Machine Learning: A Bayesian and Optimization Perspective by Sergios Theodoridis

By Sergios Theodoridis

This instructional textual content offers a unifying point of view on desktop studying through overlaying either probabilistic and deterministic techniques -which are in response to optimization options – including the Bayesian inference technique, whose essence lies within the use of a hierarchy of probabilistic versions. The publication offers the main laptop studying tools as they've been constructed in several disciplines, resembling information, statistical and adaptive sign processing and computing device technological know-how. concentrating on the actual reasoning at the back of the maths, the entire a variety of tools and methods are defined extensive, supported by means of examples and difficulties, giving a useful source to the coed and researcher for knowing and using computer studying concepts.

The e-book builds conscientiously from the fundamental classical ways to the newest traits, with chapters written to be as self-contained as attainable, making the textual content compatible for various classes: trend attractiveness, statistical/adaptive sign processing, statistical/Bayesian studying, in addition to brief classes on sparse modeling, deep studying, and probabilistic graphical models.

  • All significant classical strategies: Mean/Least-Squares regression and filtering, Kalman filtering, stochastic approximation and on-line studying, Bayesian category, choice bushes, logistic regression and boosting methods.
  • The most recent developments: Sparsity, convex research and optimization, on-line allotted algorithms, studying in RKH areas, Bayesian inference, graphical and hidden Markov versions, particle filtering, deep studying, dictionary studying and latent variables modeling.
  • Case experiences - protein folding prediction, optical personality attractiveness, textual content authorship identity, fMRI facts research, switch aspect detection, hyperspectral picture unmixing, objective localization, channel equalization and echo cancellation, express how the idea will be applied.
  • MATLAB code for all of the major algorithms can be found on an accompanying site, permitting the reader to scan with the code.

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Additional resources for Machine Learning: A Bayesian and Optimization Perspective

Sample text

1 Linear Regression: The Nonwhite Gaussian Noise Case . . . . . . . . . . . . . . . . . 11 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The Maximum A Posteriori Probability Estimation Method . . . . . . . . . . . . . . . . 12 Curse of Dimensionality . . . . . . . . . . . . . . .

14 Expected and Empirical Loss Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Nonparametric Modeling and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

For a < 1, it is strictly decreasing and p(x)−−→∞ as x−−→0 and p(x)−−→0 as x−−→∞. 8 shows the resulting graphs for various values of the parameters. 5 (red), a = 1, b = 2 (dotted). 1. • • Setting in the gamma distribution a to be an integer (usually a = 2), the Erlang distribution results. This distribution is being used to model waiting times in queueing systems. The chi-squared is also a special case of the gamma distribution, and it is obtained if we set b = 1/2 and a = ν/2. The chi-squared distribution results if we sum up ν squared normal variables.

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