The Application Of Several Types Of Supervised Learning Algorithms In The Parameter Estimation Of Stochastic Biological Models

Parameter estimation of random biological models has received much concern all the time.However,most researches use mathematical knowledge to solve the problem,such as dynamic behavior,stochastic differential equations.With the development of computer science,the theory of machine learning is gradually enriched.Furthermore,because the parameter estimation of biological models involves the analysis of data,the algorithm about machine learning plays an unique role in the parameter estimation of biological models.This paper mainly introduces three kinds of supervised learning algorithms.And based on the specific biological problems,these three types of algorithms are used to estimate the parameters of the relevant random biological models.In the third chapter,we briefly introduce the principle and steps of the Expectation-Maximization(EM)algorithm which is mainly used to solve the problems of parameter estimation in the case of incomplete data due to data missing.Due to the disadvantages that the integral of the E step in the EM algorithm cannot calculate,our paper discusses the Monte Carlo EM(MCEM)algorithm aimed at the inability to calculate the integral of the E step.The MCEM algorithm uses Monte Carlo simulation to effectively estimate the integral in the E step,which significantly improves the practicability of the EM algorithm.In addition,we apply MCEM algorithm to the simple Logit-Normal model.Firstly,the samples are draw by Metropolis-Hastings(MH)sampling.Then we approximate the integral by these simulations.Finally,the estimations are computed by iteration method.In the fourth chapter,we describe the MCWM algorithm and GIMH algorithm based on MCMC algorithm.These two algorithms obtain samples subjected to the marginal distribution by sampling from the joint distribution.Therefore,they are collectively referred to as pseudo-edge methods.Besides,algorithms are used to estimate parameter in the case of data missing.The samples obtained by these algorithms can be regarded as being from approximate posterior distribution.By simulating the latent variables,we transform the parameter estimation problem of incomplete data into the parameter estimation of the complete data.Combining the random infectious disease model,firstly,the Gillespie algorithm is used to simulate the true infectious disease development process,and then the accuracy of the two algorithms is verified based on the observed data.Finally,the algorithm is applied to the case of influenza outbreaks in boarding schools in the UK,which further proves the effectiveness of the algorithm.Taking the escape problem of si RNA in RNA interference as background in the fifth chapter,we peruse the estimation of the escaping amount.The amount of short interfering RNA(si RNA)escaping from endosome has a significant impact on the efficiency of RNA interference(RNAi).In general,it is impossible to measure the amount of si RNAs which escape from the endosome and really take part in the chemical reaction of RNAi by detecting the biological organism and its tissues.Inspired by the methods of estimation about bottleneck size,this chapter introduces Bayesian inference to estimate the escape of single-type and multi-type si RNA,and gives the corresponding algorithms.However,in the actual operation process,we find the high computation complexity of the accurate posterior distribution,and so the algorithm has a lower running efficiency.Therefore,we propose to sample by the improved MCMC method,and the corresponding algorithms are also given.Taking the RNA interference on chitin synthesis and multi-target tumor gene therapy as examples,the escape amount of si RNAs was accurately estimated,and we found that the improved MCMC methods have higher operational efficiency.Our research may provide a standardized statistical method for estimating escape amount of si RNA.