We study minimax rates for estimating high-dimensional nonparametric regression models with sparse additive structure and smoothness constraints. More precisely, our goal is to estimate a function f* : ℝp → ℝ that ha...
ISBN:
(纸本)9781615679119
We study minimax rates for estimating high-dimensional nonparametric regression models with sparse additive structure and smoothness constraints. More precisely, our goal is to estimate a function f* : ℝp → ℝ that has an additive decomposition of the form f*(X1,..., Xp) = ∑j∈s h*j(Xj), where each component function h*j lies in some class H of "smooth" functions, and S ⊂ {1,...,p} is an unknown subset with cardinality s = |S|. Given n i.i.d. observations of f*(X) corrupted with additive white Gaussian noise where the covariate vectors (X1, X2, X3, Xp) are drawn with i.i.d. components from some distribution P, we determine lower bounds on the minimax rate for estimating the regression function with respect to squared-L2 (ℙ) error. Our main result is a lower bound on the minimax rate that scales as max (s log(p/s)/n, s ∊2n(H)). The first term reflects the sample size required for performing subset selection, and is independent of the function class H. The second term s ∊2n(H) is an s-dimensional estimation term corresponding to the sample size required for estimating a sum of s univariate functions, each chosen from the function class H. It depends linearly on the sparsity index s but is independent of the global dimension p. As a special case, if H corresponds to functions that are m-times differentiable (an mth-order Sobolev space), then the s-dimensional estimation term takes the form ∊2n(H) ≍ s n-2m/(2m+1). Either of the two terms may be dominant in different regimes, depending on the relation between the sparsity and smoothness of the additive decomposition.
The relevance feedback track in TREC 2009 focuses on two sub tasks: actively selecting good documents for users to provide relevance feedback and retrieving documents based on user relevance feedback. For the first ta...
The relevance feedback track in TREC 2009 focuses on two sub tasks: actively selecting good documents for users to provide relevance feedback and retrieving documents based on user relevance feedback. For the first task, we tried a clustering based method and the Transductive Experimental Design (TED) method proposed by Yu et al. [5] For clustering based method, we use the K-means algorithm to cluster the top retrieved documents and choose the most representative document of each cluster. The TED method aims to find documents that are hard-to-predict and representative of the unlabeled documents. For the second task, we did query expansion based on a relevance model learned on the relevant documents.
Recently we have proposed a new image device called the gigavision camera. The main feature of this camera is that the pixels have a binary response. The response function of a gigavision sensor is non-linear and simi...
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Modern embedded compute platforms increasingly contain both microprocessors and field-programmable gate arrays (FPGAs). The FPGAs may implement accelerators or other circuits to speedup performance. Many such circuits...
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ISBN:
(纸本)9781605584706
Modern embedded compute platforms increasingly contain both microprocessors and field-programmable gate arrays (FPGAs). The FPGAs may implement accelerators or other circuits to speedup performance. Many such circuits have been previously designed for acceleration via application-specific integrated circuits (ASICs). Redesigning an ASIC circuit for FPGA implementation involves several challenges. We describe a case study that highlights a common challenge related to memories. The study involves converting a pattern counting circuit architecture, based on a pipelined binary tree and originally designed for ASIC implementation, into a circuit suitable for FPGAs. The original ASIC-oriented circuit, when mapped to a Spartan 3e FPGA, could process 10 million patterns per second and handle up to 4,096 patterns. The redesigned circuit could instead process 100 million patterns per second and handle up to 32,768 patterns, representing a 10x performance improvement and a 4x utilization improvement. The redesign involved partitioning large memories into smaller ones at the expense of redundant control logic. Through this and other case studies, design patterns may emerge that aid designers in redesigning ASIC circuits for FPGAs as well as in building new high-performance and efficient circuits for FPGAs. Copyright 2008 ACM.
We consider the problem of measuring user contributions to ver-sioned, collaborative bodies of information, such as wikis. Measuring the contributions of individual authors can be used to divide revenue, to recognize ...
This paper introduces an accumulative prediction method to predict the eye diagram for high speed signaling systems. We use the step responses of pull-up and pull-down to extract the worst-case eye diagram, including ...
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ISBN:
(纸本)9781424428205
This paper introduces an accumulative prediction method to predict the eye diagram for high speed signaling systems. We use the step responses of pull-up and pull-down to extract the worst-case eye diagram, including the eye height and jitter. Furthermore, the method produces the input patterns of the worst-case intersymbol interference. The algorithm handles signals of either symmetric or asymmetric rise/fall time. Experimental results demonstrate the accuracy and efficiency of the proposed method.
We show that silicon waveguides can simultaneously be utilized as focusing device and also as detectors in nonlinear fluorescence imaging. Detection and imaging of
ISBN:
(纸本)9781424419326
We show that silicon waveguides can simultaneously be utilized as focusing device and also as detectors in nonlinear fluorescence imaging. Detection and imaging of
The Wikipedia is a collaborative encyclopedia: anyone can contribute to its articles simply by clicking on an "edit" button. The open nature of the Wikipedia has been key to its success, but has also created...
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