Peter Martin Jacobs

Peter Matthew Jacobs, Foad Namjoo, Jeff M. Phillips

We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multidimensional setting and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the difference over orthogonal dominating rectangular ranges (d-sided rectangles in R^d), and is an integral probability metric. We also prove that the distance between a distribution and a sample from the distribution converges to 0 as the sample size grows, and bound this rate. Moreover, we show that one can, up to this same approximation error, compute the distance efficiently in 4 or fewer dimensions; specifically the runtime is near-linear in the size of the sample needed for that error. With this, we derive a delta-precision two-sample hypothesis test using this distance. Finally, we show these metric and approximation properties do not hold for other popular variants.

Jiongqian Liang, Peter Jacobs, Jiankai Sun et al.

In this paper, we propose a novel framework, called Semi-supervised Embedding in Attributed Networks with Outliers (SEANO), to learn a low-dimensional vector representation that systematically captures the topological proximity, attribute affinity and label similarity of vertices in a partially labeled attributed network (PLAN). Our method is designed to work in both transductive and inductive settings while explicitly alleviating noise effects from outliers. Experimental results on various datasets drawn from the web, text and image domains demonstrate the advantages of SEANO over state-of-the-art methods in semi-supervised classification under transductive as well as inductive settings. We also show that a subset of parameters in SEANO is interpretable as outlier score and can significantly outperform baseline methods when applied for detecting network outliers. Finally, we present the use of SEANO in a challenging real-world setting -- flood mapping of satellite images and show that it is able to outperform modern remote sensing algorithms for this task.