Haussler’s convolution kernel provides a successful framework for engineering new positive semidefinite kernels, and has been applied to a wide range of data types and applications. In the framework, each data object represents a finite set of finer grained components. Then, Haussler’s convolution kernel takes a pair of data objects as input, and returns the sum of the return values of the predetermined primitive positive semidefinite kernel calculated for all the possible pairs of the components of the input data objects. On the other hand, the mapping kernel that we introduce in this paper is a natural generalization of Haussler’s convolution kernel, in that the input to the primitive kernel moves over a predetermined subset rather than the entire cross product. Although we have plural instances of the mapping kernel in the literature, their positive semidefiniteness was investigated in caseby-case manners, and worse yet, was sometimes incorrectly concluded. In fact, there exists a simple and easily checkable necessary and sufficient condition, which is generic in the sense that it enables us to investigate the positive semidefiniteness of an arbitrary instance of the mapping kernel. This is the first paper that presents and proves the validity of the condition. In addition, we introduce two important instances of the mapping kernel, which we refer to as the size-ofindex-structure-distribution kernel and the editcost-distribution kernel. Both of them are naturally derived from well known (dis)similarity measurements in the literature (e.g. the maximum agreement tree, the edit distance), and are reasonably expected to improve the performance of the existing measures by evaluating their distributional features rather than their peak (maximum/minimum) features.

We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speed-ups in the Gram matrix computation. Finally, we test the novel kernel on a wide range of chemoinformatics tasks, from antiviral to anticarcinogenic to toxicological activity prediction, and observe competitive performance when compared against several recent graph kernel methods. 1.

We develop kernels for measuring the similarity between relational instances using background knowledge expressed in first-order logic. The method allows us to bridge the gap between traditional inductive logic programming (ILP) representations and statistical approaches to supervised learning. Logic programs are first used to generate proofs of given visitor programs that use predicates declared in the available background knowledge. A kernel is then defined over pairs of proof trees. The method can be used for supervised learning tasks and is suitable for classification as well as regression. We report positive empirical results on Bongard-like and M-of-N problems that are difficult or impossible to solve with traditional ILP techniques, as well as on real bioinformatics and chemoinformatics data sets.

Abstract. In this work we study string kernel methods for sequence analysis and focus on the problem of species-level identification based on short DNA fragments known as barcodes. We introduce efficient sorting-based algorithms for exact string k-mer kernels and then describe a divide-and-conquer technique for kernels with mismatches. Our algorithms for mismatch kernel matrix computations improve currently known time bounds for these computations. We then consider the mismatch kernel problem with feature selection, and present efficient algorithms for it. Our experimental results show that, for string kernels with mismatches, kernel matrices can be computed 100-200 times faster than traditional approaches. Kernel vector evaluations on new sequences show similar computational improvements. On several DNA barcode datasets, k-mer string kernels considerably improve identification accuracy compared to prior results. String kernels with feature selection demonstrate competitive performance with substantially fewer computations. 1

Abstract. In this chapter, we describe a view of statistical learning in the inductive logic programming setting based on kernel methods. The relational representation of data and background knowledge are used to form a kernel function, enabling us to subsequently apply a number of kernel-based statistical learning algorithms. Different representational frameworks and associated algorithms are explored in this chapter. In kernels on Prolog proof trees, the representation of an example is obtained by recording the execution trace of a program expressing background knowledge. In declarative kernels, features are directly associated with mereotopological relations. Finally, in kFOIL, features correspond to the truth values of clauses dynamically generated by a greedy search algorithm guided by the empirical risk. 1

Abstract. Chemical and biological research is facilitated by big data repositories of chemical compounds from ultra-high-throughput screening techniques, where large numbers of molecules are tested and classified based on their activities against given target. With the increasing availability of data, it is quite necessary to develop accurate and robust models to predict chemical and biological properties of novel molecules based on their structural representations of different dimensions. In this report, we will briefly review literatures of several machine learning approaches on molecular classification problem. These approaches include mining statistically significant molecular substructures, graph walk kernel, and molecular fingerprints. We will focus on recently developed methodology of mining statistically significant molecular substructures. Then, we will propose our novel method which we call atom properties enrichment kernel. The new method can incorporate huge amount of atom level properties. Finally, we will give experimental results of these methods by applying them on standard datasets. 1