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Cross-conformal predictors
[article]
2012
arXiv
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This note introduces the method of cross-conformal prediction, which is a hybrid of the methods of inductive conformal prediction and cross-validation, and studies its validity and predictive efficiency empirically.
arXiv:1208.0806v1
fatcat:qqzyvcxg4vgqlhe5qnfwhe5qv4
Negative probabilities
[article]
2020
arXiv
pre-print
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We explain, on the example of Wigner's quasiprobability distribution, how negative probabilities may be used in the foundations of probability.
arXiv:2011.12393v1
fatcat:bpn6nvlbojgordryoasg3b2ej4
Training conformal predictors
[article]
2020
arXiv
pre-print
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The idea is to use existing criteria of efficiency for conformal prediction, such as those defined in Vovk et al. [2017] . ...
A dataset is a bag of elements of Z, where a bag is a collection of elements (observations in this case) some of which may be identical [Vovk et al., 2005 , Section 2.2]. ...
arXiv:2005.07037v1
fatcat:mycwe2ylq5gztbogfurjtzehn4
Game-theoretic Brownian motion
[article]
2008
arXiv
pre-print
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This paper suggests a perfect-information game, along the lines of Levy's characterization of Brownian motion, that formalizes the process of Brownian motion in game-theoretic probability. This is perhaps the simplest situation where probability emerges in a non-stochastic environment.
arXiv:0801.1309v1
fatcat:eozebct6qzezzl5hho2wkgmgv4
Defensive forecasting
[article]
2005
arXiv
pre-print
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We consider how to make probability forecasts of binary labels. Our main mathematical result is that for any continuous gambling strategy used for detecting disagreement between the forecasts and the actual labels, there exists a forecasting strategy whose forecasts are ideal as far as this gambling strategy is concerned. A forecasting strategy obtained in this way from a gambling strategy demonstrating a strong law of large numbers is simplified and studied empirically.
arXiv:cs/0505083v1
fatcat:x7yaamqir5e4hews3iorhwwxoa
Cross-conformal e-prediction
[article]
2020
arXiv
pre-print
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The precursor of conformal prediction developed in the 1990s by Gammerman, Vapnik, and Vovk was also based on e-values and is called conformal e-prediction in this note. ...
arXiv:2001.05989v1
fatcat:uiwq43n6nrg7jhhu56j7vn4scu
On the concept of Bernoulliness
[article]
2016
arXiv
pre-print
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[3] Vladimir V. V'yugin. Algorithmic entropy (complexity) of finite ob-
jects and its applications to defining randomness and amount of infor-
mation. ...
arXiv:1612.08859v1
fatcat:mctbvj6z4bhgdaggst7qrjtf5a
Competing with Markov prediction strategies
[article]
2006
arXiv
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Assuming that the loss function is convex in the prediction, we construct a prediction strategy universal for the class of Markov prediction strategies, not necessarily continuous. Allowing randomization, we remove the requirement of convexity.
arXiv:cs/0607136v1
fatcat:wmhkqydmebgarnbffs6ep7engi
Competing with stationary prediction strategies
[article]
2006
arXiv
pre-print
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In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to
arXiv:cs/0607067v1
fatcat:pyc3qttozbeanflsmfriht5oqe
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... r only stationary strategies even for highly non-stationary environments.
Predictions as statements and decisions
[article]
2006
arXiv
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Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory of competitive on-line learning can benefit from the kinds of prediction that are now foreign to it.
arXiv:cs/0606093v1
fatcat:j5sqersdhzgptp23xjg6ylp3fq
Strong confidence intervals for autoregression
[article]
2007
arXiv
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In this short note I apply the methodology of game-theoretic probability to calculating non-asymptotic confidence intervals for the coefficient of a simple first order scalar autoregressive model. The most distinctive feature of the proposed procedure is that with high probability it produces confidence intervals that always cover the true parameter value when applied sequentially.
arXiv:0707.0660v1
fatcat:puuts7fxrjawllixvfs2iggvbq
Conformal calibrators
[article]
2019
arXiv
pre-print
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Most existing examples of full conformal predictive systems, split-conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In this paper we develop split-conformal and cross-conformal predictive systems that are fully adaptive. Our method consists in calibrating existing predictive systems; the input predictive system is not supposed to satisfy any properties of validity, whereas
arXiv:1902.06579v1
fatcat:wcn3nnq445hjzkbly254o47squ
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... output predictive system is guaranteed to be calibrated in probability. It is interesting that the method may also work without the IID assumption, standard in conformal prediction.
Non-algorithmic theory of randomness
[article]
2019
arXiv
pre-print
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[4] refer to e-values as "s-values" ("s" for "safe"), • and Gammerman and Vovk [3] refer to the inverses of e-values as "i-values" ("i" for "integral"). ...
arXiv:1910.00585v1
fatcat:whoemla7p5ftxavetqqqrxrsrm
Hoeffding's inequality in game-theoretic probability
[article]
2007
arXiv
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This note makes the obvious observation that Hoeffding's original proof of his inequality remains valid in the game-theoretic framework. All details are spelled out for the convenience of future reference.
arXiv:0708.2502v1
fatcat:63gvhsdykrberkolohlfqtogwy
Prequential probability: game-theoretic = measure theoretic
[article]
2009
arXiv
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This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea goes back to von Mises and Ville, and measure-theoretic, whose idea goes back to Kolmogorov. The main
arXiv:0905.1673v1
fatcat:f4vqtbokk5gn5pakcwf764hnli
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... ult of this article is that, in the case of predicting binary outcomes, the two notions of probability in fact coincide on the analytic sets (in particular, on the Borel sets).
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