Unique negative dimension

Unique negative dimension (UND) is a complexity measure for the model of learning from positive examples. The unique negative dimension of a class $C$ of concepts is the size of the maximum subclass $D\subseteq C$ such that for every concept $c\in D$ , we have $\cap (D\setminus \{c\})\setminus c$ is nonempty.

This concept was originally proposed by M. Gereb-Graus in "Complexity of learning from one-side examples", Technical Report TR-20-89, Harvard University Division of Engineering and Applied Science, 1989.^[1]^[2]^[3]

References

↑ Darnstädt, Malte; Simon, Hans Ulrich; Szörényi, Balázs (30 January 2014). "Supervised learning and Co-training". Theoretical Computer Science. 519: 68–87. doi:10.1016/j.tcs.2013.09.020.
↑ Geréb-Graus, Mihály (1989). Lower bounds on parallel, distributed and automata computations (Thesis). OCLC 1243704701. OSTI 5815133. TR-20-89.
↑ Ehrenfeucht, Andrzej; Haussler, David; Kearns, Michael; Valiant, Leslie (1 September 1989). "A general lower bound on the number of examples needed for learning". Information and Computation. 82 (3): 247–261. doi:10.1016/0890-5401(89)90002-3. S2CID 1925579.

P ≟ NP

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[1] Darnstädt, Malte; Simon, Hans Ulrich; Szörényi, Balázs (30 January 2014). "Supervised learning and Co-training". Theoretical Computer Science. 519: 68–87. doi:10.1016/j.tcs.2013.09.020.

[2] Geréb-Graus, Mihály (1989). Lower bounds on parallel, distributed and automata computations (Thesis). OCLC 1243704701. OSTI 5815133. TR-20-89.

[3] Ehrenfeucht, Andrzej; Haussler, David; Kearns, Michael; Valiant, Leslie (1 September 1989). "A general lower bound on the number of examples needed for learning". Information and Computation. 82 (3): 247–261. doi:10.1016/0890-5401(89)90002-3. S2CID 1925579.

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Unique negative dimension

See also

References