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Deep neural networks are known to be vulnerable to adversarial attacks. Current methods of defense from such attacks are based on either implicit or explicit regularization, e.g., adversarial training. Randomized smoothing, the averaging of…
We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time an adversary chooses an input distribution with density function bounded above by $\tfrac{1}{\sigma}$ times that…
Robustness to adversarial attacks is an important concern due to the fragility of deep neural networks to small perturbations and has received an abundance of attention in recent years. Distributionally Robust Optimization (DRO), a…
We study certified robustness of machine learning classifiers against adversarial perturbations. In particular, we propose the first universally approximated certified robustness (UniCR) framework, which can approximate the robustness…
Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
Feature attributions are a popular tool for explaining the behavior of Deep Neural Networks (DNNs), but have recently been shown to be vulnerable to attacks that produce divergent explanations for nearby inputs. This lack of robustness is…
Dimension is an inherent bottleneck to some modern learning tasks, where optimization methods suffer from the size of the data. In this paper, we study non-isotropic distributions of data and develop tools that aim at reducing these…
Modern machine learning models with very high accuracy have been shown to be vulnerable to small, adversarially chosen perturbations of the input. Given black-box access to a high-accuracy classifier $f$, we show how to construct a new…
Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…
Recently, few certified defense methods have been developed to provably guarantee the robustness of a text classifier to adversarial synonym substitutions. However, all existing certified defense methods assume that the defenders are…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…
Randomized smoothing (RS) has been shown to be a fast, scalable technique for certifying the robustness of deep neural network classifiers. However, methods based on RS require augmenting data with large amounts of noise, which leads to…
The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
Randomized smoothing is the state-of-the-art approach to construct image classifiers that are provably robust against additive adversarial perturbations of bounded magnitude. However, it is more complicated to construct reasonable…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…