0.020 2.3554 3.1706 0.8152 2.5057 9.8058 42
qrnn qrnn.fit_none 0.208 2.7773 3.9015 1.1242 2.8959 13.2058 43
radiant.model nn_none 0.046 2.6848 3.4127 0.7279 2.7026 10.5356 44
rminer fit_none 0.062 2.3033 2.3232 0.0199 1.8528 7.0323 45
RSNNS mlp_BackpropBatch 3.274 6.7104 9.7422 3.0318 7.6756 23.2263 46
mlp_BackpropChunk 0.320 2.9280 3.8323 0.9043 3.0061 11.0342 47
mlp_BackpropMomentum 0.320 2.9271 3.2533 0.3262 2.6246 8.8194 48
mlp_BackpropWeightDecay 0.360 2.8723 3.0215 0.1492 2.3931 8.5837 49
mlp_Quickprop 3.518 27.8595 28.8119 0.9524 22.8776 59.8157 50
mlp_Rprop 0.352 2.9609 8.8744 5.9135 6.0200 30.1870 51
mlp_SCG 0.538 3.3416 3.7196 0.3780 2.9009 11.2479 52
mlp_Std_Backpropagation 0.316 3.0294 3.2409 0.2115 2.6432 9.4181 53
snnR snnR_none 0.032 5.2818 5.2818 0.0000 4.0957 15.6475 54
traineR train.nnet_none 0.020 2.2976 2.8669 0.5693 2.2422 7.9607 55
validann ann_BFGS 0.744 2.3046 2.8185 0.5139 2.2078 7.5077 56
ann_CG 37.490 2.4990 3.5798 1.0808 2.7264 11.3586 57
ann_L-BFGS-B 0.870 2.5172 3.5450 1.0278 2.7137 10.7114 58
ann_Nelder-Mead 30.822 4.9577 5.3229 0.3652 4.3142 15.0154 59
ann_SANN 0.210 6.9649 10.8474 3.8825 8.3651 26.5278 60

