Efficient and Local Parallel Random Walks

• URL: http://arxiv.org/abs/2112.00655v1
• Date: Wed, 1 Dec 2021 17:06:11 GMT
• Title: Efficient and Local Parallel Random Walks
• Authors: Michael Kapralov, Silvio Lattanzi, Navid Nouri, Jakab Tardos
• Abstract summary: Random walks are a fundamental primitive used in many machine learning algorithms. We present a new algorithm that overcomes this limitation by building random walk efficiently and locally. We show that our technique is both memory and round efficient, and in particular yields an efficient parallel local clustering algorithm.
• Score: 21.29022677162416
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks has been introduced very recently (Lacki et al.). Unfortunately their method has a fundamental shortcoming: their algorithm is non-local in that it heavily relies on computing random walks out of all nodes in the input graph, even though in many practical applications one is interested in computing random walks only from a small subset of nodes in the graph. In this paper, we present a new algorithm that overcomes this limitation by building random walk efficiently and locally at the same time. We show that our technique is both memory and round efficient, and in particular yields an efficient parallel local clustering algorithm. Finally, we complement our theoretical analysis with experimental results showing that our algorithm is significantly more scalable than previous approaches.

Related papers

• Optimizing Tensor Contraction Paths: A Greedy Algorithm Approach With Improved Cost Functions [1.3812010983144802]
  We introduce a novel approach based on the greedy algorithm by opt_einsum that computes efficient contraction paths in less time. With our approach, we are even able to compute paths for large problems where modern algorithms fail.
  arXiv  Detail & Related papers  (2024-05-08T09:25:39Z)
• Learning the Positions in CountSketch [49.57951567374372]
  We consider sketching algorithms which first compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem. In this work, we propose the first learning-based algorithms that also optimize the locations of the non-zero entries.
  arXiv  Detail & Related papers  (2023-06-11T07:28:35Z)
• Fast Optimal Locally Private Mean Estimation via Random Projections [58.603579803010796]
  We study the problem of locally private mean estimation of high-dimensional vectors in the Euclidean ball. We propose a new algorithmic framework, ProjUnit, for private mean estimation. Our framework is deceptively simple: each randomizer projects its input to a random low-dimensional subspace, normalizes the result, and then runs an optimal algorithm.
  arXiv  Detail & Related papers  (2023-06-07T14:07:35Z)
• Practical, Provably-Correct Interactive Learning in the Realizable Setting: The Power of True Believers [12.09273192079783]
  We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-11-09T02:33:36Z)
• Degree-Based Random Walk Approach for Graph Embedding [0.0]
  A computationally less intensive and node connectivity aware uniform sampling method is proposed. The advantages of the proposed algorithm become more enhanced when the algorithm is applied to large graphs.
  arXiv  Detail & Related papers  (2021-10-21T19:16:16Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering [6.4805900740861]
  We introduce a new notion of well-separation to reduce the work and space of our algorithm for HDBSCAN$*$. We show that our algorithms are theoretically efficient: they have work (number of operations) matching their sequential counterparts, and polylogarithmic depth (parallel time) Our experiments on large real-world and synthetic data sets using a 48-core machine show that our fastest algorithms outperform the best serial algorithms for the problems by 11.13--55.89x, and existing parallel algorithms by at least an order of magnitude.
  arXiv  Detail & Related papers  (2021-04-02T16:05:00Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)
• Efficient Computation of Expectations under Spanning Tree Distributions [67.71280539312536]
  We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms.
  arXiv  Detail & Related papers  (2020-08-29T14:58:26Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.