{"title":"Semi-Supervised Learning Using Semi-Definite Programming","authors":"T. D. Bie, N. Cristianini","doi":"10.7551/mitpress/9780262033589.003.0007","DOIUrl":"https://doi.org/10.7551/mitpress/9780262033589.003.0007","url":null,"abstract":"We discuss the problem of support vector machine (SVM) transduction, which is a combinatorial problem with exponential computational complexity in the number of unlabeled samples. Different approaches to such combinatorial problems exist, among which are exact integer programming approaches (only feasible for very small sample sizes, e.g. [1]) and local search heuristics starting from a suitably chosen start value such as the approach explained in Chapter 5, Transductive Support Vector Machines , and introduced in [2] (scalable to large problem sizes, but sensitive to local optima). In this chapter, we discuss an alternative approach introduced in [3], which is based on a convex relaxation of the optimization problem associated to support vector machine transduction. The result is a semi-definite programming (SDP) problem which can be optimized in polynomial time, the solution of which is an approximation of the optimal labeling as well as a bound on the true optimum of the original transduction objective function. To further decrease the computational complexity, we propose an approximation that allows to solve transduction problems of up to 1000 unlabeled samples. Lastly, we extend the formulation to more general settings of semi-supervised learning, where equivalence and inequivalence constraints are given on labels of some of the samples.","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131910770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Taxonomy for Semi-Supervised Learning Methods","authors":"M. Seeger","doi":"10.7551/MITPRESS/9780262033589.003.0002","DOIUrl":"https://doi.org/10.7551/MITPRESS/9780262033589.003.0002","url":null,"abstract":"We propose a simple taxonomy of probabilistic graphical models for the semi-supervised learning problem. We give some broad classes of algorithms for each of the families and point to specific realizations in the literature. Finally, we shed more detailed light on the family of methods using input-dependent regularization (or conditional prior distributions) and show parallels to the Co-training paradigm.","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131036148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of Benchmarks","authors":"O. Chapelle, B. Scholkopf, A. Zien","doi":"10.7551/MITPRESS/9780262033589.003.0021","DOIUrl":"https://doi.org/10.7551/MITPRESS/9780262033589.003.0021","url":null,"abstract":"This chapter contains sections titled: The Benchmark, Application of SSL Methods, Results and Discussion","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121419338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Semi-Supervised Text Classification Using EM","authors":"K. Nigam, A. McCallum, Tom Michael Mitchell","doi":"10.7551/mitpress/9780262033589.003.0003","DOIUrl":"https://doi.org/10.7551/mitpress/9780262033589.003.0003","url":null,"abstract":"For several decades, statisticians have advocated using a combination of labeled and unlabeled data to train classifiers by estimating parameters of a generative model through iterative Expectation-Maximization (EM) techniques. This chapter explores the effectiveness of this approach when applied to the domain of text classification. Text documents are represented here with a bag-of-words model, which leads to a generative classification model based on a mixture of multinomials. This model is an extremely simplistic representation of the complexities of written text. This chapter explains and illustrates three key points about semi-supervised learning for text classification with generative models. First, despite the simplistic representation, some text domains have a high positive correlation between generative model probability and classification accuracy. In these domains, a straightforward application of EM with the naive Bayes text model works well. Second, some text domains do not have this correlation. Here we can adopt a more expressive and appropriate generative model that does have a positive correlation. In these domains, semi-supervised learning again improves classification accuracy. Finally, EM suffers from the problem of local maxima, especially in high dimension domains such as text classification. We demonstrate that deterministic annealing, a variant of EM, can help overcome the problem of local maxima and increase classification accuracy further when the generative model is appropriate.","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115174010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discrete Regularization","authors":"Dengyong Zhou, B. Scholkopf","doi":"10.7551/mitpress/9780262033589.003.0013","DOIUrl":"https://doi.org/10.7551/mitpress/9780262033589.003.0013","url":null,"abstract":". In this paper we discuss discrete regularization, more specifically about how to add finite dissipation to the discretized Euler equations so as to ensure the stability and convergence of numerical solutions of high Reynolds number flows. We will briefly review regularization strategies widely used in Lagrangian shockwave simulations (artificial viscosity), in Eulerian nonoscillatory finite volume simulations, and in Eulerian simulations of turbulent flow (explicit and implicit large eddy simulations). We will describe an alternate strategy for regularization in which we introduce a finite length scale into the discrete model by volume averaging the equations over a computational cell. The new equations, which we term Finite Scale Navier–Stokes, contain ex- plicit (inviscid) dissipation in a uniquely specified form and obey an entropy principle. We will describe features of the new equations including control of the small scales of motion by the larger resolved scales, a principle concerning the partition of total flux of conserved quantities into advective and diffusive components, and a physical basis for the inviscid dissipation.","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124918961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Discussion of Semi-Supervised Learning and Transduction","authors":"O. Chapelle, B. Scholkopf, A. Zien","doi":"10.7551/MITPRESS/9780262033589.003.0025","DOIUrl":"https://doi.org/10.7551/MITPRESS/9780262033589.003.0025","url":null,"abstract":"In the field of machine learning, semi-supervised learning (SSL) occupies the middle ground, between supervised learning (in which all training examples are labeled) and unsupervised learning (in which no label data are given). Interest in SSL has increased in recent years, particularly because of application domains in which unlabeled data are plentiful, such as images, text, and bioinformatics. This first comprehensive overview of SSL presents state-of-the-art algorithms, a taxonomy of the field, selected applications, benchmark experiments, and perspectives on ongoing and future research.Semi-Supervised Learning first presents the key assumptions and ideas underlying the field: smoothness, cluster or low-density separation, manifold structure, and transduction. The core of the book is the presentation of SSL methods, organized according to algorithmic strategies. After an examination of generative models, the book describes algorithms that implement the low-density separation assumption, graph-based methods, and algorithms that perform two-step learning. The book then discusses SSL applications and offers guidelines for SSL practitioners by analyzing the results of extensive benchmark experiments. Finally, the book looks at interesting directions for SSL research. The book closes with a discussion of the relationship between semi-supervised learning and transduction.Olivier Chapelle and Alexander Zien are Research Scientists and Bernhard SchA¶lkopf is Professor and Director at the Max Planck Institute for Biological Cybernetics in TA?bingen. SchA¶lkopf is coauthor of Learning with Kernels (MIT Press, 2002) and is a coeditor of Advances in Kernel Methods: Support Vector Learning (1998), Advances in Large-Margin Classifiers (2000), and Kernel Methods in Computational B iology (2004), all published by The MIT Press.","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129479115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Semi-Supervised Learning","authors":"O. Chapelle, B. Scholkopf, A. Zien","doi":"10.7551/mitpress/9780262033589.003.0001","DOIUrl":"https://doi.org/10.7551/mitpress/9780262033589.003.0001","url":null,"abstract":"This chapter contains sections titled: Supervised, Unsupervised, and Semi-Supervised Learning, When Can Semi-Supervised Learning Work?, Classes of Algorithms and Organization of This Book","PeriodicalId":345393,"journal":{"name":"Semi-Supervised Learning","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129231060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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