相关论文: Fast K-Means with Accurate Bounds

We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…

Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical…

The range, segment and rectangle query problems are fundamental problems in computational geometry, and have extensive applications in many domains. Despite the significant theoretical work on these problems, efficient implementations can…

Finding the best K-sparse approximation of a signal in a redundant dictionary is an NP-hard problem. Suboptimal greedy matching pursuit (MP) algorithms are generally used for this task. In this work, we present an acceleration technique and…

In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…

The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…

Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…

In the online checkpointing problem, the task is to continuously maintain a set of k checkpoints that allow to rewind an ongoing computation faster than by a full restart. The only operation allowed is to replace an old checkpoint by the…

In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…

The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…

Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by…

We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…

Various performance measures based on the ground truth and without ground truth exist to evaluate the quality of a developed tracking algorithm. The existing popular measures - average center location error (ACLE) and average tracking…

In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…