Density Derivative Estimation and its Applications

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06103
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Intelligent informatics
• Research Institution: Nara Institute of Science and Technology
• Principal Investigator: Sasaki Hiroaki 奈良先端科学技術大学院大学, 情報科学研究科, 助教 (80756916)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 機械学習 / 確率密度微分 / 次元削減 / クラスタリング / 多様体 / モード回帰

Outline of Final Research Achievements

Estimating the derivatives of probability density functions is one of the important challenges in statistical data analysis. To estimate the derivatives, a naive approach is first to estimate the probability density function from data, and then to compute its derivatives. However, this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator. To overcome this challenge, we took a different approach that directly estimates density derivatives without going through density estimation. Based on the direct approach, we proposed two methods to estimate the derivatives of conditional density functions and the ratios of density derivatives to its density. With the proposed methods, we developed supervised dimensionality reduction and density ridge estimation methods.

Free Research Field

知能情報学