107,363 research outputs found
Rapid computation of far-field statistics for random obstacle scattering
In this article, we consider the numerical approximation of far-field
statistics for acoustic scattering problems in the case of random obstacles. In
particular, we consider the computation of the expected far-field pattern and
the expected scattered wave away from the scatterer as well as the computation
of the corresponding variances. To that end, we introduce an artificial
interface, which almost surely contains all realizations of the random
scatterer. At this interface, we directly approximate the second order
statistics, i.e., the expectation and the variance, of the Cauchy data by means
of boundary integral equations. From these quantities, we are able to rapidly
evaluate statistics of the scattered wave everywhere in the exterior domain,
including the expectation and the variance of the far-field. By employing a
low-rank approximation of the Cauchy data's two-point correlation function, we
drastically reduce the cost of the computation of the scattered wave's
variance. Numerical results are provided in order to demonstrate the
feasibility of the proposed approach
Generalized Functional Additive Mixed Models
We propose a comprehensive framework for additive regression models for
non-Gaussian functional responses, allowing for multiple (partially) nested or
crossed functional random effects with flexible correlation structures for,
e.g., spatial, temporal, or longitudinal functional data as well as linear and
nonlinear effects of functional and scalar covariates that may vary smoothly
over the index of the functional response. Our implementation handles
functional responses from any exponential family distribution as well as many
others like Beta- or scaled non-central -distributions. Development is
motivated by and evaluated on an application to large-scale longitudinal
feeding records of pigs. Results in extensive simulation studies as well as
replications of two previously published simulation studies for generalized
functional mixed models demonstrate the good performance of our proposal. The
approach is implemented in well-documented open source software in the "pffr()"
function in R-package "refund"
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
"Influence Sketching": Finding Influential Samples In Large-Scale Regressions
There is an especially strong need in modern large-scale data analysis to
prioritize samples for manual inspection. For example, the inspection could
target important mislabeled samples or key vulnerabilities exploitable by an
adversarial attack. In order to solve the "needle in the haystack" problem of
which samples to inspect, we develop a new scalable version of Cook's distance,
a classical statistical technique for identifying samples which unusually
strongly impact the fit of a regression model (and its downstream predictions).
In order to scale this technique up to very large and high-dimensional
datasets, we introduce a new algorithm which we call "influence sketching."
Influence sketching embeds random projections within the influence computation;
in particular, the influence score is calculated using the randomly projected
pseudo-dataset from the post-convergence Generalized Linear Model (GLM). We
validate that influence sketching can reliably and successfully discover
influential samples by applying the technique to a malware detection dataset of
over 2 million executable files, each represented with almost 100,000 features.
For example, we find that randomly deleting approximately 10% of training
samples reduces predictive accuracy only slightly from 99.47% to 99.45%,
whereas deleting the same number of samples with high influence sketch scores
reduces predictive accuracy all the way down to 90.24%. Moreover, we find that
influential samples are especially likely to be mislabeled. In the case study,
we manually inspect the most influential samples, and find that influence
sketching pointed us to new, previously unidentified pieces of malware.Comment: fixed additional typo
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