Research On Set-valued Approximation And Incremental Learning Algorithms

Set-valued stochastic differential equations have been applied in finance,control and other fields.We have a deeper understanding of random phenomena in life.However,the operating state of some systems is not only related to time t,but also to the state before time t.Sometimes it is an interval data,which is not an accurate value,that is,the set-valued time delay phenomenon.With the in-depth study of a large number of scholars,it is found that before the introduction of set-valued random variables,the study of interval-valued random variables will be more in line with the usual situation.Therefore,based on the study of set-valued stochastic differential equations,this paper mainly studies set-valued delay stochastic differential equations and interval-valued incremental learning algorithms.This article will be divided into four parts to study.The first part expounds the significance of the research and summarizes the development status of set-valued approximation at home and abroad.Secondly,the role of interval-valued data in promoting machine learning under the background of big data is introduced.The second part introduces the basic knowledge and development of set-valued stochastic integral.The definition of stochastic integral is modified by the method of decomposable closure.On this basis,the necessity of modifying stochastic integral is discussed.The definition and properties of square integrable boundedness of set-valued stochastic integrals,set-valued Lebesgue integrals and set-valued square integrable martingales are mainly introduced.The third part studies the set-valued delay stochastic differential equations to find approximate solutions.The properties of the approximate solution are discussed.By using the error distance between the real solution and the approximate solution,the approximate solution of the set-valued delay stochastic differential equation is found,which is the Caratheodory type approximate solution.The main tools used are Picard iteration,set-valued Lebesgue integral and set-valued square integrable martingale inequalities.The fourth part studies the incremental learning algorithm of interval-valued random variables.In the case of natural learning scenarios,the data arrives in an incremental manner.In order to make the interval-valued data information incremental arrival or dynamic evolution of the scene effective learning metrics,this paper proposes an incremental learning algorithm based on support vector method.This algorithm can flexibly update the measurement according to the new information received,and the related algorithm process is given.