The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model...
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The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carr
The use of MEMS to study the effect of mechanical compression on neurogenesis has been demonstrated. Polydimethylsiloxane- (PDMS)-based stretchable platforms were used on neurosphere assay to investigate the role of m...
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Magnetic resonance elastography (MRE) is an emerging technique for noninvasive imaging of tissue elasticity. Proprietary algorithms are used to reconstruct tissue elasticity from the images of wave propagation within ...
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ISBN:
(纸本)9783642156984
Magnetic resonance elastography (MRE) is an emerging technique for noninvasive imaging of tissue elasticity. Proprietary algorithms are used to reconstruct tissue elasticity from the images of wave propagation within soft tissue. Elasticity reconstruction suffers from interfering noise and outliers. The interference causes biased elasticity and undesired artifacts in the reconstructed elasticity map. Anisotropic geometric diffusion is able to suppress image noise while enhance inherent features. Therefore we integrate anisotropic diffusion with level set methods for numerical enhancement of MRE wave images. Performance evaluation of the proposed level set diffusion (LSD) approach was conducted on both synthetic and real MRE datasets. Experimental results confirm the effectiveness of LSD for MRE image enhancement and direct inversion.
This paper summarizes dynamic measurements of shear modulus constants acquired for spontaneously growing rat mammary tumors. Measurements are compared with histology to determine tumor types. We also report on 3D shea...
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Recently, some variants of the l_1 norm, particularly matrix norms such as the l_(1,2) and l_(1,∞) norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity v...
ISBN:
(纸本)9781617823800
Recently, some variants of the l_1 norm, particularly matrix norms such as the l_(1,2) and l_(1,∞) norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity via joint regularized on. In this paper, we unify the l_(1,2) and l_(1,∞) norms by considering a family of l_(1,q) norms for 1 < q < ∞ and study the problem of determining the most appropriate sparsity enforcing norm to use in the context of multi-task feature selection. Using the generalized normal distribution, we provide a probabilistic interpretation of the general multi-task feature selection problem using the l_(1,q) norm. Based on this probabilistic interpretation, we develop a probabilistic model using the noninfor-mative Jeffreys prior. We also extend the model to learn and exploit more general types of pairwise relationships between tasks. For both versions of the model, we devise expectation-maximization (EM) algorithms to learn all model parameters, including q, automatically. Experiments have been conducted on two cancer classification applications using microarray gene expression data.
In recent years,much attention has been given to the increase in the Earth-Sun distance,with the modern rate reported as 5-15 m/cy on the basis of astronomical ***,traditional methods cannot measure the ancient leavin...
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In recent years,much attention has been given to the increase in the Earth-Sun distance,with the modern rate reported as 5-15 m/cy on the basis of astronomical ***,traditional methods cannot measure the ancient leaving rates,so a myriad of research attempting to provide explanations were met with unmatched *** this paper we consider that the growth patterns on fossils could reflect the ancient Earth-Sun *** mechanical analysis of both the Earth-Sun and Earth-Moon systems,these patterns confirmed an increase in the Earth-Sun *** a large number of well-preserved specimens and new technology available,both the modern and ancient leaving rates could be measured with high precision,and it was found that the Earth has been leaving the Sun over the past 0.53 billion *** Earth's semi-major axis was 146 million kilometers at the beginning of the Phanerozoic Eon,equating to 97.6% of its current *** modern leaving rates are 5-14 m/cy,whereas the ancient rates were much *** results indicate a special expansion with an average expansion coefficient of 0.57H0 and deceleration in the form of Hubble *** the basis of experimental results,the Earth's semi-major axis could be represented by a simple formula that matches fossil measurements.
This paper presents a comparison among different strategies to coordinate the use of heterogeneous wireless sensors aimed for area surveillance. The heterogeneity among the sensor nodes is related to their sensing and...
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K562 mammalian cells are sorted using a highly integrated microfabricated fluorescence-activated cell sorter (∝FACS). The sample cells are purified with an enrichment factor of 230 at a high throughput (> 1,000 ce...
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This paper describes a fully autonomous mobile urban robot-X1, which can perform multiple tasks autonomously in an unknown urban environment without human guidance, including mobile reconnaissance, target searching, a...
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