On Revealing the Hidden Problem Structure in Real-World and Theoretical Problems Using Walsh Coefficient Influence

• URL: http://arxiv.org/abs/2504.13949v1
• Date: Wed, 16 Apr 2025 08:22:59 GMT
• Title: On Revealing the Hidden Problem Structure in Real-World and Theoretical Problems Using Walsh Coefficient Influence
• Abstract summary: Gray-box optimization employs Walsh decomposition to obtain non-linear variable dependencies.<n>In some problems, all variables are non-linearly dependent, making the aforementioned masks useless.<n>We analyze the features of the real-world instances of such problems and show that many of their dependencies may have noise-like origins.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Gray-box optimization employs Walsh decomposition to obtain non-linear variable dependencies and utilize them to propose masks of variables that have a joint non-linear influence on fitness value. These masks significantly improve the effectiveness of variation operators. In some problems, all variables are non-linearly dependent, making the aforementioned masks useless. We analyze the features of the real-world instances of such problems and show that many of their dependencies may have noise-like origins. Such noise-caused dependencies are irrelevant to the optimization process and can be ignored. To identify them, we propose extending the use of Walsh decomposition by measuring variable dependency strength that allows the construction of the weighted dynamic Variable Interaction Graph (wdVIG). wdVIGs adjust the dependency strength to mixed individuals. They allow the filtering of irrelevant dependencies and re-enable using dependency-based masks by variation operators. We verify the wdVIG potential on a large benchmark suite. For problems with noise, the wdVIG masks can improve the optimizer's effectiveness. If all dependencies are relevant for the optimization, i.e., the problem is not noised, the influence of wdVIG masks is similar to that of state-of-the-art structures of this kind.

