Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models

• URL: http://arxiv.org/abs/2202.08081v4
• Date: Tue, 7 May 2024 08:38:27 GMT
• Title: Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models
• Authors: Thierry Denoeux,
• Abstract summary: This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty.
• Score: 4.6684925321613076
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random fuzzy sets are combined by the generalized product-intersection rule, which extends both Dempster's rule for combining belief functions, and the product conjunctive combination of possibility distributions. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty about scalar or vector quantities. Closed-form expressions for the combination, projection and vacuous extension of Gaussian random fuzzy numbers and vectors are derived.

Related papers

• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Universal distributions of overlaps from unitary dynamics in generic quantum many-body systems [0.0]
  We study the preparation of a quantum state using a circuit of depth $t$ from a factorized state of $N$ sites. We argue that in the appropriate scaling limit of large $t$ and $N$, the overlap between states evolved under generic many-body chaotic dynamics.
  arXiv  Detail & Related papers  (2024-04-15T18:01:13Z)
• Simplex Random Features [53.97976744884616]
  We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels. We show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.
  arXiv  Detail & Related papers  (2023-01-31T18:53:39Z)
• An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers [6.713564212269253]
  We introduce a distance-based neural network model for regression. The model interprets the intersection of the input vector to prototypes as pieces of evidence. Experiments with real datasets demonstrate the very good performance of the method.
  arXiv  Detail & Related papers  (2022-08-01T07:13:31Z)
• A Fundamental Probabilistic Fuzzy Logic Framework Suitable for Causal Reasoning [0.0]
  We introduce a fundamental framework to create a bridge between Probability and Fuzzy Logic. Our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy attribute. Several formulas are presented, which make it easier to compute different conditional probabilities and expected values of random variables.
  arXiv  Detail & Related papers  (2022-05-30T11:59:35Z)
• More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize [94.70343385404203]
  We find that most theoretical analyses fall short of capturing qualitative phenomena even for kernel regression. We prove that the classical GCV estimator converges to the generalization risk whenever a local random matrix law holds. Our findings suggest that random matrix theory may be central to understanding the properties of neural representations in practice.
  arXiv  Detail & Related papers  (2022-03-11T18:59:01Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)
• Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
  An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
  arXiv  Detail & Related papers  (2020-06-22T16:57:52Z)
• Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators [72.62940905965267]
  Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. Are CF-INNs universal approximators for invertible functions? We prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes.
  arXiv  Detail & Related papers  (2020-06-20T02:07:37Z)
• Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence [6.713564212269253]
  We generalize Zadeh's notion of "evidence of the second kind" We show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.
  arXiv  Detail & Related papers  (2020-04-24T10:14:54Z)
• At the Interface of Algebra and Statistics [0.0]
  This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. Every joint probability distribution on a finite set can be modeled as a rank one density operator. We show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution.
  arXiv  Detail & Related papers  (2020-04-12T15:22:07Z)

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.