Publications | Empirical Inference - Max Planck Institute for Intelligent Systems

We consider the problem of transductive inference. In many real-world problems, unlabeled data is far easier to obtain than labeled data. Hence transductive inference is very significant in many practical problems. According to Vapnik's point of view, one should predict the function value only on the given points directly rather than a function defined on the whole space, the latter being a more complicated problem. Inspired by this idea, we develop discrete calculus on finite discrete spaces, and then build discrete regularization. A family of transductive algorithms is naturally derived from this regularization framework. We validate the algorithms on both synthetic and real-world data from text/web categorization to bioinformatics problems. A significant by-product of this work is a powerful way of ranking data based on examples including images, documents, proteins and many other kinds of data. This talk is mainly based on the followiing contribution: (1) D. Zhou and B. Sch{\"o}lkopf: Transductive Inference with Graphs, MPI Technical report, August, 2004; (2) D. Zhou, B. Sch{\"o}lkopf and T. Hofmann. Semi-supervised Learning on Directed Graphs. NIPS 2004; (3) D. Zhou, O. Bousquet, T.N. Lal, J. Weston and B. Sch{\"o}lkopf. Learning with Local and Global Consistency. NIPS 2003.

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Zhou, D. Discrete vs. Continuous: Two Sides of Machine Learning October 2004 (talk)

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Grundlagen von Support Vector Maschinen und Anwendungen in der Bildverarbeitung

Eichhorn, J.

September 2004 (talk)

Abstract

Invited talk at the workshop "Numerical, Statistical and Discrete Methods in Image Processing" at the TU M{\"u}nchen (in GERMAN)

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Eichhorn, J. Grundlagen von Support Vector Maschinen und Anwendungen in der Bildverarbeitung September 2004 (talk)

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Riemannian Geometry on Graphs and its Application to Ranking and Classification

Zhou, D.

June 2004 (talk)

Abstract

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Zhou, D. Riemannian Geometry on Graphs and its Application to Ranking and Classification June 2004 (talk)

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Learning from Labeled and Unlabeled Data: Semi-supervised Learning and Ranking

Zhou, D.

January 2004 (talk)

Abstract

We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.

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Zhou, D. Learning from Labeled and Unlabeled Data: Semi-supervised Learning and Ranking January 2004 (talk)

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Introduction to Category Theory

Bousquet, O.

Internal Seminar, January 2004 (talk)

Abstract

A brief introduction to the general idea behind category theory with some basic definitions and examples. A perspective on higher dimensional categories is given.

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