Related papers: It's All in the Mix: Wasserstein Classification an…
Most research designing novel predictive models, or employing existing ones, assumes that training and testing data are independent and identically distributed. In practice, the data encountered at serving time often deviate from the…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…
Supervised learning is classically formulated as training a model to minimize a fixed loss function over a fixed distribution, or task. However, an emerging paradigm instead views model training as extracting enough information from data so…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
In prescriptive analytics, the decision-maker observes historical samples of $(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the concurrent covariate, without knowing the joint distribution. Given an additional covariate…
Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image…
Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…
In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…
In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…
The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that…
In this paper, we propose a novel semi-supervised feature selection framework by mining correlations among multiple tasks and apply it to different multimedia applications. Instead of independently computing the importance of features for…
We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite programs. We give an exchange method…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…