Combining Terrier with Apache Spark to Create Agile Experimental Information Retrieval Pipelines

Experimentation using IR systems has traditionally been a procedural and laborious process. Queries must be run on an index, with any parameters of the retrieval models suitably tuned. With the advent of learning-to-rank, such experimental processes (including the appropriate folding of queries to achieve cross-fold validation) have resulted in complicated experimental designs and hence scripting. At the same time, machine learning platforms such as Scikit Learn and Apache Spark have pioneered the notion of an experimental pipeline , which naturally allows a supervised classification experiment to be expressed a series of stages, which can be learned or transformed. In this demonstration, we detail Terrier-Spark, a recent adaptation to the Terrier Information Retrieval platform which permits it to be used within the experimental pipelines of Spark. We argue that this (1) provides an agile experimental platform for information retrieval, comparable to that enjoyed by other branches of data science; (2) aids research reproducibility in information retrieval by facilitating easily-distributable notebooks containing conducted experiments; and (3) facilitates the teaching of information retrieval experiments in educational environments

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce

The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very complex as it requires the complete data matrix to be calculated and stored. Further, the kernelized nature of the kernel $k$-means algorithm hinders the parallelization of its computations on modern infrastructures for distributed computing. In this paper, we are defining a family of kernel-based low-dimensional embeddings that allows for scaling kernel $k$-means on MapReduce via an efficient and unified parallelization strategy. Afterwards, we propose two methods for low-dimensional embedding that adhere to our definition of the embedding family. Exploiting the proposed parallelization strategy, we present two scalable MapReduce algorithms for kernel $k$-means. We demonstrate the effectiveness and efficiency of the proposed algorithms through an empirical evaluation on benchmark data sets.Comment: Appears in Proceedings of the SIAM International Conference on Data Mining (SDM), 201