Download Advanced Lectures on Machine Learning: ML Summer Schools by Elad Yom-Tov (auth.), Olivier Bousquet, Ulrike von Luxburg, PDF

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 medical questions and theoretical difficulties alike. To stimulate discussions and to disseminate new effects, a summer time college sequence used to be begun in February 2002, the documentation of that is released as LNAI 2600.

This e-book provides revised lectures of 2 next summer time faculties held in 2003 in Canberra, Australia, and in Tübingen, Germany. the educational lectures incorporated are dedicated to statistical studying thought, unsupervised studying, Bayesian inference, and functions in development reputation; they supply in-depth overviews of intriguing new advancements and comprise plenty of references.

Graduate scholars, teachers, researchers and pros alike will locate this publication an invaluable source in studying and instructing computing device learning.

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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

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A common way of doing this is via ‘regularisation’. 2 Complexity Control: Regularisation A common, and generally very reasonable, assumption is that we typically expect that data is generated from smooth, rather than complex, functions. In a linear model framework, smoother functions typically have smaller weight magnitudes, so we can penalise complex functions by adding an appropriate penalty term to the cost function that we minimise: E(w) = ED (w) + λEW (w). (5) M 2 , A standard choice is the squared-weight penalty, EW (w) = 12 m=1 wm which conveniently gives the “penalised least-squares” (PLS) estimate for w: wP LS = (ΦT Φ + λI)−1 ΦT t.

Within the appealingly well-defined and axiomatic framework of propositional logic, we ‘answer’ the question with complete certainty, but this logic is clearly too rigid to cope with the realities of real-world modelling, where uncertainty over ‘truth’ is ubiquitous. Our measurements of both the dependent (B) and independent (A) variables are inherently noisy and inexact, and the relationships between the two are invariably non-deterministic. This is where probability theory comes to our aid, as it furnishes us with a principled and consistent framework for meaningful reasoning in the presence of uncertainty.

WM ) is the vector of adjustable model parameters. Here, we consider linear models (strictly, “linear-in-the-parameter”) models which are a linearlyweighted sum of M fixed (but potentially nonlinear) basis functions φm (x): M wm φm (x). y(x; w) = (2) m=1 For our purposes here, we make the common choice to utilise Gaussian datacentred basis functions φm (x) = exp −(x − xm )2 /r2 , which gives us a ‘radial basis function’ (RBF) type model. “Least-Squares” Approximation. e. it models the underlying generative function.

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