uNeuroOne

Package Algorithm Time mean RMSE min RMSE median RMSE D51 MAE median WAE median NPFA
AMORE train_ADAPTgd 0.020 0.2958 0.2965 0.0007 0.2451 0.6433 1
train_ADAPTgdwm 0.028 0.2854 0.2854 0.0000 0.2285 0.6436 2
train_BATCHgd 1.232 0.2931 0.2935 0.0004 0.2421 0.6309 3
train_BATCHgdwm 1.240 0.2924 0.2933 0.0009 0.2419 0.6303 4
ANN2 neuralnetwork_adam 0.008 0.3082 0.3485 0.0403 0.2776 0.7493 5
neuralnetwork_rmsprop 0.008 0.2904 0.2912 0.0008 0.2376 0.6015 6
neuralnetwork_sgd 0.010 0.3069 0.3088 0.0019 0.2535 0.6226 7
automl automl_train_manual_trainwgrad_adam 1.214 0.2844 0.2895 0.0051 0.2378 0.6469 8
automl_train_manual_trainwgrad_RMSprop 1.090 0.2842 0.2888 0.0046 0.2403 0.6528 9
automl_train_manual_trainwpso 4.896 0.2847 0.2878 0.0031 0.2350 0.5413 10
brnn brnn_Gauss-Newton 0.008 0.3523 0.3523 0.0000 0.2848 0.8271 11
CaDENCE cadence.fit_optim 0.298 0.2831 0.2831 0.0000 0.2310 0.5816 12
cadence.fit_psoptim 4.244 0.5523 0.7577 0.2054 0.5800 1.9676 13
cadence.fit_Rprop 2.786 0.3054 0.3248 0.0194 0.2626 0.7872 14
caret avNNet_none 0.010 0.2904 0.2946 0.0042 0.2437 0.6434 15
deepdive deepnet_adam 0.562 0.2946 0.2946 0.0000 0.2459 0.5582 16
deepnet_gradientDescent 5.160 0.3666 0.3666 0.0000 0.3105 0.6748 17
deepnet_momentum 5.348 0.3544 0.3544 0.0000 0.3001 0.6152 18
deepnet_rmsProp 0.552 0.3161 0.3161 0.0000 0.2695 0.5981 19
deepnet nn.train_BP 0.084 0.2830 0.2830 0.0000 0.2314 0.5653 20
elmNNRcpp elm_train_extremeML 0.000 0.8650 0.9526 0.0876 0.7905 2.2943 21
ELMR OSelm_train.formula_extremeML 0.000 0.9735 1.0466 0.0731 0.8640 2.4817 22
EnsembleBase Regression.Batch.Fit_none 0.012 0.2826 0.2831 0.0005 0.2326 0.5543 23
h2o h2o.deeplearning_first-order 3.344 0.2831 0.2832 0.0001 0.2331 0.5539 24
keras fit_adadelta 19.378 0.2871 0.2879 0.0008 0.2377 0.5887 25
fit_adagrad 13.868 0.2893 0.2936 0.0043 0.2429 0.5637 26
fit_adam 1.320 0.2869 0.2875 0.0006 0.2340 0.5886 27
fit_adamax 2.502 0.2841 0.2864 0.0023 0.2366 0.5789 28
fit_nadam 1.518 0.2855 0.2896 0.0041 0.2437 0.6055 29
fit_rmsprop 1.108 0.3042 0.3629 0.0587 0.3049 0.7486 30
fit_sgd 3.468 0.2901 0.2922 0.0021 0.2410 0.5769 31
MachineShop fit_none 0.010 0.2830 0.2830 0.0000 0.2313 0.5675 32
minpack.lm nlsLM_none 0.004 1.2720 1.2720 0.0000 1.1104 2.5150 33
monmlp monmlp.fit_BFGS 0.194 0.2831 0.2834 0.0003 0.2312 0.5810 34
monmlp.fit_Nelder-Mead 0.224 0.3020 0.3266 0.0246 0.2601 0.6451 35
neuralnet neuralnet_backprop 0.152 0.2898 0.2926 0.0028 0.2423 0.5889 36
neuralnet_rprop- 0.010 0.2864 0.2935 0.0071 0.2480 0.6059 37
neuralnet_rprop+ 0.000 0.2848 0.3165 0.0317 0.2586 0.6196 38
neuralnet_sag 0.056 0.2893 0.3212 0.0319 0.2638 0.6316 39
neuralnet_slr 0.052 0.2923 0.3203 0.0280 0.2607 0.8073 40
nlsr nlxb_none 0.008 0.2830 0.2830 0.0000 0.2313 0.5675 41
nnet nnet_none 0.000 0.2830 0.2830 0.0000 0.2313 0.5675 42
qrnn qrnn.fit_none 0.094 0.2939 0.2939 0.0000 0.2258 0.7231 43
radiant.model nn_none 0.010 0.2830 0.2830 0.0000 0.2313 0.5677 44
rminer fit_none 0.004 0.2830 0.2830 0.0000 0.2313 0.5675 45
RSNNS mlp_BackpropBatch 0.788 0.6867 0.6888 0.0021 0.5629 1.6534 46
mlp_BackpropChunk 0.074 0.2912 0.6365 0.3453 0.5156 1.6363 47
mlp_BackpropMomentum 0.074 0.2968 0.3315 0.0347 0.2742 0.7631 48
mlp_BackpropWeightDecay 0.082 0.3096 0.6423 0.3327 0.5179 1.6618 49
mlp_Quickprop 0.764 0.5304 0.5304 0.0000 0.4235 1.2829 50
mlp_Rprop 0.076 0.2830 0.3141 0.0311 0.2531 0.7252 51
mlp_SCG 0.104 0.2855 0.6216 0.3361 0.5100 1.4782 52
mlp_Std_Backpropagation 0.082 0.2834 0.3135 0.0301 0.2457 0.7675 53
snnR snnR_none 0.004 0.6793 0.6793 0.0000 0.5564 1.6288 54
traineR train.nnet_none 0.000 0.2830 0.2830 0.0000 0.2313 0.5675 55
validann ann_BFGS 0.104 0.2830 0.2830 0.0000 0.2313 0.5675 56
ann_CG 23.762 0.2830 0.2830 0.0000 0.2313 0.5675 57
ann_L-BFGS-B 0.222 0.2830 0.2830 0.0000 0.2313 0.5675 58
ann_Nelder-Mead 9.006 0.3256 0.3341 0.0085 0.2793 0.8397 59
ann_SANN 0.168 0.3084 0.3344 0.0260 0.2773 0.6937 60



Summary statistics for top-10 packages on bWoodN1 Dataset

The table provides the summary statistics of top-10 NN packages over 20 runs on the large dataset bWoodN1 which contains 20,000 rows with 6 inputs valued in [0,1] for a (single) numeric output.

Package Time (mean) RMSE (min) RMSE (median) RMSE (D51) MAE (median) WAE (median)
rminer 10.2890 3.3662 3.56120 0.19500 2.86775 14.83000
traineR 3.2575 3.5488 4.57530 1.02650 3.72975 15.38630
CaDENCE 228.5210 3.3667 4.60750 1.24080 3.78875 16.57340
validann 145.0263 3.3800 4.62390 1.24390 3.75110 16.36570
h2o 127.9933 4.5704 4.64945 0.07905 3.76315 17.46895
monmlp 8.6500 4.5442 4.70060 0.15640 3.80100 15.31885
nlsr 73.3358 3.5512 4.70250 1.15130 3.80060 16.72755
nnet 3.4488 3.5499 4.70570 1.15580 3.79840 16.51300
MachineShop 3.6589 3.5518 4.77470 1.22290 3.84850 15.30465
radiant.model 0.0036 10.9572 10.95720 0.00000 8.76850 42.61880