This paper optimizes exclusive sparsity norm minimization with random groupings.
problem Sparse feature selection with even distribution across groups.
method Developed efficient algorithms for exclusive sparsity norm minimization with smooth and non-smooth losses, and proposed random grouping scheme for unknown group information.
result Achieved optimal convergence rate for exclusive sparsity norm minimization.
New method selects variables in groups with few nonzeros, improving support recovery.
problem Structured variable selection with sparse patterns across groups.
method Composite norm and proximal algorithm for exclusive group sparsity.
result Asymptotic consistency in signed support recovery under conventional assumptions.
Localized Lasso improves interpretable models for high-dimensional data.
problem High-dimensional regression with small sample size and interpretability.
method Sample-wise network regularization and exclusive group sparsity.
result Localized Lasso outperforms alternatives in simulated and genomic data.
Exclusive Group Lasso improves feature selection in correlated biological data.
problem Correlated features hinder Lasso performance in biological classification problems.
method Proposes and solves the exclusive group Lasso, combining stability selection and random group allocation.
result Exclusive Group Lasso outperforms Lasso in comprehensive selection of informative features.
Exclusive Lasso improves survival prediction in cancer datasets.
problem Enhanced survival prediction in cancer datasets with high-dimensional genomic and clinical data.
method Proposes Exclusive Lasso regularization for feature selection in Cox regression models for grouped variables.
result Demonstrates improved survival prediction performance using Exclusive Lasso compared to standard Cox regression.
A new travel time tomography method uses adaptive dictionaries to model slowness variations.
problem Modeling and reconstructing slowness maps with varying scales and discontinuities.
method Local model (sparse patches) and global model (smooth constraints) integrated into a maximum a posteriori formulation.
result The LST approach effectively models both smooth and discontinuous slowness features.
New study shows fairness measures are mutually exclusive when groups differ.
problem Fairness measures conflict when group prevalence differs.
method Examined various fairness measures and their incompatibility.
result No predictor can be fair under two out of three criteria.
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 algorithm learns PTFs with noisy data efficiently.
problem Learning low-degree PTFs with noisy data efficiently.
method Structural result and novel robust Chow vector estimation.
result PAC learns PTFs with nasty noise using efficient samples.
New interactive greedy algorithm for group sparsity in high dimensions.
problem Benefits of group sparsity for greedy-type methods in high-dimensional data analysis.
method Interactive Greedy Approach
result Proposed algorithm attains desired benefits of group sparsity under high dimensional settings.
Exclusive row biclustering for gene expression data.
problem Identifying groups of cancer patients with unique types of cancer.
method Combination of biclustering algorithms and combinatorial auction techniques.
result Identification of large span non-overlapping row submatrices.
Paper proposes a method to recover task groups and sparsity patterns in sparse learning.
problem Learning task structure when multiple tasks share relevant features.
method Formulates a joint optimization problem to recover task groups and sparsity patterns, encouraging sparse learning and correct recovery of task groups.
result Proposed method accurately recovers task groups and sparsity patterns in task parameters.
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.
The girth of a finitely generated group G is the supremum of the girth of Cayley graphs for G over all finite generating sets. Let G be a finitely generated subgroup of the mapping class group Mod(S), where S is a compact orientable surface. Then, either G is virtually abelian or it has infinite girth; moreover, if we …
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.
Paper analyzes and improves GPSP algorithm for block sparse signal recovery.
problem Recovering block sparse signals from noisy data.
method Group Projected Subspace Pursuit (GPSP) with convergence analysis and feature selection criteria.
result GPSP exactly recovers true block sparse signals under certain conditions.
Proposes a boosting framework for sparsity in grouped covariates.
problem Sparsity and selection bias in grouped covariates.
method Component-wise and group-wise gradient boosting with adjusted degrees of freedom.
result Reduces bias and improves predictability in variable selection.
Research quantifies financial exclusion risks in UK, focusing on cash infrastructure and socio-economic factors.
problem Localised financial exclusion in the UK as cash infrastructure declines.
method Developed a composite indicator using various input variables.
result Financial exclusion is more prevalent in deprived communities and affluent areas.
