High-accuracy parameter estimation using constrained variable selection based on mixed-integer optimization

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K12983
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Social systems engineering/Safety system
• Research Institution: University of Tsukuba
• Principal Investigator: Takano Yuichi 筑波大学, システム情報系, 准教授 (40602959)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 数理最適化 / 機械学習 / アルゴリズム / 計算機統計

Outline of Final Research Achievements

Mixed-integer optimization has been attracting attention in recent years as an exact solution for variable selection in regression and discriminant analyses. On the other hand, variable selection based on mixed-integer optimization has the disadvantage that multicollinearity often remains in the set of selected explanatory variables, and the prior knowledge inherent in the data is not utilized. Thus, in this study we combined "mixed-integer optimization" with "removal of multicollinearity" and "structured regularization (model construction using prior information)" to propose constrained variable selection methods that enable high-accuracy parameter estimation. Numerical experiments using synthetic and actual data were conducted to verify the effectiveness of the proposed methods.

Free Research Field

数理最適化

Academic Significance and Societal Importance of the Research Achievements

回帰分析や判別分析における変数選択の先行研究では、発見的解法が用いられる場合が多く、パラメータ推定の精度に着目した変数選択の厳密解法は先駆的かつ実用上重要な研究だと言える。多重共線性を除去する制約条件は扱いが難しく、有効な求解アルゴリズムを考案することは最適化理論の観点からも意義がある。本研究の目的である高精度パラメータ推定は、データ分析の信頼性向上に直結し、多くの企業や行政機関の意思決定に寄与することが期待される。