Related papers: An inverse problem for the collapsing sum

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics…

Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…

Inverse problems play a central role for many classical computer vision and image processing tasks. Many inverse problems are ill-posed, and hence require a prior to regularize the solution space. However, many of the existing priors, like…

We introduce collapsed compilation, a novel approximate inference algorithm for discrete probabilistic graphical models. It is a collapsed sampling algorithm that incrementally selects which variable to sample next based on the partial…

Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…

We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral…

Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS,…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is…

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…

We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…