Paper proposes a new sparse group k-max regularization for sparsity constraints.
problem Linear inverse problems with sparsity constraints are NP-hard.
method Sparse group k-max regularization, iterative soft thresholding algorithm.
result Approximates l0 norm more closely and enhances group-wise and in-group sparsity.
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
A fast method for discrete OT with group-sparse regularization for class label preservation.
problem Efficiently measuring the distance between two discrete distributions with class labels.
method Fast discrete OT with group-sparse regularizers using gradient-based algorithms.
result Up to 8.6 times faster than original method without degrading accuracy.
New FGSPCA method captures grouping and sparse structures in PCA without prior info.
problem Capture grouping and sparse structures in PCA without prior info.
method Truncated regularization with alternating algorithm.
result FGSPCA method reduces model complexity and increases interpretability.
New theoretical framework improves error rates for sparse learning with convex regularization.
problem Improving error rates for sparse learning with convex regularization.
method Proposed a new theoretical framework using common assumptions to derive high-dimensional estimation bounds.
result Improved error rates for L1, Slope, and Group L1-L2 regularizations, matching or exceeding existing results.
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using l1/l2 regularization upon the activation possibilities of hidden unit…
OMP improves text classification accuracy with sparse models.
problem Overfitting in text classification due to high dimensionality.
method Greedy variable selection algorithm (OMP) and overlapping Group OMP.
result OMP and overlapping GOMP produce effective and very sparse models.
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a no…
Proposes an algorithm for infinite-dimensional sparse learning in system identification.
problem System identification without known model structures.
method Atomic norm regularization and greedy algorithm for solving an infinite-dimensional group lasso problem.
result The proposed algorithm outperforms benchmark methods in impulse response fitting and pole location estimation.
Sparse group matrix completion reduces complexity and improves performance.
problem Matrix completion with non-informative side features.
method Group-Lasso regularization for feature selection in matrix factorization.
result Theoretical sample complexity is significantly lower than competitors.
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We es…
The paper introduces regularized OT to create sparse transportation plans.
problem Lack of sparsity in entropic regularization of OT.
method Regularizing primal and dual OT formulations with strongly convex terms, leading to sparse transportation plans.
result Regularized OT can lead to sparser transportation plans than entropic regularization.
Gradient descent implicitly favors group sparsity in neural networks.
problem Understanding implicit regularization in neural networks for structured sparsity.
method Novel neural reparameterization for diagonally grouped linear networks.
result Gradient descent without explicit regularization biases towards group sparsity.
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is …
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the ℓ1- and ℓ2-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
Sparse regularization reduces NLP model complexity without sacrificing accuracy.
problem Excessive parameter usage in neural models for NLP leads to high memory and runtime usage.
method Apply group lasso to rational RNNs to learn sparse, parameter-efficient models.
result Sparse rational RNNs can have significantly fewer parameters than non-sparse models without losing performance.
SR3 framework improves sparse regression solutions.
problem Sparse regression problems in various fields.
method SR3 framework solves relaxed regularized regression problems.
result SR3 provides superior solutions with faster algorithms.
The paper improves machine learning for heavy-tailed panel data.
problem Improving estimates for financial and economic data with fat tails.
method Sparse-group LASSO regularization and Fuk-Nagaev concentration inequality.
result Oracle inequalities for panel data estimators.
We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…
Novel approach reduces DNN redundancy and enhances computational efficiency.
problem Redundant parameters in large-scale DNNs pose hardware deployment challenges.
method WGSEF regularization technique for structured sparsity.
result Reduces redundancy and enhances computational efficiency.
sgboost reduces variable selection bias in boosting with balanced group selection.
problem Reduces variable selection bias in boosting algorithms.
method Simulation-based approach to balance selection frequencies of base-learners.
result Demonstrates efficacy through simulations and flexible group variable selection.
Sparse mapping has been a key methodology in many high-dimensional scientific problems. When multiple tasks share the set of relevant features, learning them jointly in a group drastically improves the quality of relevant feature selection. However, in practice this technique is used limitedly since such grouping infor…
Framework for inferring latent structure from sparse, imperfectly detected bipartite networks.
problem Recovering latent structure from sparse, imperfectly detected bipartite networks in ecology.
method Structured sparse nonnegative low-rank factorization with detection probability estimation and ADMM-based algorithm.
result Improved recovery of latent factors and structure compared to existing methods.
A new estimator learns sparse linear models with context-dependent coefficients.
problem Sparse linear models lack flexibility compared to deep neural networks for handling feature groups.
method Contextual lasso estimator using a deep neural network with lasso regularization.
result Learned models can be sparser than standard lasso without sacrificing predictive power.
