Related papers: On greedy approximation in complex Banach spaces
We investigate various aspects of the "weighted" greedy algorithm with respect to a Schauder basis. For a weight w, we describe w-greedy, w-almost-greedy and w-partially-greedy bases, and show some properties of w-semi-greedy bases. To…
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N- term error of approximation times a function of N which depends on the democracy…
We analyse the problem of controllability for parameter-dependent linear finite-dimensional systems. The goal is to identify the most distinguished realisations of those parameters so to better describe or approximate the whole range of…
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
One classical result in greedy approximation theory is that almost-greedy and semi-greedy bases are equivalent in the context of Schauder bases in Banach spaces with finite cotype. This result was proved by S. J. Dilworth, N. J. Kalton and…
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…
Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the…
We discuss the upper and lower estimates for the rate of convergence of Pure and Orthogonal Greedy Algorithms for dictionary with bounded cumulative coherence.
We consider the approximation capability of orthogonal super greedy algorithms (OSGA) and its applications in supervised learning. OSGA is concerned with selecting more than one atoms in each iteration step, which, of course, greatly…
In this paper we consider the generalized Walsh system and a problem $L^1- convergence$ of greedy algorithm of functions after changing the values on small set.
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…
A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are…
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
In this paper we study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding greedy algorithm. We measure how far these bases are from…
In this paper we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgue-type parameters associated with them. We prove that this…
We investigate properties of the $m$-th error of approximation by polynomials with constant coefficients $\mathcal{D}_{m}(x)$ and with modulus-constant coefficients $\mathcal{D}_{m}^{\ast}(x)$ introduced by Bern\'a and Blasco (2016) to…
It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of $\mathbb{N}$. In…
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…
We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent and leads to sharper convergence rates than the classical…