907 research outputs found
Sparse kernel SVMs via cutting-plane training
Appeal from a decision of the Board of Review, Industrial Commission of Utah on February 7, 1989
Efficient Multi-Template Learning for Structured Prediction
Conditional random field (CRF) and Structural Support Vector Machine
(Structural SVM) are two state-of-the-art methods for structured prediction
which captures the interdependencies among output variables. The success of
these methods is attributed to the fact that their discriminative models are
able to account for overlapping features on the whole input observations. These
features are usually generated by applying a given set of templates on labeled
data, but improper templates may lead to degraded performance. To alleviate
this issue, in this paper, we propose a novel multiple template learning
paradigm to learn structured prediction and the importance of each template
simultaneously, so that hundreds of arbitrary templates could be added into the
learning model without caution. This paradigm can be formulated as a special
multiple kernel learning problem with exponential number of constraints. Then
we introduce an efficient cutting plane algorithm to solve this problem in the
primal, and its convergence is presented. We also evaluate the proposed
learning paradigm on two widely-studied structured prediction tasks,
\emph{i.e.} sequence labeling and dependency parsing. Extensive experimental
results show that the proposed method outperforms CRFs and Structural SVMs due
to exploiting the importance of each template. Our complexity analysis and
empirical results also show that our proposed method is more efficient than
OnlineMKL on very sparse and high-dimensional data. We further extend this
paradigm for structured prediction using generalized -block norm
regularization with , and experiments show competitive performances when
A Feature Selection Method for Multivariate Performance Measures
Feature selection with specific multivariate performance measures is the key
to the success of many applications, such as image retrieval and text
classification. The existing feature selection methods are usually designed for
classification error. In this paper, we propose a generalized sparse
regularizer. Based on the proposed regularizer, we present a unified feature
selection framework for general loss functions. In particular, we study the
novel feature selection paradigm by optimizing multivariate performance
measures. The resultant formulation is a challenging problem for
high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed
to solve this problem, and the convergence is presented. In addition, we adapt
the proposed method to optimize multivariate measures for multiple instance
learning problems. The analyses by comparing with the state-of-the-art feature
selection methods show that the proposed method is superior to others.
Extensive experiments on large-scale and high-dimensional real world datasets
show that the proposed method outperforms -SVM and SVM-RFE when choosing a
small subset of features, and achieves significantly improved performances over
SVM in terms of -score
Block-Coordinate Frank-Wolfe Optimization for Structural SVMs
We propose a randomized block-coordinate variant of the classic Frank-Wolfe
algorithm for convex optimization with block-separable constraints. Despite its
lower iteration cost, we show that it achieves a similar convergence rate in
duality gap as the full Frank-Wolfe algorithm. We also show that, when applied
to the dual structural support vector machine (SVM) objective, this yields an
online algorithm that has the same low iteration complexity as primal
stochastic subgradient methods. However, unlike stochastic subgradient methods,
the block-coordinate Frank-Wolfe algorithm allows us to compute the optimal
step-size and yields a computable duality gap guarantee. Our experiments
indicate that this simple algorithm outperforms competing structural SVM
solvers.Comment: Appears in Proceedings of the 30th International Conference on
Machine Learning (ICML 2013). 9 pages main text + 22 pages appendix. Changes
from v3 to v4: 1) Re-organized appendix; improved & clarified duality gap
proofs; re-drew all plots; 2) Changed convention for Cf definition; 3) Added
weighted averaging experiments + convergence results; 4) Clarified main text
and relationship with appendi
Structured Learning of Tree Potentials in CRF for Image Segmentation
We propose a new approach to image segmentation, which exploits the
advantages of both conditional random fields (CRFs) and decision trees. In the
literature, the potential functions of CRFs are mostly defined as a linear
combination of some pre-defined parametric models, and then methods like
structured support vector machines (SSVMs) are applied to learn those linear
coefficients. We instead formulate the unary and pairwise potentials as
nonparametric forests---ensembles of decision trees, and learn the ensemble
parameters and the trees in a unified optimization problem within the
large-margin framework. In this fashion, we easily achieve nonlinear learning
of potential functions on both unary and pairwise terms in CRFs. Moreover, we
learn class-wise decision trees for each object that appears in the image. Due
to the rich structure and flexibility of decision trees, our approach is
powerful in modelling complex data likelihoods and label relationships. The
resulting optimization problem is very challenging because it can have
exponentially many variables and constraints. We show that this challenging
optimization can be efficiently solved by combining a modified column
generation and cutting-planes techniques. Experimental results on both binary
(Graz-02, Weizmann horse, Oxford flower) and multi-class (MSRC-21, PASCAL VOC
2012) segmentation datasets demonstrate the power of the learned nonlinear
nonparametric potentials.Comment: 10 pages. Appearing in IEEE Transactions on Neural Networks and
Learning System
Training linear ranking SVMs in linearithmic time using red-black trees
We introduce an efficient method for training the linear ranking support
vector machine. The method combines cutting plane optimization with red-black
tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time
complexity, where m is the number of training examples, and s the average
number of non-zero features per example. Best previously known training
algorithms achieve the same efficiency only for restricted special cases,
whereas the proposed approach allows any real valued utility scores in the
training data. Experiments demonstrate the superior scalability of the proposed
approach, when compared to the fastest existing RankSVM implementations.Comment: 20 pages, 4 figure
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