Related papers: The Preliminary Results on Super Robustness
This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal…
This paper investigates the theory of robustness against adversarial attacks. It focuses on the family of randomization techniques that consist in injecting noise in the network at inference time. These techniques have proven effective in…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…
We prove stability results in hypercontractivity estimates for the Hopf--Lax semigroup in $\mathbb R^n$ and apply them to deduce stability results for the Euclidean $L^p$-logarithmic Sobolev inequality for any $p>1$. As a main tool, we use…
It is widely recognised that semiparametric efficient estimation can be hard to achieve in practice: estimators that are in theory efficient may require unattainable levels of accuracy for the estimation of complex nuisance functions. As a…
The robust estimator presented in this paper processes each structure independently. The scales of the structures are estimated adaptively and no threshold is involved in spite of different objective functions. The user has to specify only…
A class of robust estimators which are obtained from dual representation of $\phi$-divergences, are studied empirically for the normal location model. Members of this class of estimators are compared, and it is found that they are efficient…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…
In a missing-data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar outcomes y_i are missing by happenstance on some individuals. In this work we propose robust estimates…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
I propose a locally robust semiparametric framework for estimating causal effects using the popular examiner IV design, in the presence of many examiners and possibly many covariates relative to the sample size. The key ingredient of this…
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…