4,455 research outputs found
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
Improving compressed sensing with the diamond norm
In low-rank matrix recovery, one aims to reconstruct a low-rank matrix from a
minimal number of linear measurements. Within the paradigm of compressed
sensing, this is made computationally efficient by minimizing the nuclear norm
as a convex surrogate for rank.
In this work, we identify an improved regularizer based on the so-called
diamond norm, a concept imported from quantum information theory. We show that
-for a class of matrices saturating a certain norm inequality- the descent cone
of the diamond norm is contained in that of the nuclear norm. This suggests
superior reconstruction properties for these matrices. We explicitly
characterize this set of matrices. Moreover, we demonstrate numerically that
the diamond norm indeed outperforms the nuclear norm in a number of relevant
applications: These include signal analysis tasks such as blind matrix
deconvolution or the retrieval of certain unitary basis changes, as well as the
quantum information problem of process tomography with random measurements.
The diamond norm is defined for matrices that can be interpreted as order-4
tensors and it turns out that the above condition depends crucially on that
tensorial structure. In this sense, this work touches on an aspect of the
notoriously difficult tensor completion problem.Comment: 25 pages + Appendix, 7 Figures, published versio
Knowledge Base Population using Semantic Label Propagation
A crucial aspect of a knowledge base population system that extracts new
facts from text corpora, is the generation of training data for its relation
extractors. In this paper, we present a method that maximizes the effectiveness
of newly trained relation extractors at a minimal annotation cost. Manual
labeling can be significantly reduced by Distant Supervision, which is a method
to construct training data automatically by aligning a large text corpus with
an existing knowledge base of known facts. For example, all sentences
mentioning both 'Barack Obama' and 'US' may serve as positive training
instances for the relation born_in(subject,object). However, distant
supervision typically results in a highly noisy training set: many training
sentences do not really express the intended relation. We propose to combine
distant supervision with minimal manual supervision in a technique called
feature labeling, to eliminate noise from the large and noisy initial training
set, resulting in a significant increase of precision. We further improve on
this approach by introducing the Semantic Label Propagation method, which uses
the similarity between low-dimensional representations of candidate training
instances, to extend the training set in order to increase recall while
maintaining high precision. Our proposed strategy for generating training data
is studied and evaluated on an established test collection designed for
knowledge base population tasks. The experimental results show that the
Semantic Label Propagation strategy leads to substantial performance gains when
compared to existing approaches, while requiring an almost negligible manual
annotation effort.Comment: Submitted to Knowledge Based Systems, special issue on Knowledge
Bases for Natural Language Processin
BlockDrop: Dynamic Inference Paths in Residual Networks
Very deep convolutional neural networks offer excellent recognition results,
yet their computational expense limits their impact for many real-world
applications. We introduce BlockDrop, an approach that learns to dynamically
choose which layers of a deep network to execute during inference so as to best
reduce total computation without degrading prediction accuracy. Exploiting the
robustness of Residual Networks (ResNets) to layer dropping, our framework
selects on-the-fly which residual blocks to evaluate for a given novel image.
In particular, given a pretrained ResNet, we train a policy network in an
associative reinforcement learning setting for the dual reward of utilizing a
minimal number of blocks while preserving recognition accuracy. We conduct
extensive experiments on CIFAR and ImageNet. The results provide strong
quantitative and qualitative evidence that these learned policies not only
accelerate inference but also encode meaningful visual information. Built upon
a ResNet-101 model, our method achieves a speedup of 20\% on average, going as
high as 36\% for some images, while maintaining the same 76.4\% top-1 accuracy
on ImageNet.Comment: CVPR 201
Cooperative Active Learning based Dual Control for Exploration and Exploitation in Autonomous Search
In this paper, a multi-estimator based computationally efficient algorithm is developed for autonomous search in an unknown environment with an unknown source. Different from the existing approaches that require massive computational power to support nonlinear Bayesian estimation and complex decision-making process, an efficient cooperative active learning based dual control for exploration and exploitation (COAL-DCEE) is developed for source estimation and path planning. Multiple cooperative estimators are deployed for environment learning process, which is helpful to improving the search performance and robustness against noisy measurements. The number of estimators used in COAL-DCEE is much smaller than that of particles required for Bayesian estimation in information-theoretic approaches. Consequently, the computational load is significantly reduced. As an important feature of this study, the convergence and performance of COAL-DCEE are established in relation to the characteristics of sensor noises and turbulence disturbances. Numerical and experimental studies have been carried out to verify the effectiveness of the proposed framework. Compared with existing approaches, COAL-DCEE not only provides convergence guarantee, but also yields comparable search performance using much less computational power
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