  Many kinds of data are naturally amenable to being treated as sequences. An
example is text data, where a text may be seen as a sequence of words. Another
example is clickstream data, where a data instance is a sequence of clicks made
by a visitor to a website. This is also common for data originating in the
domains of speech processing and computational biology. Using such data with
statistical learning techniques can often prove to be cumbersome since most of
them only allow fixed-length feature vectors as input. In casting the data to
fixed-length feature vectors to suit these techniques, we lose the convenience,
and possibly information, a good sequence-based representation can offer. The
framework of rational kernels partly addresses this problem by providing an
elegant representation for sequences, for algorithms that use kernel functions.
In this report, we take a comprehensive look at this framework, its various
extensions and applications. We start with an overview of the core ideas, where
we look at the characterization of rational kernels, and then extend our
discussion to extensions, applications and use at scale. Rational kernels
represent a family of kernels, and thus, learning an appropriate rational
kernel instead of picking one, suggests a convenient way to use them; we
explore this idea in our concluding section. Rational kernels are not as
popular as the many other learning techniques in use today; however, we hope
that this summary effectively shows that not only is their theory
well-developed, but also that various practical aspects have been carefully
studied over time.
