We study the error of linear regression in face adversarial attacks. In this framework, an adversary changes input to model order maximize prediction error. provide bounds on presence as a function parameter norm and absence such adversary. show how these make it possible using analysis from non-adversarial setups. The obtained results shed light robustness overparameterized models Adding featu...

This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize as an instance of Follow-The-Leader (FTL). Standard results in convex optimization then imply that, even when outcomes are chosen by adversary, predictions counterfactual for the treated unit perform almost well oracle weighted average units' outcomes. Synthetic on differenced data per...

Tensor regression is an important and useful tool for analyzing multidimensional array data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in (penalized) loss functions. However, besides well-known non-identifiability issue of CP parameters, we demonstrate that corresponding optimization may not have any attai...

Motivated by the newly developed max-linear competing copula factor models and max-stable nonlinear time series models, we propose a new class of regression to take advantages easy interpretable features embedded in linear models. It can be seen that relation is special case relation. We develop an EM algorithm based maximum likelihood estimation procedure. The consistency asymptotics estimator...

Field observations form the basis of many scientific studies, especially in ecological and social sciences. Despite efforts to conduct such surveys a standardized way, can be prone systematic measurement errors. The removal variability introduced by observation process, if possible, greatly increase value this data. Existing non-parametric techniques for correcting errors assume linear additive...

In order to calculate confidence intervals and hypothesis tests, it is assumed that the errors are independent and normally distributed with mean zero and variance 2 σ . Given a sample of N observations on X and Y, the method of least squares estimates β0 and β1 as well as various other quantities that describe the precision of the estimates and the goodness-of-fit of the straight line to the d...

The errors ei in (1.1) are assumed to be independent and identically distributed, but are not necessarily normal and may be heavy-tailed. Assume for convenience that β is one dimensional. Then (1.1) is a simple linear regression. However, most of the following extends more-or-less easily to higher-dimensional β, in which case (1.1) is a multiple regression. Given β, define Ri(β) as the rank (or...

Ordinary Least Squares (OLS) is omnipresent in regression modeling. Occasionally Least Absolute Deviations (LAD) or other methods are used as an alternative when there are outliers. Although some data adaptive estimators have been proposed they are typically difficult to implement. In this note, we propose an easy to compute adaptive estimator which is simply a linear combination of OLS and LAD...