2011 Fiscal Year Final Research Report
Model selection and machine learning theory via large-scale random matrices
| Project/Area Number |
20700258
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
KOBAYASHI Kei 統計数理研究所, 数理・推論研究系, 助教 (90465922)
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| Project Period (FY) |
2008 – 2011
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| Keywords | カーネルグラム行列 / カーネルマシン / モデル選択 / 大規模ランダム行列 |
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| Research Abstract |
Nystrom approximation method for kernel gram matrices reduces the rank of each matrix in two steps. In order to approximate those matrices efficiently, it is important to set an adequate reduction rate for each step and handle the tradeoff between accuracy of the approximation and cost of the computation. In this research program, we used methods of computational physics for analyzing large-scale random matrices and optimized the reduction rates. We checked experimentally that the proposed method attains high accuracy even with very low computational cost for real data of hand-written characters. We derived an upper bound for approximation error of Nystrom method and proved the statistical consistency. Moreover, the proposed method can be used not only for Nystrom method but also for other approximation methods including the sparse greedy approximation and the incomplete Cholesky decomposition. In parallel with this research, we studied commutative algebraic statistics and proposed a novel statistical estimator by applying the computational algebra to the asymptotic estimation theory. In addition, we proposed a statistical method to analyze dendrograms of mental lexicon, which is an example of models holding an algebraic structure.
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