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image Algorithmic Learning in a Random World

Vladimir Vovk, Alexander Gammerman, Glenn Shafer
BookSpringer | 2005 | ISBN-10: 0387001522
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Summary

Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness.

Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.

image Algorithmic Learning Theory

Marcus Hunter, Frank Stephan, Vladimir Vovk, Thomas Zeugmann
BookSpringer | 2010 | ISBN 978-3-642-16108-7
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Summary

This volume contains the papers presented at the 21st International Conference on Algorithmic Learning Theory (ALT 2010), which was held in Canberra, Australia, October 6–8, 2010. The conference was co-located with the 13th International Conference on Discovery Science (DS 2010) and with the Machine Learning Summer School, which was held just before ALT 2010.

The techniccal program of ALT 2010, contained 26 papers selected from 44 submissions and invited talks. The invited talks were presented in joint sessions of both conferences. ALT 2010 was dedicated to the theoretical foundations of machine learning and took place on the campus of the Australian National University, Canberra, Australia.

image Causal Models and Intelligent Data Management

Alexander Gammerman
BookSpringer | 1999 | ISBN 978-3-642-58648-4
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Summary

Data analysis and inference have traditionally been research areas of statistics. However, the need to electronically store, manipulate and analyze large-scale, high-dimensional data sets requires new methods and tools, new types of databases, new efficient algorithms, new data structures, etc. - in effect new computational methods.

This monograph presents new intelligent data management methods and tools, such as the support vector machine, and new results from the field of inference, in particular of causal modeling. In 11 well-structured chapters, leading experts map out the major tendencies and future directions of intelligent data analysis. The book will become a valuable source of reference for researchers exploring the interdisciplinary area between statistics and computer science as well as for professionals applying advanced data analysis methods in industry and commerce. Students and lecturers will find the book useful as an introduction to the area.

image Computational Learning and Probabilistic Reasoning

Alexander Gammerman
BookWiley | 1996 | ISBN-10: 0471962791
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Summary

This book is devoted to two interrelated techniques in solving some important problems in machine intelligence and pattern recognition, namely probabilistic reasoning and computational learning.

It is divided into four parts, the first of which describes several new inductive principles and techniques used in computational learning. The second part contains papers on Bayesian and Causal Belief networks. Part three includes chapters on case studies and descriptions of several hybrid systems and the final part describes some related theoretical work in the field of probabilistic reasoning.

image Conformal Prediction for Reliable Machine Learning: Theory, Adaptations and Applications

Vineeth Balasubramanian, Shen-Shyang Ho, Vladimir Vovk
BookMorgan Kaufmann | 2014 | ISBN-10: 0123985374
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Summary

The conformal predictions framework is a recent development in machine learning that can associate a reliable measure of confidence with a prediction in any real-world pattern recognition application, including risk-sensitive applications such as medical diagnosis, face recognition, and financial risk prediction.

Conformal Predictions for Reliable Machine Learning: Theory, Adaptations and Applications captures the basic theory of the framework, demonstrates how to apply it to real-world problems, and presents several adaptations, including active learning, change detection, and anomaly detection. As practitioners and researchers around the world apply and adapt the framework, this edited volume brings together these bodies of work, providing a springboard for further research as well as a handbook for application in real-world problems.

image Conformal and Probabilistic Prediction with Applications

Alexander Gammerman, Zhiyuan Luo, Jesus Vega, Vladimir Vovk
BookSpringer | 2016 | ISBN-10: 3319333941
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Summary

This book constitutes the refereed proceedings of the 5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016, held in Madrid, Spain, in April 2016.

The 14 revised full papers presented together with 1 invited paper were carefully reviewed and selected from 23 submissions and cover topics on theory of conformal prediction; applications of conformal prediction; and machine learning.



image Empirical Inference

Bernhard Scholkopf, Zhiyuan Luo, Vladimir Vovk
BookSpringer | 2016 | ISBN-10: 3662525119
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Summary

This book celebrates the work of Vladimir Vapnik, developer of the support vector machine, which combines methods from statistical learning and functional analysis to create a new approach to learning problems, and who continues as active as ever in his field.






image Estimation of Dependences Based on Empirical Data

Vladimir Vapnik
BookSpringer | 2010 | ISBN-10: 1441921583
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Summary

Twenty-five years have passed since the publication of the Russian version of the book Estimation of Dependencies Based on Empirical Data (EDBED for short). Twenty-five years is a long period of time. During these years many things have happened. Looking back, one can see how rapidly life and technology have changed, and how slow and difficult it is to change the theoretical foundation of the technology and its philosophy.

I pursued two goals writing this Afterword: to update the technical results presented in EDBED (the easy goal) and to describe a general picture of how the new ideas developed over these years (a much more difficult goal). The picture which I would like to present is a very personal (and therefore very biased) account of the development of one particular branch of science, Empirical inference Science. Such accounts usually are not included in the content of technical publications. I have followed this rule in all of my previous books. But this time I would like to violate it for the following reasons. First of all, for me EDBED is the important milestone in the development of empirical inference theory and I would like to explain why. Second, during these years, there were a lot of discussions between supporters of the new 1 paradigm (now it is called the VC theory) and the old one (classical statistics).

image Measures of Complexity

Vladimir Vovk, Harris Papadopoulos, Alexander Gammerman
BookSpringer | 2016 | ISBN-10: 3319357786
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Summary

This book brings together historical notes, reviews of research developments, fresh ideas on how to make VC (Vapnik–Chervonenkis) guarantees tighter, and new technical contributions in the areas of machine learning, statistical inference, classification, algorithmic statistics, and pattern recognition.

