Joachim Buhmann, "Empirical Risk Approximation: An Induction Principle for Unsupervised Learning" Technical Report IAI-TR-98-3, Institut for Informatik III, Universitat Bonn. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....optimum. Indeed this conjecture is supported by experimental results (Hofmann et al. 1998) which indicate that although no final global optimum can be guaranteed, the clustering performance of DA is superior in this domain. Recently also some deeper theoretical justification has been given by Buhmann (1998). 8 4 Combined Complexity Control Within the discrete control scheme as proposed by Tipping and Bishop (1999) different proportions of horizontal and vertical complexity constitute a finite set of models which have to be compared in order to find the most appropriate one for the problem at ....

Buhmann, J. M. (1998). Empirical Risk Approximation: An induction principle for unsupervised learning. Technical report, Dept. of Computer Science III, University of Bonn.

....in 4. 3.2 Estimation by entropy minimization In learning we minimize a sum of entropies which measure the ambiguity in a probability distribution and cross entropies which measure the divergence between distributions. The principle of minimum entropy, advocated in various forms by [23, 2, 8], seeks the simplest model that explains the data, or, equivalently, the most complex model whose parameter estimates are fully supported by the data. This maximizes the information extracted from the training data and boosts the odds of generalizing correctly beyond it. The learning objective ....

J. Buhmann. Empirical risk approximation: An induction principle for unsupervised learning. Technical Report IAI-TR-98-3, Institut f ur Informatik III, Universit at Bonn. 1998., 1998.

....the effective model complexity. Annealing, thereby, has the potential to improve the generalization for otherwise overfitting models (for supervised learning problems cf. PKM96, RMRG97] Recent theoretical investigations emphasize the benefits of annealing to avoid overfitting phenomena [Buh98] In this paper, the advantages of deterministic annealing are investigated experimentally (cf. Section 4) In statistical learning, deterministic annealing is used in the T T fin 1 limit where the stopping temperature T fin 1 in the inifinte data aspymptotics. In hard clustering ....

J. M. Buhmann. Empirical risk approximation: An induction principle for unsupervised learning. Technical Report IAI-TR-98-3, Institut fur Informatik III, University of Bonn, 1998.

....however, provides no answer whether is an optimal estimate in the sense of (34) for a nite number of measurements. Indeed, there is both theoretical and empirical evidence that deterministic annealing with an optimally selected nite stopping temperature provides uniformly better estimates [47]. As an underlying rationale replacing the cost function by the corresponding free energy implicitly reduces the degrees of freedom and thus the variance in the estimation process. The phase transition behavior illustrated in the last section can be seen as a simple consequence of this fact. ....

J. Buhmann, \Empirical risk approximation: An induction principle for unsupervised learning," IAI-TR 98-3, Institut fur Informatik III, University of Bonn, 1998.

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Joachim Buhmann, "Empirical Risk Approximation: An Induction Principle for Unsupervised Learning" Technical Report IAI-TR-98-3, Institut for Informatik III, Universitat Bonn. 1998.

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