Related papers: Random Tight Frames
A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly…
We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples…
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n \varphi \}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space. It is known that the desire…
We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single photon sources, strong…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…
This paper introduces an innovative and intuitive finite population sampling method that has been developed using a unique graphical framework. In this approach, first-order inclusion probabilities are represented as bars on a…
In recent interactive segmentation algorithms, previous probability maps are used as network input to help predictions in the current segmentation round. However, despite the utilization of previous masks, useful information contained in…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
Time-varying data with irregular structures can be described by finite time-vertex graph signals (FTVGS), which represent potential temporal and spatial relationships among multiple sources. While sampling and corresponding reconstruction…
This study addresses an image-matching problem in challenging cases, such as large scene variations or textureless scenes. To gain robustness to such situations, most previous studies have attempted to encode the global contexts of a scene…
Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Temporal point process (TPP) models combined with recurrent neural networks provide a powerful framework for modeling continuous-time event data. While such models are flexible, they are inherently sequential and therefore cannot benefit…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…