Related papers: Estimating Principal Components under Adversarial …

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of…

Randomized smoothing is a popular certified defense against adversarial attacks. In its essence, we need to solve a problem of statistical estimation which is usually very time-consuming since we need to perform numerous (usually $10^5$)…

Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted…

Intentionally crafted adversarial samples have effectively exploited weaknesses in deep neural networks. A standard method in adversarial robustness assumes a framework to defend against samples crafted by minimally perturbing a sample such…

Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. $\ell_0$-norm adversarial perturbation characterizes an attack that arbitrarily modifies some features…

Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous…

Current research on defending against adversarial examples focuses primarily on achieving robustness against a single attack type such as $\ell_2$ or $\ell_{\infty}$-bounded attacks. However, the space of possible perturbations is much…

While $\mathcal{H}_\infty$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between…

Learning distribution families over $\mathbb{R}^d$ is a fundamental problem in unsupervised learning and statistics. A central question in this setting is whether a given family of distributions possesses sufficient structure to be (at…

It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. One of the fundamental problems in adversarial machine learning is to quantify how much training data is needed in the…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

This paper considers two fundamental sequential decision-making problems: the problem of prediction with expert advice and the multi-armed bandit problem. We focus on stochastic regimes in which an adversary may corrupt losses, and we…

We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…

It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key…

The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be {\it $\epsilon$-adversarially…

Robustness and counterfactual bias are usually evaluated on a test dataset. However, are these evaluations robust? If the test dataset is perturbed slightly, will the evaluation results keep the same? In this paper, we propose a "double…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

Deep neural networks have achieved remarkable success in a wide range of classification tasks. However, they remain highly susceptible to adversarial examples - inputs that are subtly perturbed to induce misclassification while appearing…

Previous studies demonstrate DNNs' vulnerability to adversarial examples and adversarial training can establish a defense to adversarial examples. In addition, recent studies show that deep neural networks also exhibit vulnerability to…