4,032 research outputs found
Near Oracle Performance and Block Analysis of Signal Space Greedy Methods
Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block variant of the method for signals whose support obey a block structure, extending the method into the model-based compressed sensing framework. Numerical experiments confirm that the block method significantly outperforms the standard method in these settings
Oracle-order Recovery Performance of Greedy Pursuits with Replacement against General Perturbations
Applying the theory of compressive sensing in practice always takes different
kinds of perturbations into consideration. In this paper, the recovery
performance of greedy pursuits with replacement for sparse recovery is analyzed
when both the measurement vector and the sensing matrix are contaminated with
additive perturbations. Specifically, greedy pursuits with replacement include
three algorithms, compressive sampling matching pursuit (CoSaMP), subspace
pursuit (SP), and iterative hard thresholding (IHT), where the support
estimation is evaluated and updated in each iteration. Based on restricted
isometry property, a unified form of the error bounds of these recovery
algorithms is derived under general perturbations for compressible signals. The
results reveal that the recovery performance is stable against both
perturbations. In addition, these bounds are compared with that of oracle
recovery--- least squares solution with the locations of some largest entries
in magnitude known a priori. The comparison shows that the error bounds of
these algorithms only differ in coefficients from the lower bound of oracle
recovery for some certain signal and perturbations, as reveals that
oracle-order recovery performance of greedy pursuits with replacement is
guaranteed. Numerical simulations are performed to verify the conclusions.Comment: 27 pages, 4 figures, 5 table
Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation
Estimating the parameter of a Bernoulli process arises in many applications,
including photon-efficient active imaging where each illumination period is
regarded as a single Bernoulli trial. Motivated by acquisition efficiency when
multiple Bernoulli processes are of interest, we formulate the allocation of
trials under a constraint on the mean as an optimal resource allocation
problem. An oracle-aided trial allocation demonstrates that there can be a
significant advantage from varying the allocation for different processes and
inspires a simple trial allocation gain quantity. Motivated by realizing this
gain without an oracle, we present a trellis-based framework for representing
and optimizing stopping rules. Considering the convenient case of Beta priors,
three implementable stopping rules with similar performances are explored, and
the simplest of these is shown to asymptotically achieve the oracle-aided trial
allocation. These approaches are further extended to estimating functions of a
Bernoulli parameter. In simulations inspired by realistic active imaging
scenarios, we demonstrate significant mean-squared error improvements: up to
4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.Comment: 13 pages, 16 figure
Beyond binomial and negative binomial: adaptation in Bernoulli parameter estimation
Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of p and up to 1.86 dB for the estimation of log p.https://arxiv.org/abs/1809.08801https://arxiv.org/abs/1809.08801First author draf
Deep Metric Learning via Facility Location
Learning the representation and the similarity metric in an end-to-end
fashion with deep networks have demonstrated outstanding results for clustering
and retrieval. However, these recent approaches still suffer from the
performance degradation stemming from the local metric training procedure which
is unaware of the global structure of the embedding space.
We propose a global metric learning scheme for optimizing the deep metric
embedding with the learnable clustering function and the clustering metric
(NMI) in a novel structured prediction framework.
Our experiments on CUB200-2011, Cars196, and Stanford online products
datasets show state of the art performance both on the clustering and retrieval
tasks measured in the NMI and Recall@K evaluation metrics.Comment: Submission accepted at CVPR 201
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