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Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…

Unsupervised graph representation learning (UGRL) based on graph neural networks (GNNs), has received increasing attention owing to its efficacy in handling graph-structured data. However, existing UGRL methods ideally assume that the node…

Gravitational-wave detectors are affected by short-duration non-Gaussian noise transients, commonly referred to as glitches, which can obscure astrophysical signals and complicate downstream analyses. While recent work has demonstrated the…

Graph neural networks (GNNs) have achieved state-of-the-art performance for node classification on graphs. The vast majority of existing works assume that genuine node labels are always provided for training. However, there has been very…

Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic…

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to…

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and…

Dataset biases are notoriously detrimental to model robustness and generalization. The identify-emphasize paradigm appears to be effective in dealing with unknown biases. However, we discover that it is still plagued by two challenges: A,…

In many machine learning applications, we are faced with incomplete datasets. In the literature, missing data imputation techniques have been mostly concerned with filling missing values. However, the existence of missing values is…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

Many learning tasks in machine learning can be viewed as taking a gradient step towards minimizing the average loss of a batch of examples in each training iteration. When noise is prevalent in the data, this uniform treatment of examples…

We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient…