Safe screening rules improve variable selection speed in high-dimensional regression.
problem Efficiently selecting important variables in high-dimensional regression problems.
method Developing Gap Safe screening rules for generalized linear models with sparsity enforcing penalties.
result Significant speed-ups in variable selection compared to previous methods on various learning tasks.
Identification of regions of interest (ROI) associated with certain disease has a great impact on public health. Imposing sparsity of pixel values and extracting active regions simultaneously greatly complicate the image analysis. We address these challenges by introducing a novel region-selection penalty in the framew…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an l0-norm penalty. Exactly enforcing the l0-no…
When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selec…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider ℓ1 penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dim…
The paper explores MMPR to select diverse models for scientific insight.
problem Model selection often fails to bring multiple underlying patterns to light.
method Multi-model penalized regression (MMPR) to acknowledge model uncertainty.
result Different penalty settings can promote either shrinkage or sparsity of coefficients in separate models.
Two sparsity-aware NSAF algorithms improve sparse system identification with lower complexity.
problem Sparse system identification with improved performance and lower complexity.
method Gradient descent method to minimize combined cost function and l1-norm penalty on filter coefficients.
result Proposed algorithms achieve comparable performance with lower computational complexity.
HALO learns to prune neural networks by adaptively shrinking weights.
problem Sparsity and model size in deep neural networks.
method Bayesian hierarchical models and trainable parameters for adaptive sparsification.
result HALO learns to create highly sparse networks with significant performance gains.
Lap-VARD algorithm improves signal reconstruction in tomography.
problem Signal reconstruction in tomography with sparsity constraint.
method Laplacian prior and automatic relevance determination framework.
result Optimized Laplacian prior enhances balance between sparsity and accuracy.
New sparse penalty improves biclustering for gene expression data.
problem Identifying significant clusters in gene expression data.
method Prenet penalty applied to SSVD for biclustering.
result Mixed Prenet penalty effectively clusters non-overlapped data.
New model captures time series dependence across and within blocks.
problem Complex multivariate time series dependence structures.
method Time series Gaussian chain graph models with directed and undirected edges.
result Consistent recovery of time series chain graph structure.
New method reduces bias in sparse Bayesian learning.
problem High sparsity in statistical models leads to significant bias.
method Variable-coefficient ℓ1 penalty with hyperpriors. result Reduces bias in sparse Bayesian learning.
Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, the best estimator performance is not always achieved with this penalty. The …
Trimmed Lasso offers sparse modeling with robustness control.
problem Sparse modeling in linear regression with robustness.
method Trimmed Lasso penalty function and its analysis.
result Trimmed Lasso offers exact sparsity control and robustness.
This study evaluates Lx-norm penalties for resolving complex LC-MS data.
problem Resolving complex LC-MS data with rotational ambiguity.
method Simulated LC-MS data and grid search strategy to compare L0-, L1-, and L2-norm penalties.
result L1-norm penalty (Lasso) provides more sparse solutions and reduces rotational ambiguity.
A new K-means method HT K-means uses ℓ0 penalty for sparsity.
problem Cluster center regularization for improved clustering performance.
method HT K-means with ℓ0 penalty for sparsity. result HT K-means outperforms other regularized K-means methods in simulations and real data. We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vec…
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…
VCAE improves autoencoder quality on MNIST and CelebA.
problem Overfitting and poor generative/reconstruction quality in autoencoders.
method Proposes variance-constrained autoencoder (VCAE) to enforce variance constraint on latent distribution.
result VCAE outperforms Wasserstein Autoencoder and Variational Autoencoder in quality.
A new method reduces bias in adaptive Lasso estimates.
problem Bias in adaptive Lasso estimates.
method Proximal gradient approach to learn penalty coefficients as decision variables.
result Reduces bias in estimates and encourages arbitrary sparsity structure.
In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a χ2-distance function and …
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our experiments demonstrate that this strategy, implemented on the elastic-net, is computatio…
DeepHoyer introduces differentiable, scale-invariant sparsity measures for neural networks.
problem Efficiently sparsifying neural networks with scale-invariant sparsity measures.
method Developed DeepHoyer, a set of differentiable, scale-invariant sparsity-inducing regularizers based on the Hoyer measure.
result DeepHoyer produces sparser neural networks than previous methods, maintaining similar accuracy.
New adaptive learning rate improves FTRL's adaptivity to sparsity, game-dependency, and best-of-both-worlds.
problem Improving adaptivity in sequential decision-making problems.
method Developed a stability-penalty-adaptive (SPA) learning rate for FTRL.
result First BOBW algorithm with sparsity-dependent bound.
AGS-CL selectively updates penalties based on node importance for continual learning.
problem Catastrophic forgetting in continual learning.
method Adaptive Group Sparsity (AGS) with proximal gradient descent.
result Significantly outperforms baselines on various continual learning benchmarks.
