Rational Kernels: A survey

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.