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Cross-conformal predictors [article]

Vladimir Vovk
2012 arXiv   pre-print
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]

Yuri Gurevich, Vladimir Vovk
2020 arXiv   pre-print
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]

Nicolo Colombo, Vladimir Vovk
2020 arXiv   pre-print
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]

Vladimir Vovk
2008 arXiv   pre-print
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]

Vladimir Vovk, Akimichi Takemura, Glenn Shafer
2005 arXiv   pre-print
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]

Vladimir Vovk
2020 arXiv   pre-print
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]

Vladimir Vovk
2016 arXiv   pre-print
[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]

Vladimir Vovk
2006 arXiv   pre-print
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]

Vladimir Vovk
2006 arXiv   pre-print
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
more » ... r only stationary strategies even for highly non-stationary environments.
arXiv:cs/0607067v1 fatcat:pyc3qttozbeanflsmfriht5oqe

Predictions as statements and decisions [article]

Vladimir Vovk
2006 arXiv   pre-print
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]

Vladimir Vovk
2007 arXiv   pre-print
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]

Vladimir Vovk, Ivan Petej, Paolo Toccaceli, Alex Gammerman
2019 arXiv   pre-print
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
more » ... 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.
arXiv:1902.06579v1 fatcat:wcn3nnq445hjzkbly254o47squ

Non-algorithmic theory of randomness [article]

Vladimir Vovk
2019 arXiv   pre-print
[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]

Vladimir Vovk
2007 arXiv   pre-print
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]

Vladimir Vovk
2009 arXiv   pre-print
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
more » ... 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).
arXiv:0905.1673v1 fatcat:f4vqtbokk5gn5pakcwf764hnli
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