Related papers: Sampling pseudospectrum for data-driven matrices
Spectral embedding uses eigenfunctions of the discrete Laplacian on a weighted graph to obtain coordinates for an embedding of an abstract data set into Euclidean space. We propose a new pre-processing step of first using the eigenfunctions…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
In this paper, we propose and evaluate a novel algorithm for performing spectrum sensing on linear modulations based on second-order cyclic features of the received signals. The proposed approach has similar computational complexity to that…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Protecting individual privacy is crucial when releasing sensitive data for public use. While data de-identification helps, it is not enough. This paper addresses parameter estimation in scenarios where data are perturbed using the…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…
We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…
Differentially-private histograms have emerged as a key tool for location privacy. While past mechanisms have included theoretical & experimental analysis, it has recently been observed that much of the existing literature does not fully…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Sparse auto-encoders are useful for extracting low-dimensional representations from high-dimensional data. However, their performance degrades sharply when the input noise at test time differs from the noise employed during training. This…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
The problem of heterogeneous clients in federated learning has recently drawn a lot of attention. Spectral model sharding, i.e., partitioning the model parameters into low-rank matrices based on the singular value decomposition, has been…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
Data selection is essential for training deep learning models. An effective data sampler assigns proper sampling probability for training data and helps the model converge to a good local minimum with high performance. Previous studies in…
This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…