Abstract
We consider the problem of learning k-parities in the online mistake-bound model: given a hidden vector (Formula Presented) where the hamming weight of x is k and a sequence of “questions” (Formula Presented), where the algorithm must reply to each question with (Formula Presented), what is the best trade-off between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et al. [BGM10] by an (Formula Presented) factor in the time complexity. Next, we consider the problem of learning k-parities in the PAC model in the presence of random classification noise of rate (Formula Presented). Here, we observe that even in the presence of classification noise of non-trivial rate, it is possible to learn k-parities in time better than (Formula Presented), whereas the current best algorithm for learning noisy k-parities, due to Grigorescu et al. [GRV11], inherently requires time (Formula Presented) even when the noise rate is polynomially small.
| Original language | English |
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| Title of host publication | Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings |
| Publisher | SPRINGER |
| Pages | 542-553 |
| Number of pages | 12 |
| ISBN (Print) | 9783319947754 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
| MoE publication type | A4 Article in a conference publication |
| Event | International Computing and Combinatorics Conference - Qing Dao, China Duration: 2 Jul 2018 → 4 Jul 2018 Conference number: 24 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 10976 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | International Computing and Combinatorics Conference |
|---|---|
| Abbreviated title | COCOON |
| Country/Territory | China |
| City | Qing Dao |
| Period | 02/07/2018 → 04/07/2018 |