A new approach for imprecise probabilities

• URL: http://arxiv.org/abs/2402.02556v1
• Date: Sun, 4 Feb 2024 16:09:04 GMT
• Title: A new approach for imprecise probabilities
• Authors: Marcello Basili and Luca Pratelli
• Abstract summary: We characterize a broad class of interval probability measures and define their properties. As a byproduct, a formal solution to the century-old Keynes-Ramsey controversy is presented.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak complementation denoted as $\psi$. The interval probability measure of an event $H$ is defined with respect to the set of indecisive eventualities $(\psi(H))^c$, which is included in the standard complement $H^c$. We characterize a broad class of interval probability measures and define their properties. Additionally, we establish an updating rule with respect to $H$, incorporating concepts of statistical independence and dependence. The interval distribution of a random variable is formulated, and a corresponding definition of stochastic dominance between two random variables is introduced. As a byproduct, a formal solution to the century-old Keynes-Ramsey controversy is presented.

Related papers

• Statistical Learning of Distributionally Robust Stochastic Control in Continuous State Spaces [17.96094201655567]
  We explore the control of systems with potentially continuous state and action spaces, characterized by the state dynamics $X_t+1 = f(X_t, A_t, W_t)$. Here, $X$, $A$, and $W$ represent the state, action, and random noise processes, respectively, with $f$ denoting a known function that describes state transitions. This paper introduces a distributionally robust control paradigm that accommodates possibly adversarial perturbation to the noise distribution within a prescribed ambiguity set.
  arXiv  Detail & Related papers  (2024-06-17T07:37:36Z)
• On Rate-Optimal Partitioning Classification from Observable and from Privatised Data [0.0]
  We revisit the classical method of partitioning classification and study its convergence rate under relaxed conditions. The privacy constraints mean that the data $(X_i$), dots,(X_n,Y_n)$ cannot be directly observed. We add Laplace distributed noises to the discontinuations of all possible locations of the feature vector $X_i$ and to its label $Y_i$.
  arXiv  Detail & Related papers  (2023-12-22T18:07:18Z)
• Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models [4.010566541114989]
  We propose a notion of simultaneous confidence intervals called the sparsified simultaneous confidence intervals. Our intervals are sparse in the sense that some of the intervals' upper and lower bounds are shrunken to zero. The proposed method can be coupled with various selection procedures, making it ideal for comparing their uncertainty.
  arXiv  Detail & Related papers  (2023-07-14T18:37:57Z)
• High Probability Bounds for a Class of Nonconvex Algorithms with AdaGrad Stepsize [55.0090961425708]
  We propose a new, simplified high probability analysis of AdaGrad for smooth, non- probability problems. We present our analysis in a modular way and obtain a complementary $mathcal O (1 / TT)$ convergence rate in the deterministic setting. To the best of our knowledge, this is the first high probability for AdaGrad with a truly adaptive scheme, i.e., completely oblivious to the knowledge of smoothness.
  arXiv  Detail & Related papers  (2022-04-06T13:50:33Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• The intersection probability: betting with probability intervals [7.655239948659381]
  We propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty. We outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.
  arXiv  Detail & Related papers  (2022-01-05T17:35:06Z)
• Dense Uncertainty Estimation via an Ensemble-based Conditional Latent Variable Model [68.34559610536614]
  We argue that the aleatoric uncertainty is an inherent attribute of the data and can only be correctly estimated with an unbiased oracle model. We propose a new sampling and selection strategy at train time to approximate the oracle model for aleatoric uncertainty estimation. Our results show that our solution achieves both accurate deterministic results and reliable uncertainty estimation.
  arXiv  Detail & Related papers  (2021-11-22T08:54:10Z)
• CovarianceNet: Conditional Generative Model for Correct Covariance Prediction in Human Motion Prediction [71.31516599226606]
  We present a new method to correctly predict the uncertainty associated with the predicted distribution of future trajectories. Our approach, CovariaceNet, is based on a Conditional Generative Model with Gaussian latent variables.
  arXiv  Detail & Related papers  (2021-09-07T09:38:24Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• $(f,\Gamma)$-Divergences: Interpolating between $f$-Divergences and Integral Probability Metrics [6.221019624345409]
  We develop a framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs) We show that they can be expressed as a two-stage mass-redistribution/mass-transport process. Using statistical learning as an example, we demonstrate their advantage in training generative adversarial networks (GANs) for heavy-tailed, not-absolutely continuous sample distributions.
  arXiv  Detail & Related papers  (2020-11-11T18:17:09Z)
• Distributionally Robust Bayesian Quadrature Optimization [60.383252534861136]
  We study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. We propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose.
  arXiv  Detail & Related papers  (2020-01-19T12:00:33Z)

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.