| Presentation | 2016-11-17 Exhaustive search for sparse variable selection in linear regression Yasuhiko Igarashi, Hikaru Takenaka, Nakanishi-Ohno Yoshinori, Makoto Uemura, Shiro Ikeda, Masato Okada, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We proposed the $K$-sparse Exhaustive-Search (ES-$K$) method, in which, assuming the optimum combination of explanatory variables is $K$-sparse, we exhaustively search the $K$-sparse combinations for sparse variable selection in linear regression. We then obtain the density of states and can map to it solutions obtained by various approximate methods of sparse variable selection. This method enables us to integrate the previous sparse variable selection methods such as relaxation approach and sampling approach, and evaluate all the approximate methods. In addition, for the problem of combinatorial explosion of the explanatory variables, we effectively reconstructed the density of states by using the exchange Monte Carlo method and multi-histogram method. Finally, we applied the ES-$K$ method to the type Ia supernova data. As a result, there is a combination of explanatory variables with higher performance than that of previous approximate sparse variable selection methods. This result means that relaxation approach for sparse variable selection used in previous studies is incomplete. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | $K$-sparse Exhaustive-Search (ES-$K$) method / BIC / CVE / LASSO / exchange Monte Carlo method |
| Paper # | IBISML2016-90 |
| Date of Issue | 2016-11-09 (IBISML) |
| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2016/11/16(3days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyoto Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Information-Based Induction Science Workshop (IBIS2016) |
| Chair | Kenji Fukumizu(ISM) |
| Vice Chair | Masashi Sugiyama(Univ. of Tokyo) / Hisashi Kashima(Kyoto Univ.) |
| Secretary | Masashi Sugiyama(Univ. of Tokyo) / Hisashi Kashima(Nagoya Inst. of Tech.) |
| Assistant | Toshihiro Kamishima(AIST) / Tomoharu Iwata(NTT) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Exhaustive search for sparse variable selection in linear regression |
| Sub Title (in English) | |
| Keyword(1) | $K$-sparse Exhaustive-Search (ES-$K$) method |
| Keyword(2) | BIC |
| Keyword(3) | CVE |
| Keyword(4) | LASSO |
| Keyword(5) | exchange Monte Carlo method |
| 1st Author's Name | Yasuhiko Igarashi |
| 1st Author's Affiliation | The University of Tokyo(UTokyo) |
| 2nd Author's Name | Hikaru Takenaka |
| 2nd Author's Affiliation | The University of Tokyo(UTokyo) |
| 3rd Author's Name | Nakanishi-Ohno Yoshinori |
| 3rd Author's Affiliation | The University of Tokyo(UTokyo) |
| 4th Author's Name | Makoto Uemura |
| 4th Author's Affiliation | Hiroshima University(Hiroshima Univ.) |
| 5th Author's Name | Shiro Ikeda |
| 5th Author's Affiliation | The Institute of Statistical Mathematics(ISM) |
| 6th Author's Name | Masato Okada |
| 6th Author's Affiliation | The University of Tokyo(UTokyo) |
| Date | 2016-11-17 |
| Paper # | IBISML2016-90 |
| Volume (vol) | vol.116 |
| Number (no) | IBISML-300 |
| Page | pp.pp.313-320(IBISML), |
| #Pages | 8 |
| Date of Issue | 2016-11-09 (IBISML) |