nips nips2000 nips2000-144 knowledge-graph by maker-knowledge-mining
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Author: Olivier Chapelle, Jason Weston, Léon Bottou, Vladimir Vapnik
Abstract: The Vicinal Risk Minimization principle establishes a bridge between generative models and methods derived from the Structural Risk Minimization Principle such as Support Vector Machines or Statistical Regularization. We explain how VRM provides a framework which integrates a number of existing algorithms, such as Parzen windows, Support Vector Machines, Ridge Regression, Constrained Logistic Classifiers and Tangent-Prop. We then show how the approach implies new algorithms for solving problems usually associated with generative models. New algorithms are described for dealing with pattern recognition problems with very different pattern distributions and dealing with unlabeled data. Preliminary empirical results are presented.
Reference: text
sentIndex sentText sentNum sentScore
1 com Abstract The Vicinal Risk Minimization principle establishes a bridge between generative models and methods derived from the Structural Risk Minimization Principle such as Support Vector Machines or Statistical Regularization. [sent-5, score-0.534]
2 We explain how VRM provides a framework which integrates a number of existing algorithms, such as Parzen windows, Support Vector Machines, Ridge Regression, Constrained Logistic Classifiers and Tangent-Prop. [sent-6, score-0.21]
3 We then show how the approach implies new algorithms for solving problems usually associated with generative models. [sent-7, score-0.394]
4 New algorithms are described for dealing with pattern recognition problems with very different pattern distributions and dealing with unlabeled data. [sent-8, score-0.878]
5 1 Introduction Structural Risk Minimisation (SRM) in a learning system can be achieved using constraints on the parameter vectors, using regularization terms in the cost function, or using Support Vector Machines (SVM). [sent-10, score-0.041]
6 All these principles have lead to well established learning algorithms. [sent-11, score-0.087]
7 It is often said, however, that some problems are best addressed by generative models. [sent-12, score-0.389]
8 We may for instance have a few labeled patterns and a large number of unlabeled patterns. [sent-14, score-0.389]
9 Intuition suggests that these unlabeled patterns carry useful information. [sent-15, score-0.428]
10 The second problem is of discriminating classes with very different pattern distributions. [sent-16, score-0.181]
11 This also occurs often in recognition systems that reject invalid patterns by defining a garbage class for grouping all ambiguous or unrecognizable cases. [sent-18, score-0.435]
12 Although there are successful non-generative approaches (Schuurmans and Southey, 2000) (Drucker, Wu and Vapnik, 1999), the generative framework is undeniably appealing. [sent-19, score-0.395]
13 Recent results (Jaakkola, Meila and Jebara, 2000) even define generative models that contain SVM as special cases. [sent-20, score-0.285]
14 This paper discusses the Vicinal Risk Minimization (VRM) principle, summarily introduced in (Vapnik, 1999). [sent-21, score-0.064]
15 This principle was independently hinted at by Tong and Koller (Tong and Koller, 2000) with a useful generative interpretation. [sent-22, score-0.434]
16 In particular, they proved that SVM are a limiting case of their Restricted Bayesian Classifiers. [sent-23, score-0.105]
17 We extend Tong's and Koller's result by showing that VRM subsumes several well known techniques such as Ridge Regression (Hoerl and Kennard, 1970), Constrained Logistic Classifier, or Tangent Prop (Simard et aI. [sent-24, score-0.064]
18 We then go on to show how VRM naturally leads to simple algo- rithms that can deal with problems for which one would have formally considered purely generative models. [sent-26, score-0.602]
19 We provide algorithms and preliminary empirical results for dealing with unlabeled data or recognizing classes with very different pattern distributions. [sent-27, score-0.78]
20 2 Vicinal Risk Minimization The learning problem can be formulated as the search of the function f E F that minimizes the expectation of a given loss £(f(x), y) . [sent-28, score-0.102]
21 R(f) = f £(f(x), y) dP(x, y) (1) In the classification framework, y takes values ±1 and £(f(x) , y) is a step function such as 1 - Sign(yf(x)), whereas in the regression framework, y is a real number and commonly £(f(x), y) is the mean squared error (f(x) _ y)2. [sent-29, score-0.144]
22 The expectation (1) cannot be computed since the distribution P(x, y) is unknown. [sent-30, score-0.057]
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