arXiv subjects

Andreas Noack

Publications and source records attributed to Andreas Noack.

6 recordsLinked to original sources

arXiv2018

Fast computation of the principal components of genotype matrices in Julia

Finding the largest few principal components of a matrix of genetic data is a common task in genome-wide association studies (GWASs), both for dimensionality reduction and for identifying unwanted factors of variation. We describe a simple random matrix model for matrices that arise in GWASs, showing that the singular values have a bulk behavior that obeys a Marchenko-Pastur distributed with a handful of large outliers. We also implement Golub-Kahan-Lanczos (GKL) bidiagonalization in the Julia programming language, providing thick restarting and a choice between full and partial reorthogonalization strategies to control numerical roundoff. Our implementation of GKL bidiagonalization is up to 36 times faster than software tools used commonly in genomics data analysis for computing principal components, such as EIGENSOFT and FlashPCA, which use dense LAPACK routines and randomized subspace iteration respectively.

math.NA↗

arXiv2018

Cataloging the Visible Universe through Bayesian Inference at Petascale

Astronomical catalogs derived from wide-field imaging surveys are an important tool for understanding the Universe. We construct an astronomical catalog from 55 TB of imaging data using Celeste, a Bayesian variational inference code written entirely in the high-productivity programming language Julia. Using over 1.3 million threads on 650,000 Intel Xeon Phi cores of the Cori Phase II supercomputer, Celeste achieves a peak rate of 1.54 DP PFLOP/s. Celeste is able to jointly optimize parameters for 188M stars and galaxies, loading and processing 178 TB across 8192 nodes in 14.6 minutes. To achieve this, Celeste exploits parallelism at multiple levels (cluster, node, and thread) and accelerates I/O through Cori's Burst Buffer. Julia's native performance enables Celeste to employ high-level constructs without resorting to hand-written or generated low-level code (C/C++/Fortran), and yet achieve petascale performance.

cs.DC↗

arXiv2016

Game-Theoretic Model of Incentivizing Privacy-Aware Users to Consent to Location Tracking

Nowadays, mobile users have a vast number of applications and services at their disposal. Each of these might impose some privacy threats on users' "Personally Identifiable Information" (PII). Location privacy is a crucial part of PII, and as such, privacy-aware users wish to maximize it. This privacy can be, for instance, threatened by a company, which collects users' traces and shares them with third parties. To maximize their location privacy, users can decide to get offline so that the company cannot localize their devices. The longer a user stays connected to a network, the more services he might receive, but his location privacy decreases. In this paper, we analyze the trade-off between location privacy, the level of services that a user experiences, and the profit of the company. To this end, we formulate a Stackelberg Bayesian game between the User (follower) and the Company (leader). We present theoretical results characterizing the equilibria of the game. To the best of our knowledge, our work is the first to model the economically rational decision-making of the service provider (i.e., the Company) in conjunction with the rational decision-making of users who wish to protect their location privacy. To evaluate the performance of our approach, we have used real-data from a testbed, and we have also shown that the game-theoretic strategy of the Company outperforms non-strategic methods. Finally, we have considered different User privacy types, and have determined the service level that incentivizes the User to stay connected as long as possible.

cs.GT↗

arXiv2008

Multi-level algorithms for modularity clustering

Modularity is one of the most widely used quality measures for graph clusterings. Maximizing modularity is NP-hard, and the runtime of exact algorithms is prohibitive for large graphs. A simple and effective class of heuristics coarsens the graph by iteratively merging clusters (starting from singletons), and optionally refines the resulting clustering by iteratively moving individual vertices between clusters. Several heuristics of this type have been proposed in the literature, but little is known about their relative performance. This paper experimentally compares existing and new coarsening- and refinement-based heuristics with respect to their effectiveness (achieved modularity) and efficiency (runtime). Concerning coarsening, it turns out that the most widely used criterion for merging clusters (modularity increase) is outperformed by other simple criteria, and that a recent algorithm by Schuetz and Caflisch is no improvement over simple greedy coarsening for these criteria. Concerning refinement, a new multi-level algorithm is shown to produce significantly better clusterings than conventional single-level algorithms. A comparison with published benchmark results and algorithm implementations shows that combinations of coarsening and multi-level refinement are competitive with the best algorithms in the literature.

cs.DS↗

arXiv2008

Modularity clustering is force-directed layout

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan's modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because both representations are complementary and often used together.

cs.DM↗

arXiv2004

CrocoPat 2.1 Introduction and Reference Manual

CrocoPat is an efficient, powerful and easy-to-use tool for manipulating relations of arbitrary arity, including directed graphs. This manual provides an introduction to and a reference for CrocoPat and its programming language RML. It includes several application examples, in particular from the analysis of structural models of software systems.

cs.PL↗