A Fast PC Algorithm with Reversed-order Pruning and A Parallelization Strategy

• URL: http://arxiv.org/abs/2109.04626v1
• Date: Fri, 10 Sep 2021 02:22:10 GMT
• Title: A Fast PC Algorithm with Reversed-order Pruning and A Parallelization Strategy
• Authors: Kai Zhang, Chao Tian, Kun Zhang, Todd Johnson, Xiaoqian Jiang
• Abstract summary: The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed. This makes the algorithm computationally intractable when the task contains several hundred or thousand nodes. We propose a critical observation that the conditional set rendering two nodes independent is non-unique, and including certain redundant nodes do not sacrifice result accuracy.
• Score: 22.31288740171446
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an exhaustive-searching manner. This makes the algorithm computationally intractable when the task contains several hundred or thousand nodes, particularly when the true underlying causal graph is dense. We propose a critical observation that the conditional set rendering two nodes independent is non-unique, and including certain redundant nodes do not sacrifice result accuracy. Based on this finding, the innovations of our work are two-folds. First, we innovate on a reserve order linkage pruning PC algorithm which significantly increases the algorithm's efficiency. Second, we propose a parallel computing strategy for statistical independence tests by leveraging tensor computation, which brings further speedup. We also prove the proposed algorithm does not induce statistical power loss under mild graph and data dimensionality assumptions. Experimental results show that the single-threaded version of the proposed algorithm can achieve a 6-fold speedup compared to the PC algorithm on a dense 95-node graph, and the parallel version can make a 825-fold speed-up. We also provide proof that the proposed algorithm is consistent under the same set of conditions with conventional PC algorithm.

Related papers

• Quantum Hamiltonian Algorithms for Maximum Independent Sets [6.772902928686719]
  An alternative algorithm, short named the PK algorithm, reveals that the independent sets diffuse over a media graph governed by a non-abelian gauge matrix of an emergent PXP model. Although the two are mathematically equivalent, the PK algorithm exhibits more efficient and resource-saving performance.
  arXiv  Detail & Related papers  (2023-10-23T04:00:34Z)
• Linearized Wasserstein dimensionality reduction with approximation guarantees [65.16758672591365]
  LOT Wassmap is a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. We show that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.
  arXiv  Detail & Related papers  (2023-02-14T22:12:16Z)
• A Push-Relabel Based Additive Approximation for Optimal Transport [5.111364864495785]
  Exact algorithms for computing Optimal Transport can be slow. We introduce a new and very simple approach to find an $varepsilon$approximation of the OT distance. Our algorithm achieves a near-optimal execution time of $O(n2/varepsilon2)$ for computing OT distance.
  arXiv  Detail & Related papers  (2022-03-07T21:40:14Z)
• 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)
• Machine Learning for Online Algorithm Selection under Censored Feedback [71.6879432974126]
  In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. We adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon.
  arXiv  Detail & Related papers  (2021-09-13T18:10:52Z)
• 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)
• Local Algorithms for Estimating Effective Resistance [26.54556748340991]
  In this work, we design several emphlocal algorithms for estimating effective resistances on massive graphs. Our main algorithm approximates the effective resistance between any vertices pair $s,t$ with an arbitrarily small additive error. We perform an extensive empirical study on several benchmark datasets, validating our algorithms.
  arXiv  Detail & Related papers  (2021-06-07T10:08:12Z)
• 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.