用高维几何方法解决优化与数据科学中的难题。
A Geometric Approach to Problems in Optimization and Data Science
- 基于高维几何与概率工具设计新算法
- 提出流式环境下的多面体逼近与鲁棒回归新方法
- 适用于优化与数据安全领域的研究者
我们利用高维几何与概率工具，为计算与统计机器学习问题提供新结果。第一部分聚焦优化的计算问题，提出在数据流中逼近凸多面体、稀疏化与鲁棒最小二乘回归的新算法，以及对抗性优化方法。第二部分给出数据科学问题的新统计保证，构建新模型分析后门数据投毒攻击的统计特性，并研究图聚类算法对“有益”模型误设的鲁棒性。
原文摘要 · Abstract (English)
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in optimization. Specifically, we give new algorithms for approximating convex polytopes in a stream, sparsification and robust least squares regression, and dueling optimization. In Part II, we give new statistical guarantees for data science problems. In particular, we formulate a new model in which we analyze statistical properties of backdoor data poisoning attacks, and we study the robustness of graph clustering algorithms to ``helpful'' misspecification.
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