9,748 research outputs found
On Degrees of Freedom of Projection Estimators with Applications to Multivariate Nonparametric Regression
In this paper, we consider the nonparametric regression problem with
multivariate predictors. We provide a characterization of the degrees of
freedom and divergence for estimators of the unknown regression function, which
are obtained as outputs of linearly constrained quadratic optimization
procedures, namely, minimizers of the least squares criterion with linear
constraints and/or quadratic penalties. As special cases of our results, we
derive explicit expressions for the degrees of freedom in many nonparametric
regression problems, e.g., bounded isotonic regression, multivariate
(penalized) convex regression, and additive total variation regularization. Our
theory also yields, as special cases, known results on the degrees of freedom
of many well-studied estimators in the statistics literature, such as ridge
regression, Lasso and generalized Lasso. Our results can be readily used to
choose the tuning parameter(s) involved in the estimation procedure by
minimizing the Stein's unbiased risk estimate. As a by-product of our analysis
we derive an interesting connection between bounded isotonic regression and
isotonic regression on a general partially ordered set, which is of independent
interest.Comment: 72 pages, 7 figures, Journal of the American Statistical Association
(Theory and Methods), 201
Development of Information Technology Auditing Teaching Modules: An Interdisciplinary Endeavor between Seidenberg and Lubin Faculty
The original goals of the project were to develop interdisciplinary Information Technology (IT) Auditing
teaching modules, to be integrated into courses offered by both Business and Information Technology
disciplines during Fall 2009 and Spring 2010. IT Auditing is an interdisciplinary field which requires
understanding audit, control, technology and security concepts in accordance with audit standards,
guidelines, and best practices. Thus, IT Auditing requires interdisciplinary knowledge across IT and
Accounting/Auditing domains. With increasing use of IT in business processes, the demand for IT
Auditors is increasing rapidly, offering a lucrative career path. Acquiring IT Audit related knowledge and
skills will help our students improve their career opportunities by exploring this growing field.
Based upon the curriculum content areas of the CISA Exam as well as the ISACA Model Curriculum, we
proposed the following three interdisciplinary teaching modules for IT Auditing: 1) IT Auditing
Frameworks & Business Continuity; 2) IT Lifecycle Management & Service Delivery; and 3) Protection of
Information Assets.
We had developed the three teaching modules. Each individual module can be covered in one to two
weeks. The entire set of three IT Auditing modules can then be covered in 3-4 weeks of class time. For
each of the individual modules, we had developed presentation slides, reading lists and online quizzes
based on the CISA Exam. We had also identified an overarching case study to be used throughout the
three individual modules for continuity reasons
Convergence Analysis of Accelerated Stochastic Gradient Descent under the Growth Condition
We study the convergence of accelerated stochastic gradient descent for
strongly convex objectives under the growth condition, which states that the
variance of stochastic gradient is bounded by a multiplicative part that grows
with the full gradient, and a constant additive part. Through the lens of the
growth condition, we investigate four widely used accelerated methods:
Nesterov's accelerated method (NAM), robust momentum method (RMM), accelerated
dual averaging method (ADAM), and implicit ADAM (iADAM). While these methods
are known to improve the convergence rate of SGD under the condition that the
stochastic gradient has bounded variance, it is not well understood how their
convergence rates are affected by the multiplicative noise. In this paper, we
show that these methods all converge to a neighborhood of the optimum with
accelerated convergence rates (compared to SGD) even under the growth
condition. In particular, NAM, RMM, iADAM enjoy acceleration only with a mild
multiplicative noise, while ADAM enjoys acceleration even with a large
multiplicative noise. Furthermore, we propose a generic tail-averaged scheme
that allows the accelerated rates of ADAM and iADAM to nearly attain the
theoretical lower bound (up to a logarithmic factor in the variance term)
An Electrostatically Preferred Lateral Orientation of SNARE Complex Suggests Novel Mechanisms for Driving Membrane Fusion
Biological membrane fusion is a basic cellular process catalyzed by SNARE proteins and additional auxiliary factors. Yet, the critical mechanistic details of SNARE-catalyzed membrane fusion are poorly understood, especially during rapid synaptic transmission. Here, we systematically assessed the electrostatic forces between SNARE complex, auxiliary proteins and fusing membranes by the nonlinear Poisson-Boltzmann equation using explicit models of membranes and proteins. We found that a previously unrecognized, structurally preferred and energetically highly favorable lateral orientation exists for the SNARE complex between fusing membranes. This preferred orientation immediately suggests a novel and simple synaptotagmin-dependent mechanistic trigger of membrane fusion. Moreover, electrostatic interactions between membranes, SNARE complex, and auxiliary proteins appear to orchestrate a series of membrane curvature events that set the stage for rapid synaptic vesicle fusion. Together, our electrostatic analyses of SNAREs and their regulatory factors suggest unexpected and potentially novel mechanisms for eukaryotic membrane fusion proteins
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Modeling Air Handling Units to Create a Diverse Fault Dataset for FDD Innovation: Lessons Learned and Recommendations
As energy management and information systems (e.g., automated fault detection and diagnostics [AFDD] tools) become more prevalent in the commercial building stock, it is important to determine the effectiveness of these technologies by benchmarking their performance. The authors have been working to develop the largest publicly available dataset of HVAC fault datasets for performance benchmarking applications, covering the most common HVAC systems and designs including chiller plants, rooftop packaged units, dual duct air handling unit and single duct air handling units. This study covers the development, modeling, and validation of a synthetic fault dataset for the air handling unit (AHU), one of the most common HVAC configurations found in the commercial building stock. Despite this being a common system, real-world time series data are scarce and usually do not span a wide range of weather conditions. Due to this limitation, two detailed AHU models, which included the single duct AHU and dual duct AHU developed in the Modelica language and HVACSIM+ were employed to carry out annual simulations of numerous common sensor faults, mechanical faults, and control sequence faults. The fault inclusive data were then validated by comparing fault effects on system performance to expected symptoms. We summarize the nature of each fault and their impacts under different weather and operation conditions. We report some lessons learnt during the efforts of validating the high volumes of the FDD data sets. Finally, we highlight considerations for FDD developers that may want to use this dataset to assess their algorithmsβ performance and their improvement over time
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