By Elad Yom-Tov (auth.), Olivier Bousquet, Ulrike von Luxburg, Gunnar Rätsch (eds.)
Machine studying has develop into a key allowing expertise for plenty of engineering purposes, investigating clinical questions and theoretical difficulties alike. To stimulate discussions and to disseminate new effects, a summer time university sequence used to be all started in February 2002, the documentation of that's released as LNAI 2600.
This ebook offers revised lectures of 2 next summer season faculties held in 2003 in Canberra, Australia, and in Tübingen, Germany. the academic lectures integrated are dedicated to statistical studying conception, unsupervised studying, Bayesian inference, and purposes in trend acceptance; they supply in-depth overviews of intriguing new advancements and include a number of references.
Graduate scholars, academics, researchers and execs alike will locate this publication an invaluable source in studying and educating desktop learning.
Read or Download Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures PDF
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Additional info for Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures
Imposing the sum constraint then gives Pk = Z1 exp(− j λj αjk ) where the “partition function” Z is just a normalizing factor. Note that the Lagrange multipliers have shown us the form that the solution must take, but that form does not automatically satisfy the constraints - they must still be imposed as a condition on the solution. The problem of maximizing the entropy subject to linear constraints therefore gives the widely used logistic regression model, where the parameters of the model are the Lagrange multipliers λi , which are themselves constrained by Eq.
4. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004. 5. B. Buck and V. Macaualay (editors). Maximum Entropy in Action. Clarendon Press, 1991. 6. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):121–167, 1998. 7. C. Burges. Geometric Methods for Feature Extraction and Dimensional Reduction. In L. Rokach and O. Maimon, editors, Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers.
Exercise 4. What distribution maximizes the entropy for the class of univariate distributions whose argument is assumed to be positive, if only the mean is ﬁxed? How about univariate distributions whose argument is arbitrary, but which have speciﬁed, ﬁnite support, and where no constraints are imposed on the mean or the variance? Puzzle 4: The diﬀerential entropy for a uniform distribution with support in [−C, C] is h(PU ) = − C −C (1/2C) log2 (1/2C)dx = − log2 (1/2C) (7) This tends to ∞ as C → ∞.