Biological Sequence Kernels with Guaranteed Flexibility
This work addresses the challenge of improving the reliability and effectiveness of machine learning methods for biological sequences, which is crucial for applications in human health and environmental sustainability, though it is incremental as it builds on existing kernel theory.
The paper tackled the problem of unreliable machine learning methods for biological sequences by theoretically analyzing kernels, establishing conditions for universality and characteristic properties, and showing that many existing methods fail these conditions, leading to severe failures. They developed tractable modifications to existing kernels to provide strong guarantees on accuracy and reliability, with results illustrated on real biological data sets.
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning methods are ineffective or unreliable in this problem domain. We study these challenges theoretically, through the lens of kernels. Methods based on kernels are ubiquitous: they are used to predict molecular phenotypes, design novel proteins, compare sequence distributions, and more. Many methods that do not use kernels explicitly still rely on them implicitly, including a wide variety of both deep learning and physics-based techniques. While kernels for other types of data are well-studied theoretically, the structure of biological sequence space (discrete, variable length sequences), as well as biological notions of sequence similarity, present unique mathematical challenges. We formally analyze how well kernels for biological sequences can approximate arbitrary functions on sequence space and how well they can distinguish different sequence distributions. In particular, we establish conditions under which biological sequence kernels are universal, characteristic and metrize the space of distributions. We show that a large number of existing kernel-based machine learning methods for biological sequences fail to meet our conditions and can as a consequence fail severely. We develop straightforward and computationally tractable ways of modifying existing kernels to satisfy our conditions, imbuing them with strong guarantees on accuracy and reliability. Our proof techniques build on and extend the theory of kernels with discrete masses. We illustrate our theoretical results in simulation and on real biological data sets.