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Statistical learning theory

About: Statistical learning theory is a research topic. Over the lifetime, 1618 publications have been published within this topic receiving 158033 citations.


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DOI
17 Nov 2021
TL;DR: In this article, the authors derive generalization bounds for PQC-based models that depend explicitly on the strategy used for data-encoding, which imply bounds on the performance of trained PQCs on unseen data.
Abstract: A large body of recent work has begun to explore the potential of parametrized quantum circuits (PQCs) as machine learning models, within the framework of hybrid quantum-classical optimization. In particular, theoretical guarantees on the out-of-sample performance of such models, in terms of generalization bounds, have emerged. However, none of these generalization bounds depend explicitly on how the classical input data is encoded into the PQC. We derive generalization bounds for PQC-based models that depend explicitly on the strategy used for data-encoding. These imply bounds on the performance of trained PQC-based models on unseen data. Moreover, our results facilitate the selection of optimal data-encoding strategies via structural risk minimization, a mathematically rigorous framework for model selection. We obtain our generalization bounds by bounding the complexity of PQC-based models as measured by the Rademacher complexity and the metric entropy, two complexity measures from statistical learning theory. To achieve this, we rely on a representation of PQC-based models via trigonometric functions. Our generalization bounds emphasize the importance of well-considered data-encoding strategies for PQC-based models.

17 citations

Proceedings ArticleDOI
16 Dec 2007
TL;DR: This paper shall present a novel method by applying the support vector machine (SVM) approach to distinguish counterfeit banknotes from genuine ones on the basis of the statistical learning theory.
Abstract: Distinct from conventional techniques where the neural network (NN) is employed to solve the problem of paper currency verification, in this paper, we shall present a novel method by applying the support vector machine (SVM) approach to distinguish counterfeit banknotes from genuine ones. On the basis of the statistical learning theory, SVM has better generalization ability and higher performance especially when it comes to pattern classification. Besides, discrete wavelet transformation (DWT) will also be applied so as to reduce the input scale of SVM. Finally, the results of our experiment will show that the proposed method does achieve very good performance.

17 citations

01 Jan 2006
TL;DR: A framework named Granular Support Vector Machines (GSVM) is proposed to systematically and formally combine statistical learning theory, granular computing theory and soft computing theory to address challenging predictive data modeling problems effectively and/or efficiently, with specific focus on binary classification problems.
Abstract: With emergence of biomedical informatics, Web intelligence, and E-business, new challenges are coming for knowledge discovery and data mining modeling problems In this dissertation work, a framework named Granular Support Vector Machines (GSVM) is proposed to systematically and formally combine statistical learning theory, granular computing theory and soft computing theory to address challenging predictive data modeling problems effectively and/or efficiently, with specific focus on binary classification problems In general, GSVM works in 3 steps Step 1 is granulation to build a sequence of information granules from the original dataset or from the original feature space Step 2 is modeling Support Vector Machines (SVM) in some of these information granules when necessary Finally, step 3 is aggregation to consolidate information in these granules at suitable abstract level A good granulation method to find suitable granules is crucial for modeling a good GSVM Under this framework, many different granulation algorithms including the GSVM-CMW (cumulative margin width) algorithm, the GSVM-AR (association rule mining) algorithm, a family of GSVM-RFE (recursive feature elimination) algorithms, the GSVM-DC (data cleaning) algorithm and the GSVM-RU (repetitive undersampling) algorithm are designed for binary classification problems with different characteristics The empirical studies in biomedical domain and many other application domains demonstrate that the framework is promising As a preliminary step, this dissertation work will be extended in the future to build a Granular Computing based Predictive Data Modeling framework (GrC-PDM) with which we can create hybrid adaptive intelligent data mining systems for high quality prediction

17 citations

Journal ArticleDOI
TL;DR: This paper presents an alternative method, greedy stagewise algorithm for SVMs, named GS-SVMs, that can be faster than LIBSVM 2.83 without sacrificing the accuracy and employs statistical learning theory to analyze the empirical results, which shows that its success lies in that its early stopping rule can act as an implicit regularization term.
Abstract: Hard-margin support vector machines (HM-SVMs) suffer from getting overfitting in the presence of noise. Soft-margin SVMs deal with this problem by introducing a regularization term and obtain a state-of-the-art performance. However, this disposal leads to a relatively high computational cost. In this paper, an alternative method, greedy stagewise algorithm for SVMs, named GS-SVMs, is presented to cope with the overfitting of HM-SVMs without employing the regularization term. The most attractive property of GS-SVMs is that its computational complexity in the worst case only scales quadratically with the size of training samples. Experiments on the large data sets with up to 400 000 training samples demonstrate that GS-SVMs can be faster than LIBSVM 2.83 without sacrificing the accuracy. Finally, we employ statistical learning theory to analyze the empirical results, which shows that the success of GS-SVMs lies in that its early stopping rule can act as an implicit regularization term.

17 citations

Journal ArticleDOI
TL;DR: The modelling results of the real drift data from the long-term measurement system of a DTG indicate that the SVM method is available practically in the modelling of DTG drift and the proposed strategy of combining SVM with AGO is effective in improving the modelling precision and the learning performance.
Abstract: In this paper, the support vector machine (SVM), a novel learning machine based on statistical learning theory (SLT), is described and applied in the drift modelling of the dynamically tuned gyroscope (DTG). As a data preprocessing method, accumulated generating operation (AGO) is applied to the SVM for further improving the modelling precision and the learning performance of the drift model. The grey modelling method and RBF neural network are also investigated as a comparison to the SVM and AGO–SVM modelling methods. The modelling results of the real drift data from the long-term measurement system of a DTG indicate that the SVM method is available practically in the modelling of DTG drift and the proposed strategy of combining SVM with AGO is effective in improving the modelling precision and the learning performance.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20239
202219
202159
202069
201972
201847