Approximation and learning by greedy algorithms
نویسندگان
چکیده
منابع مشابه
Approximation and learning by greedy algorithms
We consider the problem of approximating a given element f from a Hilbert space H by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. ...
متن کاملSimultaneous approximation by greedy algorithms
We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = ∞ X j=1 cj(f)φj(f), φj(f) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f‖2 = j |cj(f)|. Following the paper of A. Lutoborsk...
متن کاملGreedy in Approximation Algorithms
The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1 k -factor approximation for these systems. Many seemly unrelated problems fit in our framework, e.g.: b-matching, maxi...
متن کاملSparse approximation and recovery by greedy algorithms in
We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a generalization of the Weak Orthogonal Matching Pursuit to the case of a Banach space. The main novelty of these results is a Banach space setting instead of a Hilbert space setting. The results are proved for redundant dictionaries satisfying certain cond...
متن کاملGreedy Approximation Algorithms for K-Medians by Randomized Rounding
We give an improved approximation algorithm for the general kmedians problem. Given any > 0, the algorithm nds a solution of total distance at most D(1 + ) using at most k ln(n + n= ) medians (a.k.a. sites), provided some solution of total distance D using k medians exists. This improves over the best previous bound (w.r.t. the number of medians) by a factor of (1= ) provided 1= = n. The algori...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2008
ISSN: 0090-5364
DOI: 10.1214/009053607000000631