Instability, Computational Efficiency and Statistical Accuracy
*** Update 3 June 2022: This seminar is cancelled because the speaker has an unexpected family issue. We are trying to re-schedule the seminar with him.
Speaker: Nhat Ho (University of Texas at Austin)
Time: 14-15h Friday 3 June 2022
Link: https://uni-sydney.zoom.us/j/85712683684
Abstract: Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the properties of the population-level operator in the idealized limit of infinitely many samples. We develop a general framework that yields bounds on statistical accuracy based on the interplay between the deterministic convergence rate of the algorithm at the population level, and
its degree of (in)stability when applied to an empirical object based on n samples. Using this framework, we analyze both stable forms of gradient descent and some higher-order and unstable algorithms, including Newton's method and its cubic-regularized variant, as well as the EM algorithm. We provide applications of our general results to several concrete classes of singular statistical models, including
Gaussian mixture estimation, single-index models, and informative non-response models. We exhibit cases in which an unstable algorithm can achieve the same statistical accuracy as a stable algorithm in exponentially fewer steps, namely, with the number of iterations being reduced from polynomial to logarithmic in sample size n.
Bio: Dr. Nhat Ho is currently an Assistant Professor of Statistics and Data Sciences at the University of Texas at Austin. He is also a core member of the Machine Learning Laboratory. His current research focuses on the interplay of four principles of statistics and data science: heterogeneity of data, interpretability of models, stability, and scalability of optimization and sampling algorithm.
Gaussian mixture estimation, single-index models, and informative non-response models. We exhibit cases in which an unstable algorithm can achieve the same statistical accuracy as a stable algorithm in exponentially fewer steps, namely, with the number of iterations being reduced from polynomial to logarithmic in sample size n.
Bio: Dr. Nhat Ho is currently an Assistant Professor of Statistics and Data Sciences at the University of Texas at Austin. He is also a core member of the Machine Learning Laboratory. His current research focuses on the interplay of four principles of statistics and data science: heterogeneity of data, interpretability of models, stability, and scalability of optimization and sampling algorithm.