Related papers: Beyond the Mean: Distribution-Aware Loss Functions…

State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

Deep learning provides a powerful tool for machine perception when the observations resemble the training data. However, real-world robotic systems must react intelligently to their observations even in unexpected circumstances. This…

In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient…

Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we…

In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While data augmentation techniques…

Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems,…

We study expected generalization bounds for the Hierarchical Federated Learning (HFL) setup using Wasserstein distance. We introduce a generalized framework in which data is sampled hierarchically, and we model it with a multi-layered tree…

Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments,…

We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…

Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data…

Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a…