Kronecker Determinantal Point Processes

Abstract Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large problems is still limited due to O(N 3 ) complexity of core tasks such as sampling and learning. We enable efficient sampling and learning for DPPs by introducing KRONDPP, a DPP model whose kernel matrix decomposes as a tensor product of multiple smaller kernel matrices. This decomposition immediately enables fast exact sampling. But contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult. We overcome this challenge, and derive batch and stochastic optimization algorithms for efficiently learning the parameters of a KRONDPP

Outlier Detection in Heterogeneous Datasets using Automatic Tuple Expansion

Rapidly developing areas of information technology are generating massive amounts of data. Human errors, sensor failures, and other unforeseen circumstances unfortunately tend to undermine the quality and consistency of these datasets by introducing outliers -- data points that exhibit surprising behavior when compared to the rest of the data. Characterizing, locating, and in some cases eliminating these outliers offers interesting insight about the data under scrutiny and reinforces the confidence that one may have in conclusions drawn from otherwise noisy datasets. In this paper, we describe a tuple expansion procedure which reconstructs rich information from semantically poor SQL data types such as strings, integers, and floating point numbers. We then use this procedure as the foundation of a new user-guided outlier detection framework, dBoost, which relies on inference and statistical modeling of heterogeneous data to flag suspicious fields in database tuples. We show that this novel approach achieves good classification performance, both in traditional numerical datasets and in highly non-numerical contexts such as mostly textual datasets. Our implementation is publicly available, under version 3 of the GNU General Public License