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predictive complexity and information

JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2005年第4期70卷 539-554页

作者： Vyugin, MV V'yugin, VV Russian Acad Sci Inst Informat Transmiss Problems Moscow 101447 Russia Univ London Royal Holloway & Bedford New Coll Dept Comp Sci Egham TW20 0EX Surrey England

The notions of predictive complexity and of corresponding amount of information are considered. predictive complexity is a generalization of Kolmogorov complexity which bounds the ability of any algorithm to predict elements of a sequence of outcomes. We consider predictive complexity for a wide class of bounded loss functions which are generalizations of square-loss function. Relations between unconditional KG(x) and conditional KG(x vertical bar y) predictive complexities are studied. We define an algorithm which has some "expanding property". It transforms with positive probability sequences of given predictive complexity into sequences of essentially bigger predictive complexity. A concept of amount of predictive information IG(y : x) is studied. We show that this information is noncommutative in a very strong sense and present asymptotic relations between values IG(y : x), IG(x : y), KG(x) and KG(y). (c) 2004 Elsevier Inc. All rights reserved.

关键词： machine learning algorithmic prediction predictive complexity predictive information loss functions Kolmogorov complexity expanding property

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predictive complexity and information

Predictive complexity and information

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15th Annual Conference on Computational Learning Theory

作者： Vyugin, MV V'yugin, VV Russian Acad Sci Inst Informat Transmiss Problems Moscow 101447 Russia Univ London Royal Holloway & Bedford New Coll Dept Comp Sci Egham TW20 0EX Surrey England

关键词： machine learning algorithmic prediction predictive complexity predictive information loss functions Kolmogorov complexity expanding property

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Exploring two novel features for EEG-based brain-computer interfaces: Multifractal cumulants and predictive complexity

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NEUROCOMPUTING 2012年 79卷 87-94页

作者： Brodu, Nicolas Lotte, Fabien Lecuyer, Anatole Univ Rennes 1 F-35042 Rennes France Inst Infocomm Res I2R Singapore 138632 Singapore Natl Inst Res Comp Sci & Control INRIA Bordeaux S F-33405 Talence France INRIA F-35042 Rennes France

In this paper, we introduce two new features for the design of electroencephalography (EEG) based Brain-Computer Interfaces (BCI): one feature based on multifractal cumulants and the other feature based on the predictive complexity of the EEG time series. The multifractal cumulants feature measures the signal regularity, while the predictive complexity measures the difficulty to predict the future of the signal based on its past, hence a degree of how complex it is. We have conducted an evaluation of the performance of these two novel features on EEG data corresponding to motor-imagery. We also compared them to the gold standard features used in the BC! field, namely the band-power features. We evaluated these three kinds of features and their combinations on EEG signals from 13 subjects. Results obtained show that our novel features can lead to BCI designs with improved classification performance, notably when using and combining the three kinds of feature (band-power, multifractal cumulants, predictive complexity) together. (C) 2011 Elsevier B.V. All rights reserved.

关键词： BCI Feature extraction Classification Multifractal predictive complexity

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On ordinal VC-dimension and some notions of complexity

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THEORETICAL COMPUTER SCIENCE 2006年第1期364卷 62-76页

作者： Martin, Eric Sharma, Arun Stephan, Frank Univ New S Wales Sch Engn & Comp Sci Sydney NSW 2052 Australia Queensland Univ Technol Div Res & Commercialisat Brisbane Qld 4001 Australia Natl Univ Singapore Sch Comp Singapore 117543 Singapore

We generalize the classical notion of Vapnik-Chemovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of phi in W, where phi varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity-a variation on predictive complexity-and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework. (C) 2006 Elsevier B.V. All rights reserved.

关键词： generalized VC-dimension inductive inference predictive complexity

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Loss functions, complexities, and the Legendre transformation

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THEORETICAL COMPUTER SCIENCE 2004年第2期313卷 195-207页

作者： Kalnishkan, Y Vovk, V Vyugin, MV Univ London Royal Holloway & Bedford New Coll Dept Comp Sci Egham TW20 0EX Surrey England

The paper introduces a way of re-constructing a loss function from predictive complexity. We show that a loss function and expectations of the corresponding predictive complexity w.r.t. the Bernoulli distribution are related through the Legendre transformation. It is shown that if two loss functions specify the same complexity then they are equivalent in a strong sense. The expectations are also related to the so-called generalized entropy. (C) 2003 Elsevier B.V. All rights reserved.

