8,989 research outputs found
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Data-Driven Approach to Simulating Realistic Human Joint Constraints
Modeling realistic human joint limits is important for applications involving
physical human-robot interaction. However, setting appropriate human joint
limits is challenging because it is pose-dependent: the range of joint motion
varies depending on the positions of other bones. The paper introduces a new
technique to accurately simulate human joint limits in physics simulation. We
propose to learn an implicit equation to represent the boundary of valid human
joint configurations from real human data. The function in the implicit
equation is represented by a fully connected neural network whose gradients can
be efficiently computed via back-propagation. Using gradients, we can
efficiently enforce realistic human joint limits through constraint forces in a
physics engine or as constraints in an optimization problem.Comment: To appear at ICRA 2018; 6 pages, 9 figures; for associated video, see
https://youtu.be/wzkoE7wCbu
The sorted effects method: discovering heterogeneous effects beyond their averages
Supplemental Data & Programs are available here: https://hdl.handle.net/2144/34409The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of heterogeneity, a common practice in modern empirical work is to largely ignore it by reporting average partial effects (or, at best, average effects for some groups). While average effects provide very convenient scalar summaries of typical effects, by definition they fail to reflect the entire variety of the heterogeneous effects. In order to discover these effects much more fully, we propose to estimate and report sorted effects -- a collection of estimated partial effects sorted in increasing order and indexed by percentiles. By construction the sorted effect curves completely represent and help visualize the range of the heterogeneous effects in one plot. They are as convenient and easy to report in practice as the conventional average partial effects. They also serve as a basis for classification analysis, where we divide the observational units into most or least affected groups and summarize their characteristics. We provide a quantification of uncertainty (standard errors and confidence bands) for the estimated sorted effects and related classification analysis, and provide confidence sets for the most and least affected groups. The derived statistical results rely on establishing key, new mathematical results on Hadamard differentiability of a multivariate sorting operator and a related classification operator, which are of independent interest. We apply the sorted effects method and classification analysis to demonstrate several striking patterns in the gender wage gap.https://arxiv.org/abs/1512.05635Accepted manuscrip
The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages
The partial (ceteris paribus) effects of interest in nonlinear and
interactive linear models are heterogeneous as they can vary dramatically with
the underlying observed or unobserved covariates. Despite the apparent
importance of heterogeneity, a common practice in modern empirical work is to
largely ignore it by reporting average partial effects (or, at best, average
effects for some groups). While average effects provide very convenient scalar
summaries of typical effects, by definition they fail to reflect the entire
variety of the heterogeneous effects. In order to discover these effects much
more fully, we propose to estimate and report sorted effects -- a collection of
estimated partial effects sorted in increasing order and indexed by
percentiles. By construction the sorted effect curves completely represent and
help visualize the range of the heterogeneous effects in one plot. They are as
convenient and easy to report in practice as the conventional average partial
effects. They also serve as a basis for classification analysis, where we
divide the observational units into most or least affected groups and summarize
their characteristics. We provide a quantification of uncertainty (standard
errors and confidence bands) for the estimated sorted effects and related
classification analysis, and provide confidence sets for the most and least
affected groups. The derived statistical results rely on establishing key, new
mathematical results on Hadamard differentiability of a multivariate sorting
operator and a related classification operator, which are of independent
interest. We apply the sorted effects method and classification analysis to
demonstrate several striking patterns in the gender wage gap.Comment: 62 pages, 9 figures, 8 tables, includes appendix with supplementary
material
Decentralization Estimators for Instrumental Variable Quantile Regression Models
The instrumental variable quantile regression (IVQR) model (Chernozhukov and
Hansen, 2005) is a popular tool for estimating causal quantile effects with
endogenous covariates. However, estimation is complicated by the non-smoothness
and non-convexity of the IVQR GMM objective function. This paper shows that the
IVQR estimation problem can be decomposed into a set of conventional quantile
regression sub-problems which are convex and can be solved efficiently. This
reformulation leads to new identification results and to fast, easy to
implement, and tuning-free estimators that do not require the availability of
high-level "black box" optimization routines
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