Related papers: Automatic Subspace Learning via Principal Coeffici…

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…

Unsupervised learning is becoming more and more important recently. As one of its key components, the autoencoder (AE) aims to learn a latent feature representation of data which is more robust and discriminative. However, most AE based…

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

Automatically learning features, especially robust features, has attracted much attention in the machine learning community. In this paper, we propose a new method to learn non-linear robust features by taking advantage of the data manifold…

Modeling data uncertainty is important for noisy images, but seldom explored for face recognition. The pioneer work, PFE, considers uncertainty by modeling each face image embedding as a Gaussian distribution. It is quite effective.…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii)…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…

Recently, numerous learning-based compression methods have been developed with outstanding performance for the coding of the geometry information of point clouds. On the contrary, limited explorations have been devoted to point cloud…

Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…

Robust subspace recovery (RSR) is a fundamental problem in robust representation learning. Here we focus on a recently proposed RSR method termed Dual Principal Component Pursuit (DPCP) approach, which aims to recover a basis of the…

Self-supervision can dramatically cut back the amount of manually-labelled data required to train deep neural networks. While self-supervision has usually been considered for tasks such as image classification, in this paper we aim at…