Related papers: Field theoretical approach for signal detection in…
Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address…
This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended…
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Signal detection is one of the main challenges of data science. As it often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques aimed at extracting the relevant degrees of freedom…
Signal detection in high dimensions is a critical challenge in data science. While standard methods based on random matrix theory provide sharp detection thresholds for finite-rank perturbations, such as the known Baik-Ben Arous-P\'ech\'e…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…
We introduce a new tensor norm, the average spectrum norm, to study sample complexity of tensor completion problems based on the canonical polyadic decomposition (CPD). Properties of the average spectrum norm and its dual norm are…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different…