Special cases

Destercke, Sébastien; Dubois, Didier

doi:10.1002/9781118763117.ch4

Cited by 12 publications

(10 citation statements)

References 44 publications

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“…Table 2 provides an example of a cumulative distribution that could be obtained in a ranking problem where k = 5 and for a label λ i . For other kinds of sets P i we could consider, see [17]. This approach requires to learn k different models, one for each label.…”

Section: Probability Set Modelmentioning

confidence: 99%

Cautious Label-Wise Ranking with Constraint Satisfaction

Carranza-Alarcon¹,

Messoudi²,

Destercke³

2020

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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Ranking problems are difficult to solve due to their combinatorial nature. One way to solve this issue is to adopt a decomposition scheme, splitting the initial difficult problem in many simpler problems. The predictions obtained from these simplified settings must then be combined into one single output, possibly resolving inconsistencies between the outputs. In this paper, we consider such an approach for the label ranking problem, where in addition we allow the predictive model to produce cautious inferences in the form of sets of rankings when it lacks information to produce reliable, precise predictions. More specifically, we propose to combine a rank-wise decomposition, in which every sub-problem becomes an ordinal classification one, with a constraint satisfaction problem (CSP) approach to verify the consistency of the predictions. Our experimental results indicate that our approach produces predictions with appropriately balanced reliability and precision, while remaining competitive with classical, precise approaches.

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Section: Probability Set Modelmentioning

confidence: 99%

Cautious Label-Wise Ranking with Constraint Satisfaction

Carranza-Alarcon¹,

Messoudi²,

Destercke³

2020

Information Processing and Management of Uncertainty in Knowledge-Based Systems

Self Cite

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“…Based on the false confidence theorem in Balch et al (2019), Martin (2019) argues that validity as in (3) requires that the degrees of belief be non-additive. Since we take this validity property to be fundamental to the logic of statistical inference, we focus here on genuinely non-additive degrees of belief, e.g., the belief/plausibility functions in Shafer (1976) or the special case of necessity/possibility functions in Dubois (2006), Dubois and Prade (2012), and Destercke and Dubois (2014).…”

Section: Basic Inferential Modelsmentioning

confidence: 99%

Generalized inferential models for censored data

Cahoon,

Martin

2019

Preprint

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Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent plausibility function. This construction is driven by an association between the distribution of the relative likelihood function at the interest parameter and an unobserved auxiliary variable. The plausibility function emerges from the distribution of a suitably calibrated random set designed to predict that unobserved auxiliary variable. The evaluation of this plausibility function requires a novel use of the classical Kaplan-Meier estimator to estimate the censoring rather than the event distribution. We prove that the proposed method provides valid inference, at least approximately, and our real-and simulated-data examples demonstrate its superior performance compared to existing methods.

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“…Imprecise probability consists in extending the classical probabilistic model by considering convex sets of probabilities or equivalent models such as lower expectation. This representation formally includes all the other aforementioned representations 10 (possibilities, probabilities, belief functions), and has the benefit to be fully consistent with classical Bayesian probabilistic modelling, both axiomatically (as it relaxes Bayesian axioms) and formally speaking. It can therefore be interpreted either as an uncertainty theory of its own, or as a robustification of the classical probabilistic models.…”

Section: Introductionmentioning

confidence: 99%

“…Imprecise probabilities 32 offer a very generic way to model uncertainty, including most known models of uncertainty such as precise probabilities, belief functions or possibility distributions 10 . It also comes with a fully-fledged theory to reason with such uncertainty and make decisions 32 .…”

Section: Introducing Credal Occupancy Gridsmentioning

confidence: 99%

Inference and Decision in Credal Occupancy Grids: Use Case on Trajectory Planning

Masson

Destercke

Cherfaoui

2021

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Occupancy grids are common tools used in robotics to represent the robot environment, and that may be used to plan trajectories, select additional measurements to acquire, etc. However, deriving information about those occupancy grids from sensor measurements often induce a lot of uncertainty, especially for grid elements that correspond to occluded or far away area from the robot. This means that occupancy information may be quite uncertain and imprecise at some places, while being very accurate at others. Modelling finely this occupancy information is essential to decide the optimal action the robot should take, but a refined modelling of uncertainty often implies a higher computational cost, a prohibitive feature for real-time applications. In this paper, we introduce the notion of credal occupancy grids, using the very general theory of imprecise probabilities to model occupancy uncertainty. We also show how one can perform efficient, real-time inferences with such a model, and show a use-case applying the model to an autonomous vehicle trajectory planning problem.

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Special cases

Cited by 12 publications

References 44 publications

Cautious Label-Wise Ranking with Constraint Satisfaction

Cautious Label-Wise Ranking with Constraint Satisfaction

Generalized inferential models for censored data

Inference and Decision in Credal Occupancy Grids: Use Case on Trajectory Planning

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