Estimation with extended models using generalized divergences and its applications

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K00051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Future University-Hakodate
• Principal Investigator: Takenouchi Takashi 公立はこだて未来大学, システム情報科学部, 准教授 (50403340)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 一般化ダイバージェンス / 離散確率モデル / 非負値行列因子分解

Outline of Final Research Achievements

The estimation for probabilistic models in a discrete space requires the computation of the normalization term to be a probability. However, in high-dimensional discrete spaces, the computation of the normalization term often requires a computational complexity of exponential order. In this study, we use an un-normalized non-probabilistic model (called the extended model) instead of a probabilistic model, and proposed an estimator by combining the extended model with the technique of empirical localization and homogeneous divergence, which can be constructed without the normalization term and asymptotically achieves the Cramer-Rao bound.
We also construct a unified framework for handling multi-class classification methods and　robust non-negative matrix factorization algorithm, by using generalized divergences.

Free Research Field

統計的機械学習

Academic Significance and Societal Importance of the Research Achievements

提案した推定量は正規化項の計算が不要であるうえに，漸近的にクラメール・ラオの下限を達成するため，　通常の推定量と比較して数十-数百分の一の計算コストで最尤推定量に匹敵する性能を達成可能である．
また，　多値判別手法を扱うための統一的な枠組みは多くの従来手法を特殊ケースとして含むため，　性能に関する理論的な考察や比較が用意になった．　非負値行列因子分解法については，　再下降性と呼ばれる性質を手法に付与することが出来たため，　ノイズに対して強力な頑健性をもたせることが可能となった．