Sequential Cauchy Combination Test for Multiple Testing Problems with Financial Applications

We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test recursively on a sequence of expanding subsets of $p$-values and is referred to as the sequential Cauchy combination test. While the original Cauchy combination test aims to make a global statement about a set of null hypotheses by summing transformed $p$-values, our sequential version determines which $p$-values trigger the rejection of the global null. The sequential test achieves strong familywise error rate control, exhibits less conservatism compared to existing controlling procedures when dealing with dependent test statistics, and provides a power boost. As illustrations, we revisit two well-known large-scale multiple testing problems in finance for which the test statistics have either serial dependence or cross-sectional dependence, namely monitoring drift bursts in asset prices and searching for assets with a nonzero alpha. In both applications, the sequential Cauchy combination test proves to be a preferable alternative. It overcomes many of the drawbacks inherent to inequality-based controlling procedures, extreme value approaches, resampling and screening methods, and it improves the power in simulations, leading to distinct empirical outcomes.Comment: 35 pages, 6 figure

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

Video Logo Retrieval based on local Features

Estimation of the frequency and duration of logos in videos is important and challenging in the advertisement industry as a way of estimating the impact of ad purchases. Since logos occupy only a small area in the videos, the popular methods of image retrieval could fail. This paper develops an algorithm called Video Logo Retrieval (VLR), which is an image-to-video retrieval algorithm based on the spatial distribution of local image descriptors that measure the distance between the query image (the logo) and a collection of video images. VLR uses local features to overcome the weakness of global feature-based models such as convolutional neural networks (CNN). Meanwhile, VLR is flexible and does not require training after setting some hyper-parameters. The performance of VLR is evaluated on two challenging open benchmark tasks (SoccerNet and Standford I2V), and compared with other state-of-the-art logo retrieval or detection algorithms. Overall, VLR shows significantly higher accuracy compared with the existing methods.Comment: Accepted by ICIP 20. Contact author: Bochen Guan ([email protected]

Searching for a trail of evidence in a maze

Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0,1) while under the alternative, there is an unknown path along which random variables have distribution $N(\mu,1)$, $\mu> 0$, and distribution N(0,1) away from it. For which values of the mean shift $\mu$ can one reliably detect and for which values is this impossible? Consider, for example, the usual regular lattice with vertices of the form $$\{(i,j):0\le i,-i\le j\le i and j has the parity of i\}$$ and oriented edges $(i,j)\to (i+1,j+s)$, where $s=\pm1$. We show that for paths of length $m$ starting at the origin, the hypotheses become distinguishable (in a minimax sense) if $\mu_m\gg1/\sqrt{\log m}$, while they are not if $\mu_m\ll1/\log m$. We derive equivalent results in a Bayesian setting where one assumes that all paths are equally likely; there, the asymptotic threshold is $\mu_m\approx m^{-1/4}$. We obtain corresponding results for trees (where the threshold is of order 1 and independent of the size of the tree), for distributions other than the Gaussian and for other graphs. The concept of the predictability profile, first introduced by Benjamini, Pemantle and Peres, plays a crucial role in our analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS526 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table