Paper proposes a nonconvex approach for sparse reduced rank regression.
problem Sparse reduced rank regression model estimation problem.
method Formulated as a nonconvex optimization problem with alternating minimization method.
result Nonconvex function leads to better estimation accuracy and efficiency.
Safe screening improves generalized CGM's feature selection stability.
problem Improving feature selection stability in generalized CGM.
method Coupling safe screening with generalized CGM.
result Safe screening matches solution support at rate O(1/(tδ2)). Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast…
Gradient descent can optimize penalty parameters for non-smooth penalties.
problem Optimizing penalty parameters for non-smooth penalties in regression problems.
method Modified gradient descent algorithm for non-smooth penalty functions.
result Decreased generalization error with tuned penalty parameters.
New method enforces encoder sparsity in HPF for more interpretable feature selection.
problem Lack of encoder sparsity in HPF leads to lack of column-clustering property.
method Enforces encoder sparsity using a generalized additive model (GAM).
result Gains ability to perform feature selection and relates each representation to original features.
A new filter design improves system identification accuracy.
problem Improving system identification accuracy for various system types.
method Generalized proportionate-type normalized subband adaptive filter (GPtNSAF) using least squares on subband errors with a sparsity penalty.
result GPtNSAF benefits from increasing subbands more than sparsity for quasi-sparse or dispersive systems, and both aspects are complementary for sparse systems.
Proposes sparse QSVM for better generalization and interpretability.
problem Overfitting and difficulty in interpreting full quadratic classifiers.
method Enforces ℓ0-norm constraint to promote sparsity and develops a penalty decomposition algorithm. result The proposed model enhances generalization and produces sparse solutions.
Two new regularization methods improve neural network performance and complexity control.
problem Improving neural network performance and complexity control with correlated or high-dimensional features.
method Two regularization strategies: covariance-aware ridge and covariance-aware lasso.
result Improves predictive performance and complexity control over standard penalties.
Adaptive l1-regularization controls short-selling in portfolio selection.
problem Financial markets' restrictions on short-selling and sparsity in portfolio solutions.
method Updating rule for l1-penalty parameter in Bregman iteration.
result Approach preserves properties of original l1-regularization and controls both sparsity and short positions.
We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a…
Novel optimization method detects change points in Gaussian data.
problem Detecting change points in univariate Gaussian data sequences.
method Continuous optimization for best subset selection (COMBSS) applied to a reformulated statistical inverse problem.
result Adaptation and evaluation of COMBSS for offline normal mean multiple change-point detection.
A new multi-task learning estimator improves Gaussian graphical regression model fitting.
problem High error rate in fitting Gaussian graphical regression models due to separate node-wise lasso regressions.
method Proposes a multi-task learning estimator with cross-task group sparsity and within-task element-wise sparsity penalties, solved via an efficient augmented Lagrangian algorithm.
result Error rate improvement over separate node-wise lasso estimates, demonstrated through simulations and application to gene co-expression network study.
New Bayesian method for joint sparse parameter inference.
problem Inference of jointly sparse parameter vectors from multiple measurements.
method Hierarchical Bayesian learning with joint sparsity-promoting priors.
result New algorithms consistently outperform existing methods in numerical experiments.
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, fo…
Estimates change-points and graph structures in a time-varying Ising model.
problem Detecting and understanding changes in a time-varying Ising model.
method Maximizing a penalized conditional log-likelihood to estimate neighborhood of each node, enforcing sparsity and piece-wise constant graph structures.
result First change-points consistency theorems for unknown number of change-points in time-varying Ising model.
This work shows how penalising bias terms in norm regularisation leads to sparse solutions.
problem Understanding the relation between parameter norm regularization and the sparsity of neural network solutions.
method Analyzes one hidden ReLU layer networks with unidimensional data, showing the norm required for function representation and the importance of the bias term's norm.
result Penalising the bias terms in regularisation leads to sparse solutions, enforcing the uniqueness and sparsity of the minimal norm interpolator.
Proposes ARSK for robust and sparse clustering.
problem Outliers and high-dimensional noisy variables in K-means clustering.
method Introduces redundant error component and group sparse penalty for robustness, and weights and sparsity control penalty for noisy variables.
result Superior performance in identifying clusters without outliers and informative variables.
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose y=Az+η where A satisfies the restricted isometry property (RIP) with a sufficiently small constant, and ∥η∥2≤ε. Then minimizing ∥z∥1 subject to $\Vert y - Az \Ver…
New method simplifies classifier structure via topological complexity.
problem Global regularization in classifiers is structure agnostic.
method Topological regularization using persistent homology.
result Demonstrated effectiveness on various datasets.
Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical optimization of such penalties involves solving problems with l1-norms in the ob…