Related papers

• Personalized Task Dependency Graphs for Mitigating Signal Erosion in Multi-Task Recommendation [12.788118240513791]
  We propose the Personalized Task Dependency Graphs (PTDG)<n>PTDG "rewires" the intensity of dependency pathways for each item via low-rank approximation to ensure structural robustness.<n>Experiments on KuaiRand1K and an industrial dataset show that PTDG significantly improves AUC on sparse conversion tasks by up to 1.45%.
  arXiv  Detail & Related papers  (2026-09-04T08:23:12Z)
• Obtaining Partition Crossover masks using Statistical Linkage Learning for solving noised optimization problems with hidden variable dependency structure [0.0]
  We use Statistical Learning (SLL) to decompose problems with noise and propose a new S-dedicated mask construction algorithm.<n>We prove that if the quality of the SLL-based decomposition is sufficiently high, the proposed algorithm yields clustering masks equivalent to PX masks for the noise-free instances.<n>Experiments show that the using the proposed mechanisms remains equally effective despite the noise level and outperforms state-of-the-arts for the problems with high noise.
  arXiv  Detail & Related papers  (2026-04-13T14:36:34Z)
• Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning [51.20606796019663]
  We propose ALVGL, a novel and general enhancement to the differentiable causal discovery pipeline.<n>ALVGL employs a sparse and low-rank decomposition to learn the precision matrix of the data.<n>We show that ALVGL not only achieves state-of-the-art accuracy but also significantly improves optimization efficiency.
  arXiv  Detail & Related papers  (2026-01-09T02:18:59Z)
• Variational Masked Diffusion Models [8.801239075625151]
  Variational Masked Diffusion (VMD) is a framework that introduces latent variables into the masked diffusion process.<n>We demonstrate that VMD successfully learns dependencies that conventional masked diffusion fails to capture.
  arXiv  Detail & Related papers  (2025-10-27T17:59:57Z)
• Seeking and leveraging alternative variable dependency concepts in gray-box-elusive bimodal land-use allocation problems [0.0]
  We consider a real-world multi-objective problem for which standard variable dependency discovery techniques are inapplicable.<n>To address this issue, we propose a definition of problem-dedicated variable dependency.<n>The results concerning real-world test cases show that introducing our propositions into two well-knowns (NSEA/D) significantly improves their effectiveness.
  arXiv  Detail & Related papers  (2025-04-16T09:06:55Z)
• Structural Entropy Guided Probabilistic Coding [52.01765333755793]
  We propose a novel structural entropy-guided probabilistic coding model, named SEPC.<n>We incorporate the relationship between latent variables into the optimization by proposing a structural entropy regularization loss.<n> Experimental results across 12 natural language understanding tasks, including both classification and regression tasks, demonstrate the superior performance of SEPC.
  arXiv  Detail & Related papers  (2024-12-12T00:37:53Z)
• LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data [51.47827479376251]
  LOCAL is a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures. Asymptotic Causal Learning Mask (ACML) and Dynamic Graph Learning (DGPL) Experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods.
  arXiv  Detail & Related papers  (2024-10-25T10:48:41Z)
• ColorMAE: Exploring data-independent masking strategies in Masked AutoEncoders [53.3185750528969]
  Masked AutoEncoders (MAE) have emerged as a robust self-supervised framework. We introduce a data-independent method, termed ColorMAE, which generates different binary mask patterns by filtering random noise. We demonstrate our strategy's superiority in downstream tasks compared to random masking.
  arXiv  Detail & Related papers  (2024-07-17T22:04:00Z)
• Beyond Random Missingness: Clinically Rethinking for Healthcare Time Series Imputation [7.21960656196858]
  This study investigates the impact of masking strategies on time series imputation models in healthcare settings.<n>Using the PhysioNet Challenge 2012 dataset, we analyse how different masking implementations affect both imputation accuracy and downstream clinical predictions.
  arXiv  Detail & Related papers  (2024-05-26T18:05:12Z)
• Understanding Virtual Nodes: Oversquashing and Node Heterogeneity [4.59357989139429]
  Augmenting MPNNs with a virtual node (VN) has been found to improve performance on a range of benchmarks.<n>We provide a comprehensive theoretical analysis of the role of VNs and benefits thereof.<n>We propose a variant of VN with the same computational complexity, which can have different sensitivity to nodes based on the graph structure.
  arXiv  Detail & Related papers  (2024-05-22T10:51:12Z)
• When ControlNet Meets Inexplicit Masks: A Case Study of ControlNet on its Contour-following Ability [93.15085958220024]
  ControlNet excels at creating content that closely matches precise contours in user-provided masks. When these masks contain noise, as a frequent occurrence with non-expert users, the output would include unwanted artifacts. This paper first highlights the crucial role of controlling the impact of these inexplicit masks with diverse deterioration levels through in-depth analysis. An advanced Shape-aware ControlNet consisting of a deterioration estimator and a shape-prior modulation block is devised.
  arXiv  Detail & Related papers  (2024-03-01T11:45:29Z)
• Fitness-based Linkage Learning and Maximum-Clique Conditional Linkage Modelling for Gray-box Optimization with RV-GOMEA [0.552480439325792]
  In this work, we combine fitness-based linkage learning and conditional linkage modelling in RV-GOMEA. We find that the new RV-GOMEA not only performs best on most problems, also the overhead of learning the conditional linkage models during optimization is often negligible.
  arXiv  Detail & Related papers  (2024-02-16T15:28:27Z)
• Generalization of LiNGAM that allows confounding [1.0878040851637998]
  LiNGAM determines the variable order from cause to effect using additive noise models. Previous methods required significant computational resources regardless of the presence of confounding. This paper enhances LiNGAM by introducing LiNGAM-MMI, a method that quantifies the magnitude of confounding.
  arXiv  Detail & Related papers  (2024-01-30T01:24:43Z)
• Bilateral Dependency Optimization: Defending Against Model-inversion Attacks [61.78426165008083]
  We propose a bilateral dependency optimization (BiDO) strategy to defend against model-inversion attacks. BiDO achieves the state-of-the-art defense performance for a variety of datasets, classifiers, and MI attacks.
  arXiv  Detail & Related papers  (2022-06-11T10:07:03Z)
• Hyperspectral Unmixing via Nonnegative Matrix Factorization with Handcrafted and Learnt Priors [14.032039261229853]
  We propose an NMF based unmixing framework which jointly uses a handcrafting regularizer and a learnt regularizer from data. We plug learnt priors of abundances where the associated subproblem can be addressed using various image denoisers.
  arXiv  Detail & Related papers  (2020-10-09T14:40:20Z)
• Bilevel Optimization for Differentially Private Optimization in Energy Systems [53.806512366696275]
  This paper studies how to apply differential privacy to constrained optimization problems whose inputs are sensitive. The paper shows that, under a natural assumption, a bilevel model can be solved efficiently for large-scale nonlinear optimization problems.
  arXiv  Detail & Related papers  (2020-01-26T20:15:28Z)

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.