Conditional Prediction Intervals for Linear Regression

McCullagh, Peter; Vovk, Vladimir; Nouretdinov, Ilia; Devetyarov, Dmitry; Gammerman, Alexander

doi:10.1109/icmla.2009.115

Cited by 5 publications

(6 citation statements)

References 9 publications

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“…Remark. Nontrivial set predictors having 1 − object conditional validity are constructed by McCullagh et al (2009) assuming the Gauss linear model.…”

Section: Object Conditional Validitymentioning

confidence: 99%

Conditional validity of inductive conformal predictors

2013

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Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of conformal predictors satisfying the same property of validity. However, inductive conformal predictors have been only known to control unconditional coverage probability. This paper explores various versions of conditional validity and various ways to achieve them using inductive conformal predictors and their modifications.

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“…Remark. Nontrivial set predictors having 1 − object conditional validity are constructed by McCullagh et al (2009) assuming the Gauss linear model.…”

Section: Object Conditional Validitymentioning

confidence: 99%

Conditional validity of inductive conformal predictors

2013

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“…For further examples, see McCullagh et al (2009) (Gauss linear model) and Ramdas et al (2023, Sect. 4.1).…”

Section: Pivotal Testingmentioning

confidence: 99%

Vladimir Vovk’s Contribution to The Discussion of ‘Testing by Betting: A Strategy for Statistical and Scientific Communication’ by Glenn Shafer

Vovk

2021

Journal of the Royal Statistical Society Series A: Statistics in Society

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The most widely used concept of statistical inference-the p -value-is too complicated for effective communication to a wide audience (Gigerenzer, 2018 ; McShane & Gal, 2017 ). This paper introduces a simpler way of reporting statistical evidence: report the outcome of a bet against the null hypothesis. This leads to a new role for likelihood, to alternatives to power and confidence, and to a framework for meta-analysis that accommodates both planned and opportunistic testing of statistical hypotheses and probabilistic forecasts.Testing a hypothesized probability distribution by betting is straightforward. We select a nonnegative payoff and buy it for its hypothesized expected value. If this bet multiplies the money it risks by a large factor, we have evidence against the hypothesis, and the factor measures the strength of this evidence. Multiplying our money by 5 might merit attention; multiplying it by 100 or by 1000 might be considered conclusive.

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“…To understand the nature of the restriction it will be convenient to ignore the denominator in (12), i.e., to consider the ordinary KRRPM; the difference between the (studentized) KRRPM and ordinary KRRPM will be small in the absence of high-leverage objects (an example will be given in the next section). For the ordinary KRRPM we have, in place of (13) and (14),…”

Section: Limitation Of the Krrpmmentioning

confidence: 99%

“…The property of being calibrated in probability for conformal prediction is, on the other hand, unconditional; or, in other words, it is conditional on the trivial σ-algebra. Fisher's fiducial predictive distributions satisfy an intermediate property of validity: they are calibrated in probability conditionally on what was called the σ-algebra of invariant events in [13], which is greater than the trivial σ-algebra but smaller than the σ-algebra representing the full knowledge of the past. Our plan is to give precise statements with proofs in future work.…”

Section: Fiducial Predictive Distributionsmentioning

confidence: 99%

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Conformal Predictive Distributions with Kernels

Vovk

Nouretdinov

Manokhin

et al. 2018

Braverman Readings in Machine Learning. Key Ideas From Inception to Current State

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This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine learning, whose early development was so deeply influenced by two remarkable groups at the Institute of Automation and Remote Control. The second development is combining predictive distributions with kernel methods, which were originated by one of those groups, including Emmanuel Braverman.

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Conditional Prediction Intervals for Linear Regression

Cited by 5 publications

References 9 publications

Conditional validity of inductive conformal predictors

Conditional validity of inductive conformal predictors

Vladimir Vovk’s Contribution to The Discussion of ‘Testing by Betting: A Strategy for Statistical and Scientific Communication’ by Glenn Shafer

Conformal Predictive Distributions with Kernels

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