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

In this paper four iterative algorithms for learning analysis operators are presented. They are built upon the same optimisation principle underlying both Analysis K-SVD and Analysis SimCO. The Forward and Sequential Analysis Operator…

Imbalanced distribution learning is a common and significant challenge in predictive modeling, often reducing the performance of standard algorithms. Although various approaches address this issue, most are tailored to classification…

Monocular visual-inertial odometry (VIO) is a critical problem in robotics and autonomous driving. Traditional methods solve this problem based on filtering or optimization. While being fully interpretable, they rely on manual interference…

Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces. However, their approximation properties in Sobolev norms remain poorly quantified, even though these norms control both…

State-of-the-art Variational Auto-Encoders (VAEs) for learning disentangled latent representations give impressive results in discovering features like pitch, pause duration, and accent in speech data, leading to highly controllable…

Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely…

Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…

Recent work by Locatello et al. (2018) has shown that an inductive bias is required to disentangle factors of interest in Variational Autoencoder (VAE). Motivated by a real-world problem, we propose a setting where such bias is introduced…

State-of-the-art reinforcement learning algorithms mostly rely on being allowed to directly interact with their environment to collect millions of observations. This makes it hard to transfer their success to industrial control problems,…

Pathological brain lesions exhibit diverse appearance in brain images, in terms of intensity, texture, shape, size, and location. Comprehensive sets of data and annotations are difficult to acquire. Therefore, unsupervised anomaly detection…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

Variational Auto-encoders (VAEs) are deep generative latent variable models consisting of two components: a generative model that captures a data distribution p(x) by transforming a distribution p(z) over latent space, and an inference…

Identifying unfamiliar inputs, also known as out-of-distribution (OOD) detection, is a crucial property of any decision making process. A simple and empirically validated technique is based on deep ensembles where the variance of…

We propose self-adaptive training---a new training algorithm that dynamically corrects problematic training labels by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially…

Managing noisy data is a central challenge in direct data-driven control design. We propose an approach for synthesizing model-reference controllers for linear time-invariant (LTI) systems using noisy state-input data, employing novel noise…

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural…

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and…

One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic…

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from…