Related papers: Sampling in a Union of Frame Generated Subspaces

Comparing the internal representations of neural networks is a central goal in both neuroscience and machine learning. Standard alignment metrics operate on raw neural activations, implicitly assuming that similar representations produce…

Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…

In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as…

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…

Mechanism for generation of suppressed neutrino masses, within low scale theories, is considered. The mechanism do not have extradimensional nature and is realized through extended $SU(2)_L$ scalar multiplets. Latters, in some cases, are…

The enormous size of modern deep neural networks makes it challenging to deploy those models in memory and communication limited scenarios. Thus, compressing a trained model without a significant loss in performance has become an…

We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

In this short note we show two results concerning sampling translation invariant subspaces of $\ltwod$ on unions of lattices. The first result shows that the sampling transform on a union of lattices is a constant times an isometry if and…

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…

In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…

We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

In this paper, we study the problem of direction of arrival estimation and model order selection for systems employing subarray sampling. Thereby, we focus on scenarios, where the number of active sources is not smaller than the number of…

Functions or distributions used to sample and to reconstruct signals often occur in different domains, like the Dirac delta and a band-limited bump function in classical sampling. Oblique dual frames generalize this phenomenon. In this…

This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…