New methods generalize nonlinear ICA beyond structural sparsity.
problem Identify true latent sources from nonlinear mixtures without structural sparsity assumptions.
method Propose identifiability results for undercomplete, partial sparsity, and flexible grouping structures.
result Prove identifiability in general settings of undercompleteness, partial sparsity, and flexible grouping structures.
The paper shows how particle movement on a manifold's grid approximates Brownian motion and heat diffusion.
problem Understanding particle movement on curved spaces.
method Analyzing symmetric exclusion process on random grids approximating a Riemannian manifold.
result Empirical density field converges to heat equation solution on the manifold.
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 …
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable" signals through the identification of their constituent groups. In this paper, we e…
Unified framework for generalized sparsity and RIP analysis.
problem Analyzing inverse problems with sparsity models.
method Proposed generalized notions of sparsity and a unified RIP framework.
result Extends RIP analysis to broader contexts including tensor products.
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either study the group sparsity in the parametric setting (e.g., group lasso), or addre…
Automated PDE discovery from multiple noisy experiments.
problem Inherent variability in experiments makes single experiment inference unreliable.
method Randomised adaptive group Lasso sparsity estimator in deep learning framework.
result More generalizable PDEs found from multiple datasets.
Introduces joint exclusivity (JE), a new form of negative dependence.
problem Negative dependence structures in probability distributions.
method Defines JE by exclusion of the interior of the non-negative orthant, establishes necessary and sufficient conditions for existence, proposes a canonical construction.
result Sharp necessary and sufficient condition for existence of JE random vectors with prescribed marginals.
Random groups prove length constraints on product of conjugates.
problem Quantify products of conjugates in random groups.
method Sharp van Kampen diagram argument and boundary block-counting.
result Prove a sharp inequality for products of conjugates in random groups.
Paper improves group sparse recovery bounds using ℓ1-norm minimization.
problem Recovering group sparse vectors from few measurements.
method Introduces GRNSP and GRIP, and uses convex relaxations.
result New bounds for group sparse recovery, including equal and unequal group sizes.
Improves data recovery with optimized measurements and generalized sparsity models.
problem Data recovery with optimized measurements and generalized sparsity models.
method Optimizing over families of Banach spaces, investigating preservation of difference of sparse vectors, extending RIP to group structured measurements, and extending Fourier measurement concepts to infinite dimensions.
result Optimal scaling of number of measurements for group structured measurements and improved RIP in infinite dimensions.
New algorithm reduces hyperparameter search space using group sparsity.
problem Efficient hyperparameter selection in machine learning.
method Modifies Harmonica algorithm with group-sparse recovery and HyperBand.
result Improves over existing methods like Successive Halving and Random Search.
Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets…
En nous basant sur les résultats d'Arthur annoncés dans \cite[§30]{Arthur} nous démontrons les conjectures énoncées dans \cite{IMRN,BC,SMF} dans le cas des groupes orthogonaux à l'exclusion des groupes de type 6−D4. En ce qui concerne ces derniers, nous annonçons la démonstration -- encore en préparation - que …
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a …
Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.
problem Exploring SO(3)-irreducible geometry in complex 5D.
method Defined a ternary skew-symmetric tensor, split the 10D space into irreducible SO(3) subspaces, found invariants and defined geometric structures.
result Defined a SO(3)-irreducible geometric structure on a 5D complex Hermitian manifold.
We develop a highly scalable optimization method called "hierarchical group-thresholding" for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence of several efficient optimization algorithms for tackling complex sparsity-induci…
New screening rules speed up Sparse-Group Lasso solving.
problem Efficiently solving Sparse-Group Lasso in high dimensions.
method Adapted safe screening rules for Sparse-Group Lasso.
result Significant speed-ups in computing time for coordinate descent.
Extends conformal prediction to contrastive learning for better coverage of positive samples.
problem Lack of principled guarantees on coverage in