DS Dimension
A combinatorial dimension measuring the complexity of a hypothesis class in multiclass classification, proposed by Daniely and Shalev-Shwartz. It is used to characterize the sample complexity of multiclass learning problems.
Timeline (last 90 days)
The DS dimension (Daniely-Shalev-Shwartz dimension) and the graph dimension both equal the height of the group.
In the agnostic learning setting, the gap between the sample complexity of every ERM and the known lower bound is at most the ratio of the DS dimension to the Natarajan dimension multiplied by a constant.
For every solvable Galois group, the DS dimension and the Natarajan dimension coincide exactly.
For the Galois groups A5 and S5 of the quintic equation, the DS dimension and the Natarajan dimension exhibit gaps of 2<3 and 3<4 respectively, and A5 is the smallest group for which such a gap exists.
For the Galois group Sn of a general equation of degree n, the DS dimension coincides with the Natarajan dimension if and only if n ≤ 4; in the characteristic-zero case, this is equivalent to the equation being solvable by radicals (the Abel-Ruffini theorem).
For linear, orthogonal and unitary maps on R^d or C^d, both the DS dimension and the Natarajan dimension equal d.
All Facts (6)
The DS dimension (Daniely-Shalev-Shwartz dimension) and the graph dimension both equal the height of the group.
50%UnverifiedIn the agnostic learning setting, the gap between the sample complexity of every ERM and the known lower bound is at most the ratio of the DS dimension to the Natarajan dimension multiplied by a constant.
50%UnverifiedFor every solvable Galois group, the DS dimension and the Natarajan dimension coincide exactly.
50%UnverifiedFor the Galois groups A5 and S5 of the quintic equation, the DS dimension and the Natarajan dimension exhibit gaps of 2<3 and 3<4 respectively, and A5 is the smallest group for which such a gap exists.
50%UnverifiedFor the Galois group Sn of a general equation of degree n, the DS dimension coincides with the Natarajan dimension if and only if n ≤ 4; in the characteristic-zero case, this is equivalent to the equation being solvable by radicals (the Abel-Ruffini theorem).
50%UnverifiedFor linear, orthogonal and unitary maps on R^d or C^d, both the DS dimension and the Natarajan dimension equal d.
50%