Estimating the distribution and quantiles of data is a foundational task in data mining and data science. We study algorithms which provide accurate results for extreme quantile queries using a small amount of space, thus helping to understand the tails of the input distribution. Namely, we focus on two recent state-of-the-art solutions: t-digest and ReqSketch. While t-digest is a popular compact summary which works well in a variety of settings, ReqSketch comes with formal accuracy guarantees at the cost of its size growing as new observations are inserted. In this work, we provide insight into which conditions make one preferable to the other. Namely, we show how to construct inputs for t-digest that induce an almost arbitrarily large error and demonstrate that it fails to provide accurate results even on i.i.d. samples from a highly non-uniform distribution. We propose practical improvements to ReqSketch, making it faster than t-digest, while its error stays bounded on any instance. Still, our results confirm that t-digest remains more accurate on the "non-adversarial" data encountered in practice.

Manufacturing flaws of all types, shapes, and sizes can be exhaustively detected as abnormal pixels, if process and noise variations can be learned at every pixel in the inspection area. This statistical template approach to automated visual inspection is extremely fast, effective, and flexible, while achieving false negative rate <10/sup -6/. Critical to this approach are the following novel features: 1) represent both geometry and process information in a model template; 2) align 3D surfaces with subpixel accuracy; compensate for local deformation and texture; 4) estimate bimodal distribution robustly. This novel paradigm was applied to the automatic screening of X-ray images of turbine blades. It has been validated with over 50,000 images and shown to outperform regular inspectors looking at high-pass filtered images.