The contributors are leading scientists in domains such as statistics, mathematics, and theoretical computer science, and the book will be of interest to researchers and graduate students in these domains.



image The Nature of Statistical Learning Theory

Vladimir Vapnik
BookSpringer | 1999 | ISBN-10: 0387987800
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Summary

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics.

This second edition contains three new chapters devoted to further development of the learning theory and SVM techniques. Written in a readable and concise style, the book is intended for statisticians, mathematicians, physicists, and computer scientists.



image Probability and Finance: It's Only a Game!

Glenn Shafer, Vladimir Vovk
BookWiley | 2001 | ISBN-10: 0471402265
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Summary

A new game–theoretic approach to probability and finance. Probability and Finance presents essential reading for anyone who studies or uses probability. Mathematicians and statisticians will find in it a new framework for probability: game theory instead of measure theory. Philosophers will find a surpising synthesis of the objective and the subjective. Practitioners, especially in financial engineering, will learn new ways to understand and sometimes eliminate stochastic models.

The first half of the book explains a new mathematical and philosophical framework for probability, based on a sequential game between an idealized scientist and the world. Two very accessible introductory chapters, one presenting an overview of the new framework and one reviewing its historical context, are followed by a careful mathematical treatment of probability′s classical limit theorems. The second half of the book, on finance, illustrates the potential of the new framework. It proposes greater use of the market and less use of stochastic models in the pricing of financial derivatives, and it shows how purely game–theoretic probability can replace stochastic models in the efficient–market hypothesis.

image Statistical Learning and Data Sciences

Alexander Gammerman, Vladimir Vovk, Harris Papadopoulos
BookSpringer | 2015 | ISBN-10: 3319170902
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Summary

This book constitutes the refereed proceedings of the Third International Symposium on Statistical Learning and Data Sciences, SLDS 2015, held in Egham, Surrey, UK, April 2015.

The 36 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 59 submissions. The papers are organized in topical sections on statistical learning and its applications, conformal prediction and its applications, new frontiers in data analysis for nuclear fusion, and geometric data analysis.



image Statistical Learning Theory

Vladimir Vapnik
BookWiley | 1998 | ISBN-10: 8126528923
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Summary

A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real–life problems, and much more.





Conformal prediction based on K-nearest neighbors for discrimination of ginsengs by a home-made electronic nose

Zhan Wang, Xiyang Sun, Jiacheng Miao, You Wang, Zhiyuan Luo, Guang Li
Journal Sensors, Vol. 17, No. 8.

Abstract

An estimate on the reliability of prediction in the applications of electronic nose is essential, which has not been paid enough attention. An algorithm framework called conformal prediction is introduced in this work for discriminating different kinds of ginsengs with a home-made electronic nose instrument. Nonconformity measure based on k-nearest neighbors (KNN) is implemented separately as underlying algorithm of conformal prediction.

In offline mode, the conformal predictor achieves a classification rate of 84.44% based on 1NN and 80.63% based on 3NN, which is better than that of simple KNN. In addition, it provides an estimate of reliability for each prediction.

In online mode, the validity of predictions is guaranteed, which means that the error rate of region predictions never exceeds the significance level set by a user. The potential of this framework for detecting borderline examples and outliers in the application of E-nose is also investigated. The result shows that conformal prediction is a promising framework for the application of electronic nose to make predictions with reliability and validity.

Conformal Prediction of Biological Activity of Chemical Compounds

Paolo Toccaceli, Ilia Nouretdinov, Alexander Gammerman
Journal Annals of Mathematics and Artificial Intelligence.

Abstract

The paper presents an application of Conformal Predictors to a chemoinformatics problem of predicting the biological activities of chemical compounds. The paper addresses some specific challenges in this domain: a large number of compounds (training examples), highdimensionality of feature space, sparseness and a strong class imbalance. A variant of conformal predictors called Inductive Mondrian Conformal Predictor is applied to deal with these challenges. Results are presented for several non-conformity measures extracted from underlying algorithms and different kernels. A number of performance measures are used in order to demonstrate the flexibility of Inductive Mondrian Conformal Predictors in dealing with such a complex set of data. This approach allowed us to identify the most likely active compounds for a given biological target and present them in a ranking order.

Combination of Conformal Predictors for Classification

Paolo Toccaceli, Alexander Gammerman
Paper Proceedings of Machine Learning Research.

Abstract

The paper presents some possible approaches to the combination of Conformal Predictors in the binary classification case. A first class of methods is based on p-value combination techniques that have been proposed in the context of Statistical Hypothesis Testing; a second class is based on the calibration of p-values into Bayes factors. A few methods from these two classes are applied to a real-world case, namely the chemoinformatics problem of Compound Activity Prediction. Their performance is discussed, showing the different abilities to preserve of validity and improve efficiency. The experiments show that P-value combination, in particular Fisher’s method, can be advantageous when ranking compounds by strength of evidence.

