Abstract: The low-degree polynomial framework has emerged as a versatile tool for probing the computational complexity of statistical problems by studying the power and limitations of a restricted class of algorithms: low-degree polynomials. Focusing on the setting of hypothesis testing, I will discuss some extensions of this method that allow us to tackle finer-grained questions…

Abstract: We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source…

Abstract: We consider the Error-in-Operator (EiO) problem of recovering the source x signal from the noise observation Y given by the equation Y = A x + ε in the situation when the operator A is not precisely known. Instead, a pilot estimate \hat{A} is available. The study is motivated by Hoffmann & Reiss (2008), Trabs (2018) and by recent results on high dimensional regression with random design; see e.g., Tsigler, Bartlett (2020) (Benign overfitting…