Related papers: A quantitative notion of redundancy for finite fra…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
Feature selection has attracted significant attention in data mining and machine learning in the past decades. Many existing feature selection methods eliminate redundancy by measuring pairwise inter-correlation of features, whereas the…
New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Feature matching is a crucial task in the field of computer vision, which involves finding correspondences between images. Previous studies achieve remarkable performance using learning-based feature comparison. However, the pervasive…
The typical point cloud sampling methods used in state estimation for mobile robots preserve a high level of point redundancy. This redundancy unnecessarily slows down the estimation pipeline and may cause drift under real-time constraints.…
A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
We present a method to quantify a system's resilience capacity, i.e., the set of degradation magnitudes for which all functional requirements remain satisfied. These requirements come from human stakeholders (e.g., operators, planners) who…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…