Related papers: Adaptive Quarklet Tree Approximation
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise $C^2$-functions, separated by a $C^2$ singularity curve. In this paper, we consider the more general case of…
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theory to obtain convergence results for practical adaptive…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to the second part of Question~2 from Stone (1982) on the optimal convergence…
For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…