Heuristic Algorithms for the Approximation of Mutual Coherence

• URL: http://arxiv.org/abs/2307.01639v1
• Date: Tue, 4 Jul 2023 10:47:02 GMT
• Title: Heuristic Algorithms for the Approximation of Mutual Coherence
• Abstract summary: In Germany, this system helps voters to find candidates that are the closest to their political preferences. The exact iteration of mutual coherence is highly time-consuming due to the iteration over all subsets of an opinion. This work is the first study to accelerate this computation. The accuracy is precise enough to be used in Wahl-O-Mat-like systems.
• Score: 0.22099217573031676
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mutual coherence is a measure of similarity between two opinions. Although the notion comes from philosophy, it is essential for a wide range of technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters to find candidates that are the closest to their political preferences. The exact computation of mutual coherence is highly time-consuming due to the iteration over all subsets of an opinion. Moreover, for every subset, an instance of the SAT model counting problem has to be solved which is known to be a hard problem in computer science. This work is the first study to accelerate this computation. We model the distribution of the so-called confirmation values as a mixture of three Gaussians and present efficient heuristics to estimate its model parameters. The mutual coherence is then approximated with the expected value of the distribution. Some of the presented algorithms are fully polynomial-time, others only require solving a small number of instances of the SAT model counting problem. The average squared error of our best algorithm lies below 0.0035 which is insignificant if the efficiency is taken into account. Furthermore, the accuracy is precise enough to be used in Wahl-O-Mat-like systems.

Related papers

• Finding Common Ground in a Sea of Alternatives [22.60243910902928]
  We study the problem of selecting a statement that finds common ground across diverse population preferences.<n>Generative AI is uniquely suited for this task because it can access a practically infinite set of statements.<n>We propose a formal model for finding common ground in the infinite alternative setting based on the proportional veto core from social choice.
  arXiv  Detail & Related papers  (2026-03-17T16:28:37Z)
• Pathwise optimization for bridge-type estimators and its applications [49.1574468325115]
  Pathwise methods allow to efficiently compute the full path for penalized estimators. We apply these algorithms to the penalized estimation of processes observed at discrete times.
  arXiv  Detail & Related papers  (2024-12-05T10:38:29Z)
• Simple and Provable Scaling Laws for the Test-Time Compute of Large Language Models [70.07661254213181]
  We propose two principled algorithms for the test-time compute of large language models. We prove theoretically that the failure probability of one algorithm decays to zero exponentially as its test-time compute grows.
  arXiv  Detail & Related papers  (2024-11-29T05:29:47Z)
• Semi-Bandit Learning for Monotone Stochastic Optimization [20.776114616154242]
  We provide a generic online learning algorithm for a class of "monotone" problems. Our framework applies to several fundamental problems in optimization such as prophet, Pandora's box knapsack, inequality matchings and submodular optimization.
  arXiv  Detail & Related papers  (2023-12-24T07:46:37Z)
• When can you trust feature selection? -- I: A condition-based analysis of LASSO and generalised hardness of approximation [49.1574468325115]
  We show how no (randomised) algorithm can determine the correct support sets (with probability $> 1/2$) of minimisers of LASSO when reading approximate input. For ill-posed inputs, the algorithm runs forever, hence, it will never produce a wrong answer. For any algorithm defined on an open set containing a point with infinite condition number, there is an input for which the algorithm will either run forever or produce a wrong answer.
  arXiv  Detail & Related papers  (2023-12-18T18:29:01Z)
• 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)
• Learning distributed representations with efficient SoftMax normalization [3.8673630752805437]
  We propose a linear-time approximation to compute the normalization constants of $rm SoftMax(XYT)$ for embedding vectors with bounded norms.<n>We show on some pre-trained embedding datasets that the proposed estimation method achieves higher or comparable accuracy with competing methods.<n>The proposed algorithm is interpretable and easily adapted to arbitrary embedding problems.
  arXiv  Detail & Related papers  (2023-03-30T15:48:26Z)
• Efficient One Sided Kolmogorov Approximation [7.657378889055477]
  The main application that we examine is estimation of the probability missing deadlines in series-parallel schedules. Since exact computation of these probabilities is NP-hard, we propose to use the algorithms described in this paper to obtain an approximation.
  arXiv  Detail & Related papers  (2022-07-14T10:03:02Z)
• Formalizing Preferences Over Runtime Distributions [25.899669128438322]
  We use a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. We show how to leverage a maximum-entropy approach for modeling underspecified captime distributions.
  arXiv  Detail & Related papers  (2022-05-25T19:43:48Z)
• Kernel Packet: An Exact and Scalable Algorithm for Gaussian Process Regression with Mat\'ern Correlations [23.560067934682294]
  We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat'ern correlations. The proposed algorithm is significantly superior to the existing alternatives in both the computational time and predictive accuracy.
  arXiv  Detail & Related papers  (2022-03-07T03:30:35Z)
• Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity [15.023842222803058]
  Current algorithms are designed using the block coordinate descent method or the proximal point algorithm. We propose a novel algorithm based on the two-metric projection method, incorporating a carefully designed search direction and variable partitioning scheme. Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-12-03T14:39:10Z)
• Mean-based Best Arm Identification in Stochastic Bandits under Reward Contamination [80.53485617514707]
  This paper proposes two algorithms, a gap-based algorithm and one based on the successive elimination, for best arm identification in sub-Gaussian bandits. Specifically, for the gap-based algorithm, the sample complexity is optimal up to constant factors, while for the successive elimination, it is optimal up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-11-14T21:49:58Z)
• 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)
• Grouped Variable Selection with Discrete Optimization: Computational and Statistical Perspectives [9.593208961737572]
  We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. Our methodology covers both high-dimensional linear regression and non- additive modeling with sparse programming. Our exact algorithm is based on a standalone branch-and-bound (BnB) framework, which can solve the associated mixed integer (MIP) problem to certified optimality.
  arXiv  Detail & Related papers  (2021-04-14T19:21:59Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Learning to Accelerate Heuristic Searching for Large-Scale Maximum Weighted b-Matching Problems in Online Advertising [51.97494906131859]
  Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. Existing exact and approximate algorithms usually fail in such settings due to either requiring intolerable running time or too much computation resource. We propose textttNeuSearcher which leverages the knowledge learned from previously instances to solve new problem instances.
  arXiv  Detail & Related papers  (2020-05-09T02:48:23Z)
• Ranking a set of objects: a graph based least-square approach [70.7866286425868]
  We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We propose a class of non-adaptive ranking algorithms that rely on a least-squares intrinsic optimization criterion for the estimation of qualities.
  arXiv  Detail & Related papers  (2020-02-26T16:19:09Z)

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.