Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry

• URL: http://arxiv.org/abs/2001.05263v1
• Date: Wed, 15 Jan 2020 12:21:06 GMT
• Title: Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry
• Authors: Timothy van Bremen, Ondrej Kuzelka
• Abstract summary: We present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count. The algorithm has applications to inference in a variety of first-order probabilistic representations. We show how our algorithm outperforms existing approximate and exact techniques for inference in first-order probabilistic models.
• Score: 16.574508244279098
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count in the presence of an unweighted first-order model counting oracle. The algorithm has applications to inference in a variety of first-order probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, we make no assumptions on the form of the input sentence. Instead, our algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the first-order model counting oracle in practice using the approximate hashing-based model counter ApproxMC3, we show how our algorithm outperforms existing approximate and exact techniques for inference in first-order probabilistic models. We additionally provide PAC guarantees on the generated bounds.

Related papers

• Graph-Structured Speculative Decoding [52.94367724136063]
  Speculative decoding has emerged as a promising technique to accelerate the inference of Large Language Models. We introduce an innovative approach utilizing a directed acyclic graph (DAG) to manage the drafted hypotheses. We observe a remarkable speedup of 1.73$times$ to 1.96$times$, significantly surpassing standard speculative decoding.
  arXiv  Detail & Related papers  (2024-07-23T06:21:24Z)
• MAP: Low-compute Model Merging with Amortized Pareto Fronts via Quadratic Approximation [80.47072100963017]
  Model merging is an effective approach to combine multiple single-task models, fine-tuned from the same pre-trained model, into a multitask model. Existing model-merging methods focus on enhancing average task accuracy. We introduce a novel low-compute algorithm, Model Merging with Amortized Pareto Front (MAP)
  arXiv  Detail & Related papers  (2024-06-11T17:55:25Z)
• Efficient Incremental Belief Updates Using Weighted Virtual Observations [2.7195102129095003]
  We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference. We implement and apply the solution to a number of didactic examples and case studies, showing efficiency and robustness of our approach.
  arXiv  Detail & Related papers  (2024-02-10T12:48:49Z)
• Lifted Algorithms for Symmetric Weighted First-Order Model Sampling [7.007419073974192]
  We prove the domain-liftability under sampling for the two-variables fragment of first-order logic with counting quantifiers. We then show that this result continues to hold even in the presence of cardinality constraints. Our algorithm outperforms a start-of-the-art WMS sampler by a substantial margin.
  arXiv  Detail & Related papers  (2023-08-17T07:40:47Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• Structured Reordering for Modeling Latent Alignments in Sequence Transduction [86.94309120789396]
  We present an efficient dynamic programming algorithm performing exact marginal inference of separable permutations. The resulting seq2seq model exhibits better systematic generalization than standard models on synthetic problems and NLP tasks.
  arXiv  Detail & Related papers  (2021-06-06T21:53:54Z)
• Community Detection in the Stochastic Block Model by Mixed Integer Programming [3.8073142980733]
  Degree-Corrected Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. Standard approach of community detection based on the DCSBM is to search for the model parameters that are the most likely to have produced the observed network data through maximum likelihood estimation (MLE) We present mathematical programming formulations and exact solution methods that can provably find the model parameters and community assignments of maximum likelihood given an observed graph.
  arXiv  Detail & Related papers  (2021-01-26T22:04:40Z)
• A Bayesian Approach to Block-Term Tensor Decomposition Model Selection and Computation [10.91885508254207]
  The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention. The challenge of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. A Bayesian approach is taken to addressing the problem of rank-$(L_r,L_r,1)$ BTD model selection and computation, based on the idea of imposing column sparsity emphjointly on the
  arXiv  Detail & Related papers  (2021-01-08T09:37:21Z)
• Bayes DistNet -- A Robust Neural Network for Algorithm Runtime Distribution Predictions [1.8275108630751844]
  Randomized algorithms are used in many state-of-the-art solvers for constraint satisfaction problems (CSP) and Boolean satisfiability (SAT) problems. Previous state-of-the-art methods directly try to predict a fixed parametric distribution that the input instance follows. This new model achieves robust predictive performance in the low observation setting, as well as handling censored observations.
  arXiv  Detail & Related papers  (2020-12-14T01:15:39Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Learning Gaussian Graphical Models via Multiplicative Weights [54.252053139374205]
  We adapt an algorithm of Klivans and Meka based on the method of multiplicative weight updates. The algorithm enjoys a sample complexity bound that is qualitatively similar to others in the literature. It has a low runtime $O(mp2)$ in the case of $m$ samples and $p$ nodes, and can trivially be implemented in an online manner.
  arXiv  Detail & Related papers  (2020-02-20T10:50:58Z)

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.