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We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…

Numerical Analysis · Mathematics 2007-12-11 Deanna Needell , Roman Vershynin

Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…

Machine Learning · Computer Science 2016-07-28 Quanming Yao , James T. Kwok

Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…

Information Theory · Computer Science 2014-03-24 Ishanu Chattopadhyay , Hod Lipson

We demonstrate that, even when there are moderate overlaps in the inputs of sloppy or accurate double-word addition algorithms in the QD library, these algorithms still guarantee error bounds of $O(u^2(|a|+|b|))$ in faithful rounding.…

Numerical Analysis · Mathematics 2024-04-11 Yuanyuan Yang , XinYu Lyu , Sida He , Xiliang Lu , Ji Qi , Zhihao Li

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…

Numerical Analysis · Mathematics 2026-02-24 Yuwen Li

We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function.

Optimization and Control · Mathematics 2015-05-15 Zheming Gao , Guergana Petrova

Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…

Data Structures and Algorithms · Computer Science 2023-12-14 Thomas Bläsius , Tobias Friedrich , Maximilian Katzmann

Given the proximity of many wireless users and their diversity in consuming local resources (e.g., data-plans, computation and energy resources), device-to-device (D2D) resource sharing is a promising approach towards realizing a sharing…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-23 Shuqin Gao , Costas A. Courcoubetis , Lingjie Duan

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…

Machine Learning · Statistics 2014-01-03 R. A. DeVore , V. N. Temlyakov

Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…

Data Structures and Algorithms · Computer Science 2021-02-23 Ming-Jun Lai , Jiaxin Xie , Zhiqiang Xu

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

Machine Learning · Computer Science 2022-03-04 Aditya Varre , Nicolas Flammarion

In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals, the natural greedy algorithm is $O(\log n)$-competitive,…

Data Structures and Algorithms · Computer Science 2026-04-07 Nikhil Bansal , Milind Prabhu , Sahil Singla , Siddharth M. Sundaram

Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterative algorithm onto layers of a neural network, known as…

Machine Learning · Computer Science 2025-05-22 Sina Mohammad-Taheri , Matthew J. Colbrook , Simone Brugiapaglia

Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…

Data Structures and Algorithms · Computer Science 2021-05-17 Amin Saberi , David Wajc

This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…

Optimization and Control · Mathematics 2026-05-26 Chise Ishii , Yasushi Narushima

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…

Numerical Analysis · Mathematics 2020-02-20 Albert Cohen , Wolfgang Dahmen , Ronald DeVore

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit allowing us to treat…

Combinatorics · Mathematics 2015-04-17 Spencer Backman

Consider a channel with a given input distribution. Our aim is to degrade it to a channel with at most L output letters. One such degradation method is the so called "greedy-merge" algorithm. We derive an upper bound on the reduction in…

Information Theory · Computer Science 2017-05-09 Assaf Kartowsky , Ido Tal

In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…

Optimization and Control · Mathematics 2025-06-04 Mohammad Alkousa , Fedor Stonyakin , Asmaa Abdo , Mohammad Alcheikh