Related papers: On the Sample Complexity of Subspace Learning

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…

Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find…

Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Change detection is a quite challenging task due to the imbalance between unchanged and changed class. In addition, the traditional difference map generated by log-ratio is subject to the speckle, which will reduce the accuracy. In this…

We develop machinery to design efficiently computable and consistent estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an…

Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…

Robust PCA is a standard tool for learning a linear subspace in the presence of sparse corruption or rare outliers. What about robustly learning manifolds that are more realistic models for natural data, such as images? There have been…

In this paper, we study the problem of direction of arrival estimation and model order selection for systems employing subarray sampling. Thereby, we focus on scenarios, where the number of active sources is not smaller than the number of…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from…

Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…