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Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
We study the out-of-sample properties of robust empirical optimization problems with smooth $\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness…
Randomness supports many critical functions in the field of machine learning (ML) including optimisation, data selection, privacy, and security. ML systems outsource the task of generating or harvesting randomness to the compiler, the cloud…
We study the $L_p$-discrepancy of random point sets in high dimensions, with emphasis on small values of $p$. Although the classical $L_p$-discrepancy suffers from the curse of dimensionality for all $p \in (1,\infty)$, the gap between…
Adversarial robustness measures the susceptibility of a classifier to imperceptible perturbations made to the inputs at test time. In this work we highlight the benefits of natural low rank representations that often exist for real data…
Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the…
Several existing works study either adversarial or natural distributional robustness of deep neural networks separately. In practice, however, models need to enjoy both types of robustness to ensure reliability. In this work, we bridge this…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Certified defense using randomized smoothing is a popular technique to provide robustness guarantees for deep neural networks against l2 adversarial attacks. Existing works use this technique to provably secure a pretrained non-robust model…
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial…
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
In data-driven optimization, sample average approximation (SAA) is known to suffer from the so-called optimizer's curse that causes an over-optimistic evaluation of the solution performance. We argue that a special type of distributionallly…
Data subsampling is one of the most natural methods to approximate a massively large data set by a small representative proxy. In particular, sensitivity sampling received a lot of attention, which samples points proportional to an…
Recently it has been shown that state-of-the-art NLP models are vulnerable to adversarial attacks, where the predictions of a model can be drastically altered by slight modifications to the input (such as synonym substitutions). While…
In adversarial machine learning, deep neural networks can fit the adversarial examples on the training dataset but have poor generalization ability on the test set. This phenomenon is called robust overfitting, and it can be observed when…
The safety and robustness of learning-based decision-making systems are under threats from adversarial examples, as imperceptible perturbations can mislead neural networks to completely different outputs. In this paper, we present an…