Following [Hub93, §3], we introduce the spectrum of continuous valuations Cont(A) for a Huber ring A and the adic spectrum Spa(A,A) for a Huber pair (A,A). We also draw heavily from [Con14; Wed12]. These notes are from the arithmetic geometry learning seminar on adic spaces held at the University of Michigan during the Winter 2017 semester, organized by Bhargav Bhatt. See [Dat17; Ste17] for oth...

This vignette attempts to give some background on the robust estimation method implemented in “rlmer”. Moreover, two example analyses are included that aim to facilitate the first time user to start working with this package. The text presented here is basically a summary of Koller (2013). In said reference, a detailed derivation of the methods underlying “rlmer” can be found. The model and som...

This paper proposes a new adaptive filtering algorithm called the Huber Prior Error-Feedback Least Squares Lattice (H-PEF-LSL) algorithm for robust adaptive filtering in impulse noise environment. It minimizes a modified Huber M-estimator based cost function, instead of the least squares cost function. In addition, the simple modified Huber M-estimate cost function also allows us to perform the...

This paper proposes a new adaptive filtering algorithm called the Huber Prior Error-Feedback Least Squares Lattice (H-PEF-LSL) algorithm for robust adaptive filtering in impulse noise environment. It minimizes a modified Huber M-estimator based cost function, instead of the least squares cost function. In addition, the simple modified Huber M-estimate cost function also allows us to perform the...

ÐThe robust Huber M-estimator, a differentiable cost function that is quadratic for small errors and linear otherwise, is modeled exactly, in the original primal space of the problem, by an easily solvable simple convex quadratic program for both linear and nonlinear support vector estimators. Previous models were significantly more complex or formulated in the dual space and most involved spec...

In order to avoid overfitting, it is common practice to regularize linear prediction models using squared or absolute-value norms of the model parameters. In our article we consider a new method of regularization: Huber-norm regularization imposes a combination of `1 and `2-norm regularization on the model parameters. We derive the dual optimization problem, prove an upper bound on the statisti...