Table 2.

Comparison of accuracy scores of five supervised machine learning models trained on real data and synthetic data across 19 datasets. Increase or decrease in accuracy compared with the model trained on real data shown in parentheses.

Dataset and training seta		Machine learning algorithm accuracy
		SGDb	DTc	KNNd	RFe	SVMf
A
	Real	0.962	1.000 (Wg)	0.975	0.997	0.974
	CARTh	0.966 (+0.004)	0.950 (–0.050)	0.967 (–0.008)	0.965 (–0.032)	0.969 (W) (–0.005)
	Parametric	0.932 (–0.030)	0.907 (–0.093)	0.931 (–0.044)	0.927 (–0.070)	0.946 (W) (–0.028)
	Bayesian	0.954 (–0.011)	0.924 (–0.076)	0.963 (–0.012)	0.947 (–0.050)	0.967 (W) (–0.007)
B
	Real	0.668	0.931 (W)	0.758	0.924	0.83
	CART	0.652 (–0.016)	0.698 (–0.233)	0.765 (+0.007)	0.749 (–0.175)	0.784 (W) (–0.046)
	Parametric	0.706 (+0.048)	0.700 (–0.231)	0.748 (–0.010)	0.726 (–0.198)	0.753 (W) (–0.077)
	Bayesian	0.674 (+0.006)	0.712 (–0.219)	0.744 (–0.014)	0.741 (–0.183)	0.770 (W) (–0.060)
C
	Real	0.629	1.000 (W)	0.784	0.983	0.905
	CART	0.603 (–0.026)	0.652 (–0.348)	0.662 (–0.122)	0.676 (–0.307)	0.729 (W) (–0.176)
	Parametric	0.707 (+0.078)	0.702 (–0.298)	0.652 (–0.132)	0.709 (W) (–0.272)	0.700 (–0.205)
	Bayesian	0.662 (+0.033)	0.709 (–0.291)	0.664 (–0.144)	0.747 (W) (–0.236)	0.710 (–0.195)
D
	Real	0.632	1.000 (W)	0.726	0.962	0.66
	CART	0.502 (–0.130)	0.664 (–0.336)	0.542 (–0.184)	0.706 (W) (–0.254)	0.536 (–0.124)
	Parametric	0.472 (–0.160)	0.666 (W) (–0.334)	0.508 (–0.218)	0.628 (–0.334)	0.545 (–0.115)
	Bayesian	0.438 (–0.194)	0.592 (–0.408)	0.511 (–0.215)	0.649 (W) (–0.313)	0.557 (–0.103)
E
	Real	0.995	1.000 (W)	0.981	1.000 (W)	0.995
	CART	0.972 (–0.023)	0.944 (–0.056)	0.967 (–0.014)	0.995 (W) (–0.005)	0.994 (–0.001)
	Parametric	0.964 (–0.031)	0.981 (–0.019)	0.965 (–0.016)	0.988 (W) (–0.012)	0.988 (W) (–0.007)
	Bayesian	0.986 (–0.009)	0.957 (–0.043)	0.974 (–0.007)	0.992 (–0.008)	0.993 (W) (–0.002)
F
	Real	0.89	0.985 (W)	0.912	0.982	0.913
	CART	0.869 (–0.021)	0.922 (W) (–0.063)	0.883 (–0.029)	0.921 (–0.061)	0.889 (–0.024)
	Parametric	0.873 (–0.017)	0.907 (–0.078)	0.886 (–0.026)	0.914 (W) (–0.068)	0.894 (–0.019)
	Bayesian	0.880 (–0.010)	0.918 (–0.067)	0.885 (–0.027)	0.924 (W) (–0.058)	0.893 (–0.020)
G
	Real	0.746	0.959	0.78	0.971 (W)	0.82
	CART	0.667 (–0.079)	0.848 (W) (–0.111)	0.678 (–0.102)	0.841 (–0.070)	0.748 (–0.072)
	Parametric	0.669 (–0.077)	0.805 (W) (–0.154)	0.676 (–0.104)	0.801 (–0.107)	0.737 (–0.083)
	Bayesian	0.676 (–0.070)	0.835 (W) (–0.124)	0.676 (–0.104)	0.822 (–0.149)	0.739 (–0.081)
H
	Real	1.000 (W)	0.997	0.98	0.994	0.992
	CART	0.940 (–0.060)	0.941 (–0.056)	0.891 (–0.089)	0.958 (W) (–0.036)	0.955 (–0.037)
	Parametric	0.935 (–0.065)	0.951 (–0.046)	0.898 (–0.082)	0.959 (W) (–0.135)	0.959 (W) (–0.032)
	Bayesian	0.940 (–0.060)	0.952 (–0.045)	0.899 (–0.081)	0.955 (–0.139)	0.959 (W) (–0.032)
I
	Real	0.706	0.845	0.711	0.896 (W)	0.676
	CART	0.594 (–0.112)	0.643 (–0.202)	0.634 (–0.077)	0.671 (W) (–0.225)	0.609 (–0.067)
	Parametric	0.570 (–0.136)	0.638 (–0.207)	0.624 (–0.087)	0.663 (W) (–0.233)	0.608 (–0.068)
	Bayesian	0.609 (–0.097)	0.648 (–0.197)	0.629 (–0.082)	0.667 (W) (–0.229)	0.622 (–0.054)
J
	Real	0.453	0.981 (W)	0.642	0.981 (W)	0.651
	CART	0.526 (+0.073)	0.655 (W) (–0.326)	0.579 (–0.063)	0.649 (–0.332)	0.551 (–0.100)
	Parametric	0.555 (+0.102)	0.689 (W) (–0.292)	0.606 (–0.036)	0.628 (–0.354)	0.549 (–0.102)
	Bayesian	0.545 (+0.092)	0.585 (–0.396)	0.585 (–0.057)	0.602 (W) (–0.379)	0.551 (–0.100)
K
	Real	0.551	0.845	0.864	0.885 (W)	0.551
	CART	0.510 (–0.041)	0.531 (W) (–0.314)	0.531 (W) (–0.333)	0.512 (–0.373)	0.531 (W) (–0.020)
	Parametric	0.514 (–0.037)	0.545 (W) (–0.300)	0.510 (–0.354)	0.519 (–0.366)	0.531 (–0.020)
	Bayesian	0.490 (–0.061)	0.538 (W) (–0.307)	0.510 (–0.354)	0.531 (–0.354)	0.510 (–0.041)
L
	Real	0.851	1.000 (W)	0.861	0.977	0.865
	CART	0.791 (–0.060)	0.781 (–0.219)	0.758 (–0.103)	0.803 (W) (–0.174)	0.785 (–0.080)
	Parametric	0.822 (W) (–0.029)	0.758 (–0.242)	0.786 (–0.075)	0.809 (–0.168)	0.793 (–0.072)
	Bayesian	0.785 (–0.066)	0.738 (–0.262)	0.818 (–0.043)	0.799 (–0.178)	0.834 (W) (–0.031)
M
	Real	0.899	1.000 (W)	0.838	0.986	0.939
	CART	0.726 (–0.173)	0.762 (–0.238)	0.762 (–0.076)	0.780 (–0.206)	0.782 (W) (–0.157)
	Parametric	0.739 (–0.160)	0.765 (–0.235)	0.757 (–0.081)	0.772 (–0.214)	0.796 (W) (–0.143)
	Bayesian	0.681 (–0.218)	0.662 (–0.338)	0.703 (–0.135)	0.746 (–0.240)	0.780 (W) (–0.159)
N
	Real	0.713	0.908 (W)	0.713	0.908 (W)	0.713
	CART	0.706 (–0.007)	0.667 (–0.241)	0.715 (+0.002)	0.680 (–0.228)	0.720(W) (+0.007)
	Parametric	0.644 (–0.067)	0.614 (–0.294)	0.706 (–0.007)	0.646 (–0.262)	0.708 (W) (–0.005)
	Bayesian	0.559 (–0.154)	0.591 (–0.317)	0.706 (W) (–0.007)	0.630 (–0.278)	0.694 (–0.019)
O
	Real	0.449	0.732	0.458	0.762 (W)	0.56
	CART	0.338 (–0.111)	0.401 (–0.331)	0.411 (–0.047)	0.410 (–0.352)	0.425 (W) (–0.135)
	Parametric	0.317 (–0.192)	0.377 (–0.355)	0.413 (–0.045)	0.397 (–0.365)	0.433 (W) (–0.127)
	Bayesian	0.293 (–0.156)	0.336 (–0.396)	0.375 (–0.083)	0.361 (–0.401)	0.419 (W) (–0.141)
P
	Real	0.981	0.985 (W)	0.981	0.982	0.981
	CART	0.981 (W) (0.000)	0.977 (–0.008)	0.981 (W) (0.000)	0.981 (W) (–0.001)	0.981 (W) (0.000)
	Parametric	0.981 (W) (0.000)	0.976 (–0.009)	0.981 (W) (0.000)	0.981 (W) (–0.001)	0.981 (W) (0.000)
	Bayesian	0.981 (W) (0.000)	0.977 (–0.008)	0.981 (W) (0.000)	0.981 (W) (–0.001)	0.981 (W) (0.000)
Q
	Real	0.84	0.932 (W)	0.853	0.928	0.851
	CART	0.834 (–0.006)	0.795 (–0.137)	0.850 (–0.003)	0.835 (–0.093)	0.851 (W) (0.000)
	Parametric	0.798 (–0.042)	0.811 (–0.121)	0.848 (–0.005)	0.838 (–0.090)	0.849 (W) (–0.002)
	Bayesian	0.823 (–0.017)	0.794 (–0.138)	0.846 (–0.007)	0.837 (–0.091)	0.851 (W) (0.000)
R
	Real	0.755	0.989 (W)	0.795	0.961	0.738
	CART	0.742 (–0.013)	0.819 (–0.170)	0.761 (–0.034)	0.825 (W) (–0.136)	0.733 (–0.005)
	Parametric	0.749 (–0.006)	0.786 (–0.203)	0.764 (–0.031)	0.798 (W) (–0.163)	0.734 (–0.004)
	Bayesian	0.748 (–0.007)	0.835 (W) (–0.154)	0.762 (–0.033)	0.832 (–0.129)	0.734 (–0.004)
S
	Real	0.958	1.000 (W)	0.921	1.000 (W)	0.953
	CART	0.903 (–0.055)	0.901 (–0.099)	0.899 (–0.022)	0.935 (W) (–0.065)	0.913 (–0.040)
	Parametric	0.890 (–0.068)	0.913 (–0.087)	0.912 (–0.009)	0.930 (W) (–0.060)	0.926 (–0.027)
	Bayesian	0.905 (–0.053)	0.914 (–0.086)	0.908 (–0.013)	0.936 (W) (–0.064)	0.930 (–0.023)

^aTraining dataset name indicates if real or synthetic data were used to train the model and for synthetic datasets which synthetic data generator was used (ie, CART, parametric, or Bayesian).

^bSGD: stochastic gradient descent.

^cDT: decision tree.

^dKNN: k-nearest neighbors.

^eRF: random forest.

^fSVM: support vector machine.

^g(W) highlights the winning classifier for each training set.

^hCART: classification and regression trees.