41,207 research outputs found
A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
Group Sparse CNNs for Question Classification with Answer Sets
Question classification is an important task with wide applications. However,
traditional techniques treat questions as general sentences, ignoring the
corresponding answer data. In order to consider answer information into
question modeling, we first introduce novel group sparse autoencoders which
refine question representation by utilizing group information in the answer
set. We then propose novel group sparse CNNs which naturally learn question
representation with respect to their answers by implanting group sparse
autoencoders into traditional CNNs. The proposed model significantly outperform
strong baselines on four datasets.Comment: 6, ACL 201
Fast projections onto mixed-norm balls with applications
Joint sparsity offers powerful structural cues for feature selection,
especially for variables that are expected to demonstrate a "grouped" behavior.
Such behavior is commonly modeled via group-lasso, multitask lasso, and related
methods where feature selection is effected via mixed-norms. Several mixed-norm
based sparse models have received substantial attention, and for some cases
efficient algorithms are also available. Surprisingly, several constrained
sparse models seem to be lacking scalable algorithms. We address this
deficiency by presenting batch and online (stochastic-gradient) optimization
methods, both of which rely on efficient projections onto mixed-norm balls. We
illustrate our methods by applying them to the multitask lasso. We conclude by
mentioning some open problems.Comment: Preprint of paper under revie
Sparse Additive Models
We present a new class of methods for high-dimensional nonparametric
regression and classification called sparse additive models (SpAM). Our methods
combine ideas from sparse linear modeling and additive nonparametric
regression. We derive an algorithm for fitting the models that is practical and
effective even when the number of covariates is larger than the sample size.
SpAM is closely related to the COSSO model of Lin and Zhang (2006), but
decouples smoothing and sparsity, enabling the use of arbitrary nonparametric
smoothers. An analysis of the theoretical properties of SpAM is given. We also
study a greedy estimator that is a nonparametric version of forward stepwise
regression. Empirical results on synthetic and real data are presented, showing
that SpAM can be effective in fitting sparse nonparametric models in high
dimensional data
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