Related papers: Lattices Without a Big Constant and With Noise
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…
We propose a general renormalization method, which avoids completely the use of lattice perturbation theory. We present the results from its numerical applications to two-fermion operators on a $16^3 \times 32$ lattice, at $\beta=6.0$.
In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of…
We propose a flux representation based lattice formulation of the partition function corresponding to the SU(2) principal chiral Lagrangian, including a chemical potential and scalar/pseudo-scalar source terms. Lattice simulations are then…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the…
We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
This paper presents stability and convergence analysis of a finite volume scheme (FVS) for solving aggregation, breakage and the combined processes by showing Lipschitz continuity of the numerical fluxes. It is shown that the FVS is second…
We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
It has been known for a long time that large-$N$ methods can give invaluable insights into non-perturbative phenomena such as confinement. Lattice techniques can be used to compute quantities at large $N$. In this contribution, I review…
The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…
We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…
Lasso is a seminal contribution to high-dimensional statistics, but it hinges on a tuning parameter that is difficult to calibrate in practice. A partial remedy for this problem is Square-Root Lasso, because it inherently calibrates to the…