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Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.


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Journal ArticleDOI
TL;DR: An adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in single-index models for continuous outcome and results indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity, when appropriate, noticeably improves performance.
Abstract: We consider the problem of variable selection for monotone single-index models. A single-index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates. Assuming monotonicity of the unknown function is often reasonable and allows for more straightforward inference. We present an adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome. Monotone function estimates are achieved using the pooled adjacent violators algorithm, followed by kernel regression. In the iterative estimation process, a linear approximation to the unknown function is used, therefore reducing the situation to that of linear regression and allowing for the use of standard LASSO algorithms, such as coordinate descent. Results of a simulation study indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity, when appropriate, noticeably improves performance. The proposed methods are applied to data from a randomized clinical trial for the treatment of a critical illness in the intensive care unit.

27 citations

Journal ArticleDOI
TL;DR: In order to limit the number of (usually burdensome) physical model runs inside the inversion algorithm to a reasonable level, a nonlinear approximation methodology making use of Kriging and a stochastic EM algorithm is presented.

27 citations

Proceedings ArticleDOI
18 May 2004
TL;DR: In this paper, a nonlinear MIMO system can be replaced by a linear system plus a non-linear noise source, and the optimized measurement strategy is proposed to measure the nonparametric FRF.
Abstract: In this paper it is shown that a nonlinear MIMO system can be replaced by a linear system plus a nonlinear noise source. The optimized measurement strategy is proposed to measure the nonparametric FRF.

27 citations

Journal ArticleDOI
TL;DR: In this paper, the validity of the moist tangent linear model (TLM) derived from a time-dependent 1D Eulerian cloud model is investigated by comparing TLM solutions to differences between results from a nonlinear model identically perturbed.
Abstract: The validity of the moist tangent linear model (TLM) derived from a time-dependent 1D Eulerian cloud model is investigated by comparing TLM solutions to differences between results from a nonlinear model identically perturbed. The TLM solutions are found to be highly sensitive to the amplitude of the applied perturbation, and thus the linear approximation is valid only for a specific range of perturbations. The TLM fails to describe the evolution of perturbations when the initial variation is given on a parameter in the vicinity of a nonlinear regime change, a result that has important implications for many cloud-scale processes. Uncertainty imposed on certain aspects of microphysical processes can have a significant influence on the behavior of the TLM solutions, and in some cases this behavior can be explained by the particular discretizations used to solve the equations. The frequency at which the nonlinear basic state is updated in the TLM can also have a profound effect on the TLM validity, ...

27 citations

Journal ArticleDOI
TL;DR: The objective of this paper is to design an embedding method that maps local features describing an image to a higher dimensional representation useful for the image retrieval problem and compares the proposed embedding methods with the state of the art in the context of image search.
Abstract: The objective of this paper is to design an embedding method that maps local features describing an image (e.g., SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship between the linear approximation of a nonlinear function in high dimensional space and the state-of-the-art feature representation used in image retrieval, i.e., VLAD, we propose a new approach for the approximation. The embedded vectors resulted by the function approximation process are then aggregated to form a single representation for image retrieval. Second, in order to make the proposed embedding method applicable to large scale problem, we further derive its fast version in which the embedded vectors can be efficiently computed, i.e., in the closed-form. We compare the proposed embedding methods with the state of the art in the context of image search under various settings: when the images are represented by medium length vectors, short vectors, or binary vectors. The experimental results show that the proposed embedding methods outperform existing the state of the art on the standard public image retrieval benchmarks.

27 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202229
202197
2020134
2019124
2018147