Parameter estimation Method--maximum likelihood estimation and Bayesian parameter estimation

Source: Internet
Author: User
  • Why do you use parameter estimation?
    • In Bayesian method, the prior probability and conditional density function are estimated beforehand, and then the classifier is designed. However, in most cases, the number of training samples is always too small, and when used to denote a high number of feature dimensions, the estimation of the conditional density function is computationally complex.
    • Therefore, if we know the number of parameters beforehand, and prior knowledge allows us to parameterize the conditional probability density, we can reduce the difficulty of the problem significantly.
    • For example, if we can assume that the conditional probability density p (x|wi) is a multivariate normal distribution, its mean is UI, and the covariance matrix is ōi (the specific value of the parameter is unknown). This translates the problem from estimating a completely unknown probability density p (x|wi) to an estimated parameter UI and Ōi.

  • Two more effective parameter estimation methods:
    • Maximum likelihood estimation: The parameter to be estimated is considered as a definite quantity, but its value is unknown. The best estimate is the one that gives the highest probability of generating a training sample.
    • Bayesian parameter estimation: The parameters to be measured are considered as random variables conforming to some prior probability distributions. The process of observing the sample is to convert the prior probability density into the posterior probability density, so that the initial estimation of the parameters is corrected by using the information of the sample. A typical effect is that each new observation sample makes the posterior probability density function more acute, resulting in a maximum spike near the true value of the parameter to be evaluated. (Bayesian learning process)

  • Nonparametric Estimation Method (Nonparametric procedure)
    • Firstly, the feature space is transformed and then the parametric method is used in the transformation space to achieve the purpose of simplifying the problem.

Parameter estimation Method--maximum likelihood estimation and Bayesian parameter estimation

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