An overview of statistical learning theory
TL;DR: How the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms are demonstrated and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems are demonstrated.
Abstract: Statistical learning theory was introduced in the late 1960's. Until the 1990's it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990's new types of learning algorithms (called support vector machines) based on the developed theory were proposed. This made statistical learning theory not only a tool for the theoretical analysis but also a tool for creating practical algorithms for estimating multidimensional functions. This article presents a very general overview of statistical learning theory including both theoretical and algorithmic aspects of the theory. The goal of this overview is to demonstrate how the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems.
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TL;DR: A new method for performing a nonlinear form of principal component analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
Abstract: A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map—for instance, the space of all possible five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.
8,175 citations
TL;DR: This paper compares classification algorithms used to design brain-computer interface (BCI) systems based on electroencephalography (EEG) in terms of performance and provides guidelines to choose the suitable classification algorithm(s) for a specific BCI.
Abstract: In this paper we review classification algorithms used to design brain–computer interface (BCI) systems based on electroencephalography (EEG). We briefly present the commonly employed algorithms and describe their critical properties. Based on the literature, we compare them in terms of performance and provide guidelines to choose the suitable classification algorithm(s) for a specific BCI.
2,519 citations
Cites background from "An overview of statistical learning..."
...It also deals with two classification problems especially relevant for BCI research, namely, the curse-of-dimensionality and the Bias-Variance tradeoff....
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TL;DR: A computational model is described that learns in a similar fashion and does so better than current deep learning algorithms and can generate new letters of the alphabet that look “right” as judged by Turing-like tests of the model's output in comparison to what real humans produce.
Abstract: People learning new concepts can often generalize successfully from just a single example, yet machine learning algorithms typically require tens or hundreds of examples to perform with similar accuracy. People can also use learned concepts in richer ways than conventional algorithms-for action, imagination, and explanation. We present a computational model that captures these human learning abilities for a large class of simple visual concepts: handwritten characters from the world's alphabets. The model represents concepts as simple programs that best explain observed examples under a Bayesian criterion. On a challenging one-shot classification task, the model achieves human-level performance while outperforming recent deep learning approaches. We also present several "visual Turing tests" probing the model's creative generalization abilities, which in many cases are indistinguishable from human behavior.
2,364 citations
TL;DR: What obstacles there may be to changing the practice of medicine through statistical learning approaches, and how these might be overcome are identified.
Abstract: Spurred by advances in processing power, memory, storage, and an unprecedented wealth of data, computers are being asked to tackle increasingly complex learning tasks, often with astonishing success. Computers have now mastered a popular variant of poker, learned the laws of physics from experimental data, and become experts in video games - tasks that would have been deemed impossible not too long ago. In parallel, the number of companies centered on applying complex data analysis to varying industries has exploded, and it is thus unsurprising that some analytic companies are turning attention to problems in health care. The purpose of this review is to explore what problems in medicine might benefit from such learning approaches and use examples from the literature to introduce basic concepts in machine learning. It is important to note that seemingly large enough medical data sets and adequate learning algorithms have been available for many decades, and yet, although there are thousands of papers applying machine learning algorithms to medical data, very few have contributed meaningfully to clinical care. This lack of impact stands in stark contrast to the enormous relevance of machine learning to many other industries. Thus, part of my effort will be to identify what obstacles there may be to changing the practice of medicine through statistical learning approaches, and discuss how these might be overcome.
2,062 citations
Cites background from "An overview of statistical learning..."
...ing that establishes bounds for similarity between training error and test error.(10) Although the mathematics is elaborate,...
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TL;DR: A general method for combining the classifiers generated on the binary problems is proposed, and a general empirical multiclass loss bound is proved given the empirical loss of the individual binary learning algorithms.
Abstract: We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin-based binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with error-correcting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms. The scheme and the corresponding bounds apply to many popular classification learning algorithms including support-vector machines, AdaBoost, regression, logistic regression and decision-tree algorithms. We also give a multiclass generalization error analysis for general output codes with AdaBoost as the binary learner. Experimental results with SVM and AdaBoost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms.
1,949 citations
References
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Book•
01 Jan 1995TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.
40,147 citations
TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
Abstract: The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special properties of the decision surface ensures high generalization ability of the learning machine. The idea behind the support-vector network was previously implemented for the restricted case where the training data can be separated without errors. We here extend this result to non-separable training data.
High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated. We also compare the performance of the support-vector network to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
37,861 citations
01 Jan 1998
TL;DR: 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.
Abstract: 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.
26,531 citations
01 Jan 1988
TL;DR: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion.
Abstract: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion
17,604 citations
"An overview of statistical learning..." refers methods in this paper
...A method for calculating the gradient of the empirical risk for the sigmoid approximation of NN’s, called the backpropagation method , was found [15], [12]....
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Book•
03 Jan 1986
TL;DR: In this paper, the problem of the generalized delta rule is discussed and the Generalized Delta Rule is applied to the simulation results of simulation results in terms of the generalized delta rule.
Abstract: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion
13,579 citations