Self-adaptive polynomial regression method based on cross-dimensional Markov chain Monte Carlo

Abstract

An adaptive polynomial regression method based on cross-dimensional Markov chain Monte Carlo is characterized by comprising the following steps: establishing a graph model containing polynomial ordersand polynomial coefficients in polynomial regression; aiming at a polynomial regression problem, providing two cross-dimensional parameter state transition strategies of birth and death and an invariant-dimension parameter updating strategy, and adopting a design idea of cross-dimensional joint optimization based on cross-dimensional Markov chain Monte Carlo to carry out Bayesian reasoning of parameters. According to the adaptive polynomial regression method, the optimal order of the polynomial and the coefficient of the polynomial can be determined in a self-adaptive mode according to the known data to be regressed, and good robustness is achieved.

Description

technical field [0001] The invention belongs to the technical field of signal processing, and in particular relates to a polynomial regression method based on Trans-dimensional Markov Chain Monte Carlo (TDMCMC). In the next data processing problem. Background technique [0002] Regression analysis is a statistical analysis method to determine the quantitative relationship between two or more variables. Polynomial regression is an important method in regression analysis and is used in many fields. The classic polynomial regression problem is actually still a difficult problem. The main reason is that it is still difficult to choose the polynomial order given the known data points. In the past, polynomial fitting or regression analysis was often performed under the assumption that the polynomial order was already determined. , if the polynomial order is too high, overfitting will occur; if the polynomial order is too low, the data cannot be well regressed. Therefore, it is ...

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Problems solved by technology

The classic polynomial regression problem is actually still a difficult problem. The main reason is that it is still difficult to choose the polynomial order given the known data points. In the past, polynomial fitting or regression analysis was often performed under the assumption that the polynomial order was already determined. , if the polynomial order is too high, overfitting will occur; if the polynomial order is too low, the data cannot be well regressed

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