Related papers: Nonlinear Laplacians: Tunable principal component …
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…
We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically,…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradient…
The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
We propose an algorithm to uncover the intrinsic low-rank component of a high-dimensional, graph-smooth and grossly-corrupted dataset, under the situations that the underlying graph is unknown. Based on a model with a low-rank component…
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a…
Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can…
Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper, they proposed a rankability measure that is based on a…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…