Teaching dimension

In computational learning theory, the teaching dimension^[1] of a concept class C is defined to be ${\displaystyle \max _{c\in C}\{w_{C}(c)\}}$, where ${\displaystyle {w_{C}(c)}}$ is the minimum size of a witness set for c in C.

The teaching dimension of a finite concept class can be used to give a lower and an upper bound on the membership query cost of the concept class.

In Stasys Jukna's book "Extremal Combinatorics", a lower bound is given for the teaching dimension:

Let C be a concept class over a finite domain X. If the size of C is greater than

${\displaystyle 2^{k}{|X| \choose k},}$

then the teaching dimension of C is greater than k.

References

1. Sally Goldman and Ronald Rivest and Robert Schapire (1989). "Learning Binary Relations and Total Orders". SIAM J. Computing 22: 46–51.