Algorithmic High-Dimensional Robust Statistics (Hardcover)

Robust statistics is the study of designing estimators that perform well even when the dataset significantly deviates from the idealized modeling assumptions, such as in the presence of model misspecification or adversarial outliers in the dataset. The classical statistical theory, dating back to pioneering works by Tukey and Huber, characterizes the information-theoretic limits of robust estimation for most common problems. A recent line of work in computer science gave the first computationally efficient robust estimators in high dimensions for a range of learning tasks. This reference text for graduate students, researchers, and professionals in machine learning theory, provides an overview of recent developments in algorithmic high-dimensional robust statistics, presenting the underlying ideas in a clear and unified manner, while leveraging new perspectives on the developed techniques to provide streamlined proofs of these results. The most basic and illustrative results are analyzed in each chapter, while more tangential developments are explored in the exercises.

堅固統計學是研究設計估計器的學科，即使數據集與理想化的建模假設明顯偏離，例如模型錯誤規範或數據集中存在對抗性的離群值，這些估計器仍能表現良好。經典的統計理論，追溯至Tukey和Huber的開創性工作，對於大多數常見問題的堅固估計進行了信息理論限制的刻畫。計算機科學中的最新研究方向為一系列學習任務提供了高維度的計算效率堅固估計器。這本參考書針對研究生、研究人員和機器學習理論專業人士，概述了算法高維度堅固統計學的最新發展，以清晰統一的方式呈現了其中的基本思想，同時利用新的觀點對所開發技術的結果提供了簡化的證明。每章分析了最基本且具有說明性的結果，而更偏離主題的發展則在練習中探討。