865 research outputs found
Task-Driven Dictionary Learning
Modeling data with linear combinations of a few elements from a learned
dictionary has been the focus of much recent research in machine learning,
neuroscience and signal processing. For signals such as natural images that
admit such sparse representations, it is now well established that these models
are well suited to restoration tasks. In this context, learning the dictionary
amounts to solving a large-scale matrix factorization problem, which can be
done efficiently with classical optimization tools. The same approach has also
been used for learning features from data for other purposes, e.g., image
classification, but tuning the dictionary in a supervised way for these tasks
has proven to be more difficult. In this paper, we present a general
formulation for supervised dictionary learning adapted to a wide variety of
tasks, and present an efficient algorithm for solving the corresponding
optimization problem. Experiments on handwritten digit classification, digital
art identification, nonlinear inverse image problems, and compressed sensing
demonstrate that our approach is effective in large-scale settings, and is well
suited to supervised and semi-supervised classification, as well as regression
tasks for data that admit sparse representations.Comment: final draft post-refereein
Cross-Lingual Adaptation using Structural Correspondence Learning
Cross-lingual adaptation, a special case of domain adaptation, refers to the
transfer of classification knowledge between two languages. In this article we
describe an extension of Structural Correspondence Learning (SCL), a recently
proposed algorithm for domain adaptation, for cross-lingual adaptation. The
proposed method uses unlabeled documents from both languages, along with a word
translation oracle, to induce cross-lingual feature correspondences. From these
correspondences a cross-lingual representation is created that enables the
transfer of classification knowledge from the source to the target language.
The main advantages of this approach over other approaches are its resource
efficiency and task specificity.
We conduct experiments in the area of cross-language topic and sentiment
classification involving English as source language and German, French, and
Japanese as target languages. The results show a significant improvement of the
proposed method over a machine translation baseline, reducing the relative
error due to cross-lingual adaptation by an average of 30% (topic
classification) and 59% (sentiment classification). We further report on
empirical analyses that reveal insights into the use of unlabeled data, the
sensitivity with respect to important hyperparameters, and the nature of the
induced cross-lingual correspondences
Elastic-Net Regularization in Learning Theory
Within the framework of statistical learning theory we analyze in detail the
so-called elastic-net regularization scheme proposed by Zou and Hastie for the
selection of groups of correlated variables. To investigate on the statistical
properties of this scheme and in particular on its consistency properties, we
set up a suitable mathematical framework. Our setting is random-design
regression where we allow the response variable to be vector-valued and we
consider prediction functions which are linear combination of elements ({\em
features}) in an infinite-dimensional dictionary. Under the assumption that the
regression function admits a sparse representation on the dictionary, we prove
that there exists a particular ``{\em elastic-net representation}'' of the
regression function such that, if the number of data increases, the elastic-net
estimator is consistent not only for prediction but also for variable/feature
selection. Our results include finite-sample bounds and an adaptive scheme to
select the regularization parameter. Moreover, using convex analysis tools, we
derive an iterative thresholding algorithm for computing the elastic-net
solution which is different from the optimization procedure originally proposed
by Zou and HastieComment: 32 pages, 3 figure
Deep Dictionary Learning: A PARametric NETwork Approach
Deep dictionary learning seeks multiple dictionaries at different image
scales to capture complementary coherent characteristics. We propose a method
for learning a hierarchy of synthesis dictionaries with an image classification
goal. The dictionaries and classification parameters are trained by a
classification objective, and the sparse features are extracted by reducing a
reconstruction loss in each layer. The reconstruction objectives in some sense
regularize the classification problem and inject source signal information in
the extracted features. The performance of the proposed hierarchical method
increases by adding more layers, which consequently makes this model easier to
tune and adapt. The proposed algorithm furthermore, shows remarkably lower
fooling rate in presence of adversarial perturbation. The validation of the
proposed approach is based on its classification performance using four
benchmark datasets and is compared to a CNN of similar size
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
On Security and Sparsity of Linear Classifiers for Adversarial Settings
Machine-learning techniques are widely used in security-related applications,
like spam and malware detection. However, in such settings, they have been
shown to be vulnerable to adversarial attacks, including the deliberate
manipulation of data at test time to evade detection. In this work, we focus on
the vulnerability of linear classifiers to evasion attacks. This can be
considered a relevant problem, as linear classifiers have been increasingly
used in embedded systems and mobile devices for their low processing time and
memory requirements. We exploit recent findings in robust optimization to
investigate the link between regularization and security of linear classifiers,
depending on the type of attack. We also analyze the relationship between the
sparsity of feature weights, which is desirable for reducing processing cost,
and the security of linear classifiers. We further propose a novel octagonal
regularizer that allows us to achieve a proper trade-off between them. Finally,
we empirically show how this regularizer can improve classifier security and
sparsity in real-world application examples including spam and malware
detection
Discriminative Elastic-Net Regularized Linear Regression
In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zeroone matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of theses methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available datasets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html
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