High-Dimensional Regression Analysis and Artificial Intelligence

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In this book, a novel high-dimensional linear and nonlinear regression model is introduced to address, in part, the challenges of evaluating the stability and confidence of large-scale models' interpretability. The book begins by reviewing foundational concepts in regression analysis, and discussing the current state and challenges of AI interpretability. Through an in-depth exploration of regression models, the core principles of data-driven linear regression are explained. To enhance the explanatory power of regression models, variable-parameter regression models are further investigated and extended to variable-parameter nonlinear regression models. To handle complex relationships, the Gauss-Newton iterative method is incorporated, ensuring the stability of high-dimensional nonlinear regression. The Confidence Interval-based Credibility Evaluation (CICE) framework combines statistical indicators—such as interval width, center deviation, and accuracy—into a single score to assess the stability and reliability of explanations, validated through case studies in engineering, finance, and time series prediction. Overall, the book presents a coherent framework for interpretable AI,…

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