By Tony Jebara
Machine Learning:Discriminative and Generative covers the most modern topics and instruments in desktop studying starting from Bayesian probabilistic versions to discriminative support-vector machines. in spite of the fact that, not like prior books that purely speak about those relatively various methods in isolation, it bridges the 2 colleges of notion jointly inside of a typical framework, elegantly connecting their numerous theories and making one universal big-picture. additionally, this bridge brings forth new hybrid discriminative-generative instruments that mix the strengths of either camps. This booklet serves a number of reasons to boot. The framework acts as a systematic leap forward, fusing the components of generative and discriminative studying and should be of curiosity to many researchers. in spite of the fact that, as a conceptual leap forward, this universal framework unifies many formerly unrelated instruments and methods and makes them comprehensible to a bigger element of the general public. this provides the extra practical-minded engineer, scholar and the commercial public an easy-access and extra good street map into the area of computer studying.
Machine studying: Discriminative and Generative is designed for an viewers composed of researchers & practitioners in and academia. The booklet is usually compatible as a secondary textual content for graduate-level scholars in machine technological know-how and engineering.
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Additional info for Machine Learning: Discriminative and Generative
Formal Gener alization Guar antees While emp ir ical validation can motivate the combined generativedi scriminative framework , we will also identify form al genera lizat ion guarantees from different p erspectives. Variou s arg uments from the lit erature su ch as sp arsity, VC-dimensi on and PA C-B ayes generalization bounds will be compatible with this new fram ework. • Extensib ility Ma ny extensions will be demon strated in the hybrid generat ive discr im inative approach whi ch will justify it s usefulness.
K(8) ~ logf ] - 282. ' 1) - "48t 82 8 1 . 17 log(1 + ~::= , exp( 8d)) - log e- e ) log f(8) exp(8) I Domain 8, E R U 82 E R D,D eE R D <0 eE R_ 8E R+ 8E R Definitions of A and K for some exponential family distributions. In addit ion , it is well kn own , t hat maximum likelihood estimation of the parameters of an e-family distribution with resp ect to an independent identically distributed (iid) data set is fully tractabl e, unique and straightforward. This is because log-likelihood remains concave in the parameters for the e-fa mily and products of the e-families.
Having obtained a P(ZJZ) or, more compactly a P(Z) , we' can compute the probability of any point Z in the (continuous or discrete) probability space. We can also simply compute the scalar quantity P(Z) by using the above approaches to integrate the likelihood of all observations over all models 8 under a prior P(8) . This quantity is called the evi dence and higher values indicate how appropriate this choice of parametric models 8 and prior P(8) was for this particular dataset. Bayesian evidence can then be used for model selection by finding which choice of parametric models or structures (once integrated over all its parameter settings) yields the highest P(Z) [90, 151].