Scalable Algorithms for Approximate DNF Model Counting

• URL: http://arxiv.org/abs/2601.10511v1
• Date: Thu, 15 Jan 2026 15:38:47 GMT
• Title: Scalable Algorithms for Approximate DNF Model Counting
• Abstract summary: Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability.<n>We develop a new Monte Carlo approach with an adaptive stopping rule short-circuit formula evaluation.<n>We show experimentally that it out-performs prior algorithms by orders of magnitude, and can scale to much larger problems with millions of variables.
• Score: 1.4146420810689422
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often used for query evaluation in probabilistic databases. Due to the computational intractability of exact DNF counting, there has been a line of research into a variety of approximation algorithms. These include Monte Carlo approaches such as the classical algorithms of Karp, Luby, and Madras (1989), as well as methods based on hashing (Soos et al. 2023), and heuristic approximations based on Neural Nets (Abboud, Ceylan, and Lukasiewicz 2020). We develop a new Monte Carlo approach with an adaptive stopping rule and short-circuit formula evaluation. We prove it achieves Probably Approximately Correct (PAC) learning bounds and is asymptotically more efficient than the previous methods. We also show experimentally that it out-performs prior algorithms by orders of magnitude, and can scale to much larger problems with millions of variables.

Related papers

• Quantum speedup of non-linear Monte Carlo problems [3.534338813984755]
  We propose a quantum-inside-quantum Monte Carlo algorithm that achieves a speedup for a broad class of non-linear estimation problems.<n>A key innovation of our approach is a new sequence of multilevel Monte Carlo approximations specifically designed for quantum computing.
  arXiv  Detail & Related papers  (2025-02-07T17:13:27Z)
• Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood [2.312692134587988]
  We develop continuous-time (birth-death) and discrete-time (reversible jump) Markov chain Monte Carlo (MCMC) algorithms that efficiently explore the posterior over graph space.<n>The algorithms scale to large graph spaces, enabling parallel exploration for graphs with over 1,000 nodes.
  arXiv  Detail & Related papers  (2023-06-30T20:37:40Z)
• Differentially-Private Hierarchical Clustering with Provable Approximation Guarantees [79.59010418610625]
  We study differentially private approximation algorithms for hierarchical clustering. We show strong lower bounds for the problem: that any $epsilon$-DP algorithm must exhibit $O(|V|2/ epsilon)$-additive error for an input dataset. We propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly.
  arXiv  Detail & Related papers  (2023-01-31T19:14:30Z)
• An Application of a Multivariate Estimation of Distribution Algorithm to Cancer Chemotherapy [59.40521061783166]
  Chemotherapy treatment for cancer is a complex optimisation problem with a large number of interacting variables and constraints. We show that the more sophisticated algorithm would yield better performance on a complex problem like this. We hypothesise that this is caused by the more sophisticated algorithm being impeded by the large number of interactions in the problem.
  arXiv  Detail & Related papers  (2022-05-17T15:28:46Z)
• Scalable computation of prediction intervals for neural networks via matrix sketching [79.44177623781043]
  Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals.
  arXiv  Detail & Related papers  (2022-05-06T13:18:31Z)
• Formalization of a Stochastic Approximation Theorem [0.22940141855172028]
  approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown. Originally introduced in a 1951 paper by Robbins and Monro, the field of approximation has grown enormously and has come to influence application domains.
  arXiv  Detail & Related papers  (2022-02-12T02:31:14Z)
• Benchmarking Simulation-Based Inference [5.3898004059026325]
  Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency.
  arXiv  Detail & Related papers  (2021-01-12T18:31:22Z)
• 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)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• 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)
• Scalable Distributed Approximation of Internal Measures for Clustering Evaluation [5.144809478361603]
  Internal measure for clustering evaluation is the silhouette coefficient, whose computation requires a quadratic number of distance calculations. We present the first scalable algorithm to compute such a rigorous approximation for the evaluation of clusterings based on any metric distances. We also prove that the algorithm can be adapted to obtain rigorous approximations of other internal measures of clustering quality, such as cohesion and separation.
  arXiv  Detail & Related papers  (2020-03-03T10:28:14Z)
• Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry [16.574508244279098]
  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.
  arXiv  Detail & Related papers  (2020-01-15T12:21:06Z)

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.