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온라인 미러 디센트 알고리즘의 생존분석에의 응용
Application of online mirror descent algorithm to survival analysis
Korean J Appl Stat 2024;37(6):733-749
Published online December 31, 2024
© 2024 The Korean Statistical Society.

김광수1,a
Gwangsu Kim1,a

a전북대 통계학과 (응용통계연구소)

aDepartment of Statistics (Institute of Applied Statistics), Jeonbuk National University
1Department of Statistics (Institute of Applied Statistics), Jeonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeonbuk-do 54896, Korea. E-mail: s88012@jbnu.ac.kr
Received May 6, 2024; Revised July 14, 2024; Accepted August 8, 2024.
Abstract
점차 인기를 끌고 있는 깊은 신경망을 생존분석에 적용하기 위해서는 미니 배치 방식의 확률적 경사하강법이 필요하다. 하지만 생존분석에서 사용하는 부분 가능도 함수에 위험 집합이 존재하기에 이 알고리즘의 적용에 문제가 될 수 있다. 기존의 많은 연구들이 이 문제를 해결했으며, 본 논문에서는 이런 기존 연구들과 비교하여 더욱 발전된 알고리즘인 온라인 미러 디센트 알고리즘을 생존분석에 적용하였다. 이 방법은 온라인 학습과 밀접하게 관련된 모든 볼록함수 최적화 문제에 사용할 수 있다. 알고리즘을 구성하기 위해 재매개변수화 기법과 이중 최적화가 사용되었고, 다양한 설정에서의 실험 결과는 제안된 알고리즘의 우수성을 보여준다. 이번 연구는 최적화 문제 및 반모수적 생존 모델에서 효율적인 미니 배치 기반 알고리즘을 개발하는데 기여하고 있다.
In survival analysis, the use of deep neural networks has become popular. It requires the mini-batch type stochastic gradient descent (SGD) algorithm. However, the existence of risk set in the partial likelihood can be problematic, which can be addressed by many previous works. In this paper, we proposed an advanced algorithm compared to the conventional SGD by applying an online mirror descent algorithm. It can be used for any convex optimization problem where the given tasks are closely related to online learning. A re-parameterization trick and bi-level optimization are used to construct the algorithm. The experiments on various setups reveal the superiority of the proposed algorithm. It can contribute to making an ecient mini-batch-based algorithm over the convex optimization and semi-parametric survival models.
주요어 : 생존분석, 온라인 미러 디센트, 최적화, 부분 가능도 함수
Keywords : survival analysis, online mirror descent, optimization, partial likelihood
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December 2024, 37 (6)
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