Characterisation of Density-based FM generation methods in the context of Information Fusion

• URL: http://arxiv.org/abs/2607.23243v1
• Date: Sat, 25 Jul 2026 15:06:46 GMT
• Title: Characterisation of Density-based FM generation methods in the context of Information Fusion
• Abstract summary: Fuzzy Integral (FI) based aggregation provides a powerful mechanism for nuanced aggregation.<n>This paper shows how an interval-valued FM can indeed be determined uniquely.
• Score: 2.98145045970239
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fuzzy Integral (FI) based aggregation provides a powerful mechanism for nuanced aggregation, for example, in ensemble approaches or decision-level fusion more generally. The main challenge of this approach is the appropriate parametrization of the Fuzzy Measure (FM), which captures the worths of the individual components--and their combinations--which are being fused. Here, widely used approaches including the Sugeno-$λ$ and Decomposable FMs, parametrize the FM by extrapolating from the densities, i.e. the weights associated with individual sources, while respecting the FM's monotonicity constraint. This paper articulates that this information is, in general, insufficient to uniquely identify a discrete FM; but shows how an interval-valued FM can indeed be determined uniquely. We proceed to show how the incorporation of additional information beyond the above, such as the choice of a specific FI and a dataset, then allows for obtaining even more specific interval-valued FMs. In practice, establishing the quality of an empirically determined FM is not trivial. To help address this, we show how the likelihood with which a resulting interval FM encompasses the `ideal', i.e. the commonly intangible, best, or ground-truth numeric FM, can be determined, producing a confidence interval at a given confidence level. Finally, based on a series of experiments, we demonstrate empirically that the Choquet FI output based on this FM can also be regarded as the confidence interval for the `ideal' information fusion result, providing a novel means to characterize FI fusion outcomes a priori and charting a pathway for future research.

Related papers

• Posterior Augmented Flow Matching [64.1559809786948]
  Posterior-Augmented Flow Matching (PAFM) is a generalization of flow matching (FM)<n>We show that PAFM improves over FM by up to 3.4 FID50K across different model scales.
  arXiv  Detail & Related papers  (2026-05-01T17:59:59Z)
• Earth System Foundation Model (ESFM): A unified framework for heterogeneous data integration and forecasting [52.53742727060265]
  Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets.<n>Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3Dwin UNet backbone of the pioneering model.<n>We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data.<n>Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks.
  arXiv  Detail & Related papers  (2026-04-20T11:40:39Z)
• Interactive Spatial-Frequency Fusion Mamba for Multi-Modal Image Fusion [69.13852939945433]
  Multi-Modal Image Fusion (MMIF) aims to combine images from different modalities to produce fused images.<n>We propose a novel Interactive Spatial-Frequency Fusion Mamba framework for MMIF.<n>Our ISFM can achieve better performances than other state-of-the-art methods.
  arXiv  Detail & Related papers  (2026-02-04T10:35:55Z)
• Unlocking the Duality between Flow and Field Matching [86.34409966628323]
  Conditional Flow Matching (CFM) unifies conventional generative paradigms such as diffusion models and flow matching.<n> Interaction Field Matching (IFM) is a newer framework that generalizes Electrostatic Field Matching (EFM) rooted in Poisson Flow Generative Models (PFGM)<n>We show that they coincide for a natural subclass of IFM that we call forward-only IFM.
  arXiv  Detail & Related papers  (2026-02-02T16:04:01Z)
• On The Hidden Biases of Flow Matching Samplers [4.822598110892847]
  We study the implicit bias of flow matching (FM) samplers via the lens of empirical flow matching.<n>We show that the empirical FMr is almost never a gradient field, even when each conditional flow is. Consequently, empirical FM is intrinsically energetically suboptimal.
  arXiv  Detail & Related papers  (2025-12-18T17:02:11Z)
• Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions [20.26227575771028]
  Flow Matching (FM) algorithm achieves remarkable results in generative tasks especially in robotic manipulation.<n>This paper theoretically analyzes the relation between training loss and inference error in FM.<n>We propose a method of fine-tuning FM via Maximum Likelihood Estimation of reconstructions.
  arXiv  Detail & Related papers  (2025-10-02T14:49:47Z)
• Flow matching achieves almost minimax optimal convergence [50.38891696297888]
  Flow matching (FM) has gained significant attention as a simulation-free generative model. This paper discusses the convergence properties of FM for large sample size under the $p$-Wasserstein distance. We establish that FM can achieve an almost minimax optimal convergence rate for $1 leq p leq 2$, presenting the first theoretical evidence that FM can reach convergence rates comparable to those of diffusion models.
  arXiv  Detail & Related papers  (2024-05-31T14:54:51Z)
• Boosting Factorization Machines via Saliency-Guided Mixup [125.15872106335692]
  We present MixFM, inspired by Mixup, to generate auxiliary training data to boost Factorization machines (FMs) We also put forward a novel Factorization Machine powered by Saliency-guided Mixup (denoted as SMFM)
  arXiv  Detail & Related papers  (2022-06-17T09:49:00Z)

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.