Related papers: Wavelet-Packet Content for Positive Operators
In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
New results on strong-consistency, in the Hilbert-Schmidt and trace operator norms, are obtained, in the parameter estimation of an autoregressive Hilbertian process of order one (ARH(1) process). In particular, a strongly-consistent…
The notion of {\em $p$-adic multiresolution analysis (MRA)} is introduced. We discuss a ``natural'' refinement equation whose solution (a refinable function) is the characteristic function of the unit disc. This equation reflects the fact…
We study strongly measurable random bounded operators on separable Hilbert spaces and analyze two simple iterations driven by independent random positive contractions. The first, a Kaczmarz-like iteration, converges in mean square and…
State-of-the-art methods for Transformer-based semantic segmentation typically adopt Transformer decoders that are used to extract additional embeddings from image embeddings via cross-attention, refine either or both types of embeddings…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
This work investigates the fundamental properties of the degenerate preconditioned resolvent under restricted monotonicity. We extend key notions of non-expansiveness and demiclosedness to the degenerate case. By deriving an explicit…
This paper develops intrinsic wavelet denoising methods for surfaces of Hermitian positive definite matrices, with in mind the application to nonparametric estimation of the time-varying spectral matrix of a multivariate locally stationary…
This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
Results of Haagerup and Schultz (2009) about existence of invariant subspaces that decompose the Brown measure are extended to a large class of unbounded operators affiliated to a tracial von Neumann algebra. These subspaces are used to…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…