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3.5 Kernels and Gaussian Processes
If we consider the output of a function f(x), for fixed x ? X, as f is chosen according to some distribution ? defined over
a class of realvalued functions ?, we may view the output value as a random variable, and hence
as a collection of potentially correlated random variables. Such a collection is known as a stochastic process. The
distribution over the function class ? can be regarded as our prior belief in the likelihood that the different functions will
provide the solution to our learning problem. Such a prior is characteristic of a Bayesian perspective on learning. We
will return to discuss this approach further in the next chapter and in Chapter 6 discuss how to make predictions using
Gaussian processes. At this point we wish to highlight the connection between a particular form of prior commonly
used in Bayesian learning and the kernel functions we have introduced for Support Vector Machines. Many of the
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 Spring '11
 ProfBhattacharya

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