Related papers: Error-in-variables modelling for operator learning

In this paper, online linear regression in environments corrupted by non-Gaussian noise (especially heavy-tailed noise) is addressed. In such environments, the error between the system output and the label also does not follow a Gaussian…

Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator…

The surrogate loss of variational autoencoders (VAEs) poses various challenges to their training, inducing the imbalance between task fitting and representation inference. To avert this, the existing strategies for VAEs focus on adjusting…

We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…

In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results…

We develop a framework for quantifying omitted variable bias (OVB) in nonlinear instrumental variable (IV) estimators, including the local average treatment effect (LATE), the LATE for the treated (LATT), and the partially linear IV model…

In this paper we demonstrate methods for reliable and efficient training of discrete representation using Vector-Quantized Variational Auto-Encoder models (VQ-VAEs). Discrete latent variable models have been shown to learn nontrivial…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Despite our best efforts, deep learning models remain highly vulnerable to even tiny adversarial perturbations applied to the inputs. The ability to extract information from solely the output of a machine learning model to craft adversarial…

Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of high-dimensional, parametric systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs…

Training deep generative models like Variational Autoencoders (VAEs) requires propagating gradients through stochastic latent variables, which introduces estimation variance that can slow convergence and degrade performance. In this paper,…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the linearizing transformations provided by the Cole-Hopf…

Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Advanced auditory models are useful in designing signal-processing algorithms for hearing-loss compensation or speech enhancement. Such auditory models provide rich and detailed descriptions of the auditory pathway, and might allow for…

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…