Table 3 Comparison of AFS with other methods on auditing QO and QNO from the PathMNIST dataset with a varied number of samples in the query dataset

Independent teacher

1

1

1

1

1

1

1

4.29e−01

6.29e−03

1.40e−13

4.91e−28

1.88e−60

Independent student

1

1

1

1

1

1

1

5.27e−01

5.11e−03

1.29e−10

3.38e−20

7.24e−42

Independent teacher (k = 0.75)

1

1

1

1

1

1

1

5.62e−01

2.76e−03

4.22e−16

5.52e−27

1.62e−60

Independent student (k = 0.75)

1

1

1

1

1

1

1

7.32e−01

1.89e−02

1.55e−08

5.74e−16

1.92e−30

AFS w/o Audit (k = 0.75)

1

1

5.26e−01

1.78e−01

2.54e−02

1.17e−03

1

2.95e−01

2.26e−02

9.23e−11

1.04e−19

8.21e−41

AFS (k = 0.75)

1

1

3.90e−01

3.21e−02

6.13e−04

7.19e−06

1

4.98e−01

2.34e−04

4.25e−16

3.95e−31

4.89e−65

Independent teacher (k = 0.5)

1

1

1

1

1

1

1

5.62e−01

5.03e−03

1.50e−12

3.36e−22

2.39e−48

Independent student (k = 0.5)

1

8.66e−01

1

8.64e−01

8.64e−01

5.58e−01

1

5.62e−01

4.02e−03

3.01e−10

1.91e−21

7.85e−40

AFS w/o Audit (k = 0.5)

1

1

5.11e−01

2.48e−01

1.24e−02

9.59e−04

1

6.26e−01

1.18e−02

2.99e−11

4.03e−21

2.51e−40

AFS (k = 0.5)

1

1

1.59e−01

3.45e−04

4.06e−06

1.85e−10

1

2.69e−01

9.17e−05

2.98e−16

3.84e−30

1.04e−62

Independent teacher (k = 0.25)

1

1

1

1

1

1

1

3.31e−01

5.98e−04

2.84e−12

1.62e−28

6.34e−52

Independent student (k = 0.25)

1

1

8.64e−01

6.95e−01

1.60e−01

4.54e−02

1

1.26e−01

1.24e−06

2.30e−31

2.88e−60

4.73e−109

AFS w/o Audit (k = 0.25)

1

8.66e−01

2.39e−01

3.37e−03

1.01e−05

9.15e−10

1

2.42e−01

3.64e−05

2.55e−24

3.01e−43

1.37e−90

AFS (k = 0.25)

1

8.66e−01

1.40e−01

2.71e−03

1.07e−06

1.63e−12

1

4.37e−01

7.07e−06

2.01e−27

4.45e−53

1.71e−101

SISA (10 shards)

1

1

1

1

1

1

1

6.71e−01

6.58e−03

2.11e−12

9.05e−27

5.85e−49

CF-k (k = 1)

1

1

1

8.63e−01

8.63e−01

1

1

3.75e−01

7.28e−03

9.10e−14

1.07e−21

1.48e−42

EU-k (k = 1)

1

1

1

6.96e−01

7.38e−01

6.92e−01

1

4.73e−01

1.60e−03

4.66e−11

1.47e−23

1.48e−44