Instability, Computational Efficiency and Statistical Accuracy Speaker: Nhat Ho - University of Texas at Austin Time: 14:00-15:00 Friday 12 August 2022 Location: Zoom at https://uni-sydney.zoom.us/j/89818118106 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 Newtonâs 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 stepsânamely, with the number of iterations being reduced from polynomial to logarithmic in sample size n." Bio: 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 algorithms.