关键词： on-line prediction predictive complexity generalized entropy

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On ordinal VC-dimension and some notions of complexity 14th

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14th International Conference on Algorithmic Learning Theory

ISBN: (纸本)3540202919

关键词： generalized VC-dimension inductive inference predictive complexity

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Loss functions, complexities, and the Legendre transformation 12th

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12th Annual Conference on Algorithmic Learning Theory (ALT 01)

作者： Kalnishkan, Y Vovk, V Vyugin, MV Univ London Royal Holloway & Bedford New Coll Dept Comp Sci Egham TW20 0EX Surrey England

ISBN: (纸本)3540428755

关键词： on-line prediction predictive complexity generalized entropy

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The Fundamental Nature of the Log Loss Function

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Symposium on Logic in Computer Science Celebrating Yuri Gurevich's 75th Birthday (YuriFest)

作者： Vovk, Vladimir Univ London Dept Comp Sci Royal Holloway Egham Surrey England

ISBN: (纸本)9783319235349;9783319235332

The standard loss functions used in the literature on probabilistic prediction are the log loss function, the Brier loss function, and the spherical loss function;however, any computable proper loss function can be used for comparison of prediction algorithms. This note shows that the log loss function is most selective in that any prediction algorithm that is optimal for a given data sequence (in the sense of the algorithmic theory of randomness) under the log loss function will be optimal under any computable proper mixable loss function;on the other hand, there is a data sequence and a prediction algorithm that is optimal for that sequence under either of the two other standard loss functions but not under the log loss function.

关键词： Algorithmic theory of randomness Mixability predictive complexity predictive randomness Probabilistic prediction Proper loss functions

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Depth and hierarchies in the predictive brain: From reaction to action

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WILEY INTERDISCIPLINARY REVIEWS-COGNITIVE SCIENCE 2023年第6期14卷 e1664页

作者： Muzik, Otto Diwadkar, Vaibhav A. Wayne State Univ Childrens Hosp Michigan Sch Med Dept Pediat 3901 Beaubien Blvd Detroit MI 48201 USA Wayne State Univ Sch Med Dept Psychiat & Behav Neurosci Detroit MI 48201 USA

The human brain is a prediction device, a view widely accepted in neuroscience. Prediction is a rational and efficient response that relies on the brain's ability to create and employ generative models to optimize actions over unpredictable time horizons. We argue that extant predictive frameworks while compelling, have not explicitly accounted for the following: (a) The brain's generative models must incorporate predictive depth (i.e., rely on degrees of abstraction to enable predictions over different time horizons);(b) The brain's implementation scheme to account for varying predictive depth relies on dynamic predictive hierarchies formed using the brain's functional networks. We show that these hierarchies incorporate the ascending processes (driven by reaction), and the descending processes (related to prediction), eventually driving action. Because they are dynamically formed, predictive hierarchies allow the brain to address predictive challenges in virtually any domain. By way of application, we explain how this framework can be applied to heretofore poorly understood processes of human behavioral thermoregulation. Although mammalian thermoregulation has been closely tied to deep brain structures engaged in autonomic control such as the hypothalamus, this narrow conception does not translate well to humans. In addition to profound differences in evolutionary history, the human brain is bestowed with substantially increased functional complexity (that itself emerged from evolutionary differences). We argue that behavioral thermoregulation in humans is possible because, (a) ascending signals shaped by homeostatic sub-networks, interject with (b) descending signals related to prediction (implemented in interoceptive and executive sub-networks) and action (implemented in executive sub-networks). These sub-networks cumulatively form a predictive hierarchy for human thermoregulation, potentiating a range of viable responses to known and unknown thermoregulatory ch

关键词： behavioral human regulatory hierarchy predictive complexity thermoregulation

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