Related papers: Lebesgue-Type inequalities for quasi-greedy bases
In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However,…
We prove thatthe Banach space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which is isomorphic to certain Besov spaces, has a greedy basis whenever $1\leq p \leq\infty$ and $1<q<\infty$. Furthermore, the Banach spaces $(\oplus_{n=1}^\infty…
In this effort we introduce and analyze a novel reduced basis approach, used to construct an approximating subspace for a given set of data. Our technique, which we call the Natural Greedy Algorithm (NGA), is based on a recursive approach…
We shall present new characterizations of partially greedy and almost greedy bases. A new class of basis (which we call reverse partially greedy basis) arises naturally from these characterizations of partially greedy bases. We also give…
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…
We study the problem of fairly allocating a set of indivisible goods among agents with additive valuations. The extent of fairness of an allocation is measured by its Nash social welfare, which is the geometric mean of the valuations of the…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
In \cite{O2015}, T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps. In this paper, we extend some of the notions that appear naturally in connection with these algorithms to the…
We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First,…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…