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Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

Simultaneous sparse approximation is a generalization of the standard sparse approximation, for simultaneously representing a set of signals using a common sparsity model. Generalizing the compressive sensing concept to the simultaneous…

Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…

This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Inverse problems in imaging are ill-posed, leading to infinitely many solutions consistent with the measurements due to the non-trivial null-space of the sensing matrix. Common image priors promote solutions on the general image manifold,…

Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing (CS), it is often assumed that the signal of…

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…

In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…

The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…

High-quality reconstructions of signals and images with sharp edges are needed in a wide range of applications. To overcome the large dimensionality of the parameter space and the complexity of the regularization functional,…

Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…

In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and engineering. Although the GTRS, as stated, is nonlinear and…