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EURASIP Journal on Bioinformatics and Systems Biology

Table 1 Synthetic data classification settings and prior models

From: On optimal Bayesian classification and risk estimation under multiple classes

 

D

M

ν 0,…,ν M−1

m 0,…,m M−1

κ y (k y )

\(\frac {\mathbf {S}_{y}}{k_{y} - 2}\)

Prior (cov.)

λ

Model 1

2

2

12, 2

\(\left [\begin {array}{l} 0 \\ 0 \end {array}\right ], \left [\begin {array}{l} 0.5 \\ 0.5 \end {array}\right ]\)

6 (5)

0.3 I 2

Indep. arbit.

\(\left [\begin {array}{ll} 0 & 2 \\ 1 & 0 \end {array}\right ]\)

Model 2

2

2

12, 2

\(\left [\begin {array}{l} 0 \\ 0 \end {array}\right ], \left [\begin {array}{l} 0.5 \\ 0.5 \end {array}\right ]\)

6 (5)

0.3 I 2

Homo. arbit.

\(\left [\begin {array}{ll} 0 & 2 \\ 1 & 0 \end {array}\right ]\)

Model 3

2

5

12, 2, 2, 2, 2

\(\left [\begin {array}{l} 0 \\ 0 \end {array}\right ], \left [\begin {array}{l} 1 \\ 1 \end {array}\right ], \left [\begin {array}{l} -1 \\ -1 \end {array}\right ], \left [\begin {array}{l} 1 \\ -1 \end {array}\right ], \left [\begin {array}{l} -1 \\ 1 \end {array}\right ]\)

6 (5)

0.3 I 2

Indep. arbit.

0–1 loss

Model 4

2

5

12, 2, 2, 2, 2

\(\left [\begin {array}{l} 0 \\ 0 \end {array}\right ], \left [\begin {array}{l} 1 \\ 1 \end {array}\right ], \left [\begin {array}{l} -1 \\ -1 \end {array}\right ], \left [\begin {array}{l} 1 \\ -1 \end {array}\right ], \left [\begin {array}{l} -1 \\ 1 \end {array}\right ]\)

6 (5)

0.3 I 2

Homo. arbit.

0–1 loss

Model 5

20

2

12, 2

020,(0.05)20

−20.65 (5)

0.3 I 2

Indep. iden.

\(\left [\begin {array}{ll} 0 & 2 \\ 1 & 0 \end {array}\right ]\)

Model 6

20

2

20, 20

020,020

−20.65 (5)

0.3 I 20

Indep. iden.

\(\left [\begin {array}{ll} 0 & 2 \\ 1 & 0 \end {array}\right ]\)

Model 7

20

5

12, 2, 2, 2, 2

020,(0.1)20,(−0.1)20,

−20.65 (5)

0.3 I 20

Indep. iden.

0–1 loss

    

\(\left [\begin {array}{l} {(0.1)}_{10} \\ {(-0.1)}_{10} \end {array}\right ], \left [\begin {array}{l} {(-0.1)}_{10} \\ {(0.1)}_{10} \end {array}\right ]\)

    

Model 8

20

5

20, 20, 20, 20, 20

020,020,020,020,020

−20.65 (5)

0.3 I 20

Indep. iden.

0–1 loss

  1. 0 k and (a) k represent all-zero and all-a column vectors of length k, respectively
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