Related papers: Adversarially Robust Kernel Smoothing
While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This…
Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However,…
In a reinforcement learning (RL) setting, the agent's optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent's ability to make…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted…
In this paper, we investigate distributionally robust model order reduction for linear, discrete-time, time-invariant systems. The external input is assumed to follow an uncertain distribution within a Wasserstein ambiguity set. We begin by…
Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges. To better understand adversarial robustness, we consider the underlying problem of learning robust representations. We…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
Limiting failures of machine learning systems is of paramount importance for safety-critical applications. In order to improve the robustness of machine learning systems, Distributionally Robust Optimization (DRO) has been proposed as a…
In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
A machine learning model that generalizes well should obtain low errors on unseen test examples. Thus, if we learn an optimal model in training data, it could have better generalization performance in testing tasks. However, learning such a…
Transfer learning is a popular strategy to leverage external knowledge and improve statistical efficiency, particularly with a limited target sample. We propose a novel knowledge-guided Wasserstein Distributionally Robust Optimization…