The role of measurability in game-theoretic probability

Vladimir Vovk
Journal Finance and Stochastics.

Abstract

This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit.

Valid Probabilistic Prediction of Life Status after Percutaneous Coronary Intervention procedure

Denis Volkhonskiy, Ilia Nouretdinov, Alexander Gammerman, Pitt Lim
Paper 6th Symposium on Conformal and Probabilistic Prediction with Applications (COPA 2017).

Abstract

Inductive Conformal Martingales for Change-Point Detection

Denis Volkhonskiy, Evgeny Burnaev, Ilia Nouretdinov, Alexander Gammerman, Vladimir Vovk
Paper 6th Symposium on Conformal and Probabilistic Prediction with Applications (COPA 2017).

Abstract

We consider the problem of quickest change-point detection in data streams. Classical change-point detection procedures, such as CUSUM, Shiryaev-Roberts and Posterior Probability statistics, are optimal only if the change-point model is known, which is an unrealistic assumption in typical applied problems. Instead we propose a new method for change-point detection based on Inductive Conformal Martingales, which requires only the independence and identical distribution of observations.

We compare the proposed approach to standard methods, as well as to change-point detection oracles, which model a typical practical post-change data distributions. Results of comparison provide evidence that change-point detection based on Inductive Conformal Martingales is an efficient tool, capable to work under quite general conditions unlike traditional approaches.

Universal probability-free prediction

Vladimir Vovk, Dusko Pavlovic
Journal Annals of Mathematics and Artificial Intelligence.

Abstract

We construct universal prediction systems in the spirit of Popper's falsifiability and Kolmogorov complexity and randomness. These prediction systems do not depend on any statistical assumptions (but under the IID assumption they dominate, to within the usual accuracy, conformal prediction). Our constructions give rise to a theory of algorithmic complexity and randomness of time containing analogues of several notions and results of the classical theory of Kolmogorov complexity and randomness.

Universal probability-free prediction

Vladimir Vovk, Ilia Nouretdinov, Valentina Fedorova, Ivan Petej, Alexander Gammerman
Journal Annals of Mathematics and Artificial Intelligence.

Abstract

We study optimal conformity measures for various criteria of efficiency of set-valued classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic and argue for; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.

All-solid-state carbonate-selective electrode based on screen-printed carbon paste electrode

Guang Li, Xiaofeng Lyu, Zhan Wang, Yuanzhen Rong, Ruifen Hu, Zhiyuan Luo, You Wang
Journal Measurement Science and Technology, Vol. 28, No. 2.

Abstract

A novel disposable all-solid-state carbonate-selective electrode based on a screen-printed carbon paste electrode using poly(3-octylthiophene-2,5-diyl) (POT) as an ion-to-electron transducer has been developed. The POT was dropped on the reaction area of the carbon paste electrode covered by the poly(vinyl chloride) (PVC) membrane, which contains N,N-Dioctyl-3α,12α-bis(4-trifluoroacetylbenzoyloxy)-5β-cholan-24-amide as a carbonate ionophore. The electrode showed a near-Nernstian slope of -27.5mV/decade with a detection limit of 3.6*10-5mol/L. Generally, the detection time was 30s. Because these electrodes are fast,convenient and low in cost, they have the potential to be mass produced and used in on-site testing as disposable sensors. Furthermore, the repeatability, reproducibility and stability have been studied to evaluate the properties of the electrodes. Measurement of the carbonate was also conducted in human blood solution and achieved good performance.

Nonparametric predictive distributions based on conformal prediction

Vladimir Vovk, Jieli Shen, Valery Manokhin, Minge Xie
Paper Sixth Symposium on Conformal and Probabilistic Prediction and Applications.

Abstract

This paper applies conformal prediction to derive predictive distributions that are valid under a nonparametric assumption. Namely, we introduce and explore predictive distribution functions that always satisfy a natural property of validity in terms of guaranteed coverage for IID observations. The focus is on a prediction algorithm that we call the Least Squares Prediction Machine (LSPM). The LSPM generalizes the classical Dempster-Hill predictive distributions to regression problems. If the standard parametric assumptions for Least Squares linear regression hold, the LSPM is as efficient as the Dempster-Hill procedure, in a natural sense. And if those parametric assumptions fail, the LSPM is still valid, provided the observations are IID.

Purely pathwise probability-free Ito integral

Vladimir Vovk
Journal Matematychni Studii

Abstract

This paper gives a simple construction of the pathwise Ito integral ∫ ϕ dω for an integrand ϕ and an integrator ω satisfying various topological and analytical conditions. The definition is purely pathwise in that neither ϕ nor ω are assumed to be paths of processes, and the Ito integral exists almost surely in a non-probabilistic finance-theoretic sense. For example, one of the results shows the existence of ∫ ϕ dω for a cadlag integrand ϕ and a cadlag integrator ω with jumps bounded in a predictable manner.