Related papers: Adaptive Approximation of the Minimum of Brownian …
A well-known result with respect to the one dimensional nearest-neighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the…
We study the extremes of variable speed branching Brownian motion (BBM) where the time-dependent "speed functions", which describe the time-inhomogeneous variance, converge to the identity function. We consider general speed functions lying…
This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art…
The primal-dual active set method is observed to be the limit of a sequence of penalty formulations. Using this perspective, we propose a penalty method that adaptively becomes the active set method as the residual of the iterate decreases.…
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…
Computer vision algorithms are known to be extremely sensitive to the environmental conditions in which the data is captured, e.g., lighting conditions and target density. Tuning of parameters or choosing a completely new algorithm is often…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. As it is known, the…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…
We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms…
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorithm achieves high reliability with less computational cost…
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially…