By Elad Yom-Tov (auth.), Olivier Bousquet, Ulrike von Luxburg, Gunnar Rätsch (eds.)

ISBN-10: 3540231226

ISBN-13: 9783540231226

ISBN-10: 3540286500

ISBN-13: 9783540286509

Machine studying has develop into a key permitting know-how for plenty of engineering functions, investigating clinical questions and theoretical difficulties alike. To stimulate discussions and to disseminate new effects, a summer season college sequence used to be began in February 2002, the documentation of that is released as LNAI 2600.

This e-book offers revised lectures of 2 next summer season colleges held in 2003 in Canberra, Australia, and in Tübingen, Germany. the educational lectures integrated are dedicated to statistical studying conception, unsupervised studying, Bayesian inference, and purposes in trend attractiveness; they supply in-depth overviews of interesting new advancements and include a good number of references.

Graduate scholars, academics, researchers and execs alike will locate this e-book an invaluable source in studying and instructing computing device learning.

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Additional resources for Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures

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What dimensions should you choose in order to maximize the weight that can be stored without sinking? Exercise 2. Prove that the distance between two points that are constrained to lie on the n-sphere is extremized when they are either antipodal, or equal. 3 Inequality Constraints Suppose that instead of the constraint c(x) = 0 we have the single constraint c(x) ≤ 0. Now the entire region labeled c(x) < 0 in Figure 1 has become feasible. At the solution, if the constraint is active (c(x) = 0), we again must have that ∇f is parallel to ∇c, by the same argument.

C. 7 Maximum Entropy with Linear Constraints n Suppose that you have a discrete probability distribution Pi , i Pi = 1, and suppose further that the only information that you have about the distribution is that it must satisfy a set of linear constraints: αji Pi = Cj , j = 1, . . , m (8) i The maximum entropy approach (see [5], for example) posits that, subject to the known constraints, our uncertainty about the set of events described by the distribution should be as large as possible, or specifically, that the mean number of bits required to describe an event generated from the constrained probability distribution be as large as possible.

For n independent and identically distributed points, the density is p(x1 , x2 , · · · , xn |µ, Σ) = i p(xi |µ, Σ). By taking derivatives with respect to µ and Σ and using the above results, show that the maximum likelihood values for the mean and covariance matrix are just their sample estimates. Puzzle 5: Suppose that in Exercise 9, n = 2, and that x1 = −x2 , so that the maximum likelihood estimate for the mean is zero. Suppose that Σ is chosen to have positive determinant but such that x is an eigenvector with negative eigenvalue.

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Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures by Elad Yom-Tov (auth.), Olivier Bousquet, Ulrike von Luxburg, Gunnar Rätsch (eds.)


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