A new method for sparse regression models using graph structure.
problem Sparse regression models for high-dimensional data.
method Decomposes coefficient vector into latent variables, performs regularization on latent variables, uses proximal projection.
result Stable performance compared to other models, especially for high-dimensional data.
New guarantees for Group LASSO in sparse convex optimization.
problem Sparse convex optimization with vector-valued features.
method Group LASSO regularization and analysis of gradient norms.
result Group LASSO selects the same features as Orthogonal Matching Pursuit.
New estimators improve sparse semiparametric additive modeling.
problem Sparse semiparametric additive modeling with structured sparsity.
method Combines group subset selection with shrinkage for nonconvex optimization.
result New estimators outperform alternatives in synthetic and real-world data.
We apply the OSCAR (octagonal selection and clustering algorithms for regression) in recovering group-sparse matrices (two-dimensional---2D---arrays) from compressive measurements. We propose a 2D version of OSCAR (2OSCAR) consisting of the ℓ1 norm and the pair-wise ℓ∞ norm, which is convex but non-d…
Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…
SNAM improves NAM's accuracy and feature selection via group sparsity.
problem Improving interpretability and accuracy in deep learning models.
method Employing group sparsity regularization in neural additive models (SNAM).
result SNAM provably converges to zero training loss and achieves exact support recovery.
New GIC improves model selection for structured sparse models.
problem Model selection and regularization in high-dimensional scenarios.
method Proposes a new Generalized Information Criteria (GIC) for structured sparse models.
result Obtains non-asymptotic model selection bounds and sufficient conditions for model selection consistency.
We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal ℓ1,∞-penalized recursive least squares (R…
SWCCA identifies specific subsets of samples for better correlation analysis.
problem Identify specific subsets of samples contributing to correlation between two data matrices.
method Proposes SWCCA with weights to regularize different samples, solves using alternating iterative algorithm.
result Demonstrates effectiveness and superiority over related methods on synthetic and real-world data.
Sparse MDP with entropy regularization improves reinforcement learning performance.
problem Improving reinforcement learning policies with sparse and multi-modal distributions.
method Proposes a sparse Markov decision process with causal sparse Tsallis entropy regularization.
result The proposed method achieves a constant performance error bound, outperforming soft MDPs.
Paper optimizes Laplacian regularization for sparse network clustering.
problem Improving spectral clustering in sparse networks.
method Formally determines optimal Laplacian regularization.
result Proper regularization is closely tied to state-of-the-art techniques.
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated separately. In this paper, we propose an approach to entangle these two aspects …
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
A new method solves sparse regularization problems efficiently and robustly.
problem Sparse regularization in machine learning problems.
method Iteratively reweighted least square (IRLS) with bilevel resolution and BFGS solver.
result Achieves top performances on various sparsity and regularization problems.
SRF learns sparse rule models by screening out features efficiently.
problem Learning optimal sparse rule models is computationally intractable due to the large number of possible rules.
method SRF uses meta safe screening (mSS) to efficiently screen out multiple features, improving the learning of sparse rule models.
result SRF provides a general framework for fitting sparse rule models and can handle group regularization.
New method detects nonlinear causality in multivariate time series data.
problem Detecting nonlinear causal relationships in multidimensional time series.
method Sparse additive models (SpAMs) with B-spline bases and group-lasso optimization.
result The method can accurately estimate nonlinear causal relationships in β-mixing time series.
Proposes novel wSVMs for sparse learning and accurate probability estimation.
problem Sparse features with redundant noise limit the performance of existing wSVMs.
method Develops ℓ1-norm and elastic net regularized wSVMs for automatic variable selection and probability estimation. result Elastic net regularized wSVMs achieve superior performance in variable selection and probability estimation.
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data is drawn identically from a generating distribution. Introducing sparsity a…
New method finds sparse groups of input variables for neural networks.
problem Finding optimal groups of input variables for neural networks.
method Developed a new loss function and optimization algorithm for multi-layer non-linear neural networks to achieve group sparsity.
result Achieved group sparsity in three real-world datasets, improving model performance and excluding a significant number of variables.
Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…
Proposes a neural network framework for feature selection in high-dimensional settings.
problem Challenges in feature selection and non-linear function estimation in high-dimensional settings.
method Sparse-input neural networks using group concave regularization.
result Establishes finite-sample guarantees for variable selection consistency and prediction accuracy.
MoreauGrad interprets neural nets robustly and sparsely.
problem Lack of robustness and sparsity in gradient-based interpretation methods.
method Moreau envelope for smooth and robust interpretation, combined with L1 regularization for sparsity.
result MoreauGrad provides a smooth, robust, and sparse explanation of neural nets.
We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between maximizing the variance explained by the components and promoting sparsity of the loading…