330 research outputs found
Complete enumeration of two-Level orthogonal arrays of strength with constraints
Enumerating nonisomorphic orthogonal arrays is an important, yet very
difficult, problem. Although orthogonal arrays with a specified set of
parameters have been enumerated in a number of cases, general results are
extremely rare. In this paper, we provide a complete solution to enumerating
nonisomorphic two-level orthogonal arrays of strength with
constraints for any and any run size . Our results not only
give the number of nonisomorphic orthogonal arrays for given and , but
also provide a systematic way of explicitly constructing these arrays. Our
approach to the problem is to make use of the recently developed theory of
-characteristics for fractional factorial designs. Besides the general
theoretical results, the paper presents some results from applications of the
theory to orthogonal arrays of strength two, three and four.Comment: Published at http://dx.doi.org/10.1214/009053606000001325 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A general theory of minimum aberration and its applications
Minimum aberration is an increasingly popular criterion for comparing and
assessing fractional factorial designs, and few would question its importance
and usefulness nowadays. In the past decade or so, a great deal of work has
been done on minimum aberration and its various extensions. This paper develops
a general theory of minimum aberration based on a sound statistical principle.
Our theory provides a unified framework for minimum aberration and further
extends the existing work in the area. More importantly, the theory offers a
systematic method that enables experimenters to derive their own aberration
criteria. Our general theory also brings together two seemingly separate
research areas: one on minimum aberration designs and the other on designs with
requirement sets. To facilitate the design construction, we develop a
complementary design theory for quite a general class of aberration criteria.
As an immediate application, we present some construction results on a weak
version of this class of criteria.Comment: Published at http://dx.doi.org/10.1214/009053604000001228 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A new and flexible method for constructing designs for computer experiments
We develop a new method for constructing "good" designs for computer
experiments. The method derives its power from its basic structure that builds
large designs using small designs. We specialize the method for the
construction of orthogonal Latin hypercubes and obtain many results along the
way. In terms of run sizes, the existence problem of orthogonal Latin
hypercubes is completely solved. We also present an explicit result showing how
large orthogonal Latin hypercubes can be constructed using small orthogonal
Latin hypercubes. Another appealing feature of our method is that it can easily
be adapted to construct other designs; we examine how to make use of the method
to construct nearly orthogonal and cascading Latin hypercubes.Comment: Published in at http://dx.doi.org/10.1214/09-AOS757 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques
We study the optimization aspects of personalized Federated Learning (FL). We
propose general optimizers that can be used to solve essentially any existing
personalized FL objective, namely a tailored variant of Local SGD and variants
of accelerated coordinate descent/accelerated SVRCD. By studying a general
personalized objective that is capable of recovering essentially any existing
personalized FL objective as a special case, we develop a universal
optimization theory applicable to all strongly convex personalized FL models in
the literature. We demonstrate the practicality and/or optimality of our
methods both in terms of communication and local computation. Surprisingly
enough, our general optimization solvers and theory are capable of recovering
best-known communication and computation guarantees for solving specific
personalized FL objectives. Thus, our proposed methods can be taken as
universal optimizers that make the design of task-specific optimizers
unnecessary in many cases.Comment: 65 pages, 5 figure
Polarized 3D: High-Quality Depth Sensing with Polarization Cues
Coarse depth maps can be enhanced by using the shape information from polarization cues. We propose a framework to combine surface normals from polarization (hereafter polarization normals) with an aligned depth map. Polarization normals have not been used for depth enhancement before. This is because polarization normals suffer from physics-based artifacts, such as azimuthal ambiguity, refractive distortion and fronto-parallel signal degradation. We propose a framework to overcome these key challenges, allowing the benefits of polarization to be used to enhance depth maps. Our results demonstrate improvement with respect to state-of-the-art 3D reconstruction techniques.Charles Stark Draper Laboratory (Doctoral Fellowship)Singapore. Ministry of Education (Academic Research Foundation MOE2013-T2-1-159)Singapore. National Research Foundation (Singapore University of Technology and Design
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