Some Application Of Auto-adapted Optimization Algorithms Under The Proportional Hazards Model

For the survival data with censored data,the proportional hazards model is one of the most widely used semiparametric survival models.In practical applications,the estimation of the regression hazards model regression parameters needs to be obtained by numerical methods.In recent years,with the deepening of research in the field of machine learning and deep learning,the auto-adapted optimization algorithms have developed rapidly.The auto-adapted optimization algorithms is a gradient optimization algorithm whose main idea is to continuously iterate close to the optimal value point along the negative gradient direction of the objective function.The auto-adapted optimization algorithms can avoid the difficulties encountered by many commonly used numerical algorithms,such as high dimensional matrix inversion problem,initial value selection problem and algorithm convergence problem.Therefore,the auto-adapted optimization algorithms has been rapidly developed and widely used.Application,this paper studies the auto-adapted optimization algorithms under the proportional hazards model.Firstly,we explore and apply three auto-adapted optimization algorithms—Adam algorithm,RMSprop algorithm and Adagrad algorithm to solve the numerical solution problem of parameter estimation under the proportional hazards model,and show the computational superiority of the auto-adapted algorithm.Then,we go deep into the proportional hazards model.Under the research of Adam algorithm,an improved Adam algorithm is developed,which further improves the calculation speed of the algorithm and shows its computational advantages.The contents of this thesis are as follows:In chapter 1,we introduce the research background of this paper,summarize the development status of the research direction,summarize the work of the predecessors,and put forward the main work of this paper.In chapter 2,we apply Adam algorithm,RMSprop algorithm and Adagrad algorithm to solve the numerical solution problem of parameter estimation under proportional hazards model.In chapter 3,based on the idea of “momentum forward”,we improved the Adam algorithm to make it have a faster convergence speed.In chapter 4,we compare the performance of Adagrad algorithm,RMSprop algorithm,Adam algorithm,improved Adam algorithm and Newton-Raphson algorithm by numerical simulation,and show the computational superiority of auto-adapted optimization algorithm.In chapter 5,we apply the Adam algorithm and the improved Adam algorithm to analyze two actual data,demonstrating its feasibility and goodness in practical applications.In chapter 6,we summarize the main research contents of this paper and look forward to the future research directions.