Related papers: Nonlinear Laplacians: Tunable principal component …
In a semi-supervised learning scenario, (possibly noisy) partially observed labels are used as input to train a classifier, in order to assign labels to unclassified samples. In this paper, we study this classifier learning problem from a…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…
This paper considers an anomaly detection problem in which a detection algorithm assigns anomaly scores to multi-dimensional data points, such as cellular networks' Key Performance Indicators (KPIs). We propose an optimization framework to…
Effective causal discovery is essential for learning the causal graph from observational data. The linear non-Gaussian acyclic model (LiNGAM) operates under the assumption of a linear data generating process with non-Gaussian noise in…
We consider the linearly transformed spiked model, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: \begin{align*} Y_i = A_i X_i + \varepsilon_i, \end{align*} for $i=1,\ldots,n$. The transform…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
We consider the noisy power method algorithm, which has wide applications in machine learning and statistics, especially those related to principal component analysis (PCA) under resource (communication, memory or privacy) constraints.…
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…
Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations,…
Which components of the singular value decomposition of a signal-plus-noise data matrix are most informative for the inferential task of detecting or estimating an embedded low-rank signal matrix? Principal component analysis ascribes…
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…
We address the problem of detecting the number of complex exponentials and estimating their parameters from a noisy signal using the Matrix Pencil (MP) method. We introduce the MP modes and present their informative spectral structure. We…
Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model…