Related papers: Some remarks on regularized Shannon sampling formu…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
In this paper, the paradigm of sphere decoding (SD) based on lattice Gaussian distribution is studied, where the sphere radius $D>0$ in the sense of Euclidean distance is characterized by the initial pruning size $K>1$, the standard…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid both aliasing and redundant oversampling by design. Conversely, in medical image resampling, images are considered as continuous functions, are warped by a spatial…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…
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…
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…