Learning With Coefficient-Based Regularized Regression on Markov Resampling.

Area of Science:

• Computer Science
• Statistics
• Machine Learning

Background:

• Big data research presents challenges in extracting effective information.
• Coefficient-based regularized regression (CBRR) is a key area in big data analysis.
• Existing methods may face limitations in handling large, complex datasets.

Purpose of the Study:

• To propose a novel Markov resampling algorithm for efficient sampling in big data.
• To address the challenge of information extraction in coefficient-based regularized regression (CBRR).
• To analyze the theoretical performance and generalization ability of the proposed CBRR algorithm.

Main Methods:

• Development of a selective sampling method using Markov resampling.
• Automatic selection of uniformly ergodic Markov chain (u.e.M.c.) samples based on transition probabilities.
• Theoretical analysis of CBRR algorithm performance using u.e.M.c. samples.

Main Results:

• The proposed Markov resampling algorithm effectively draws useful samples for CBRR.
• Theoretical performance analysis generalizes existing results for independent and identically distributed observations.
• Achieved learning rates arbitrarily close to $\mathcal {O}(m^{-1})$ for infinitely differentiable kernels and mild regularity conditions.
• Experimental validation on simulated and real datasets demonstrates good generalization ability.

Conclusions:

• The Markov resampling algorithm offers an effective approach for information extraction in big data.
• The proposed method enhances the performance and generalization of coefficient-based regularized regression.
• This work contributes to advancing big data learning techniques and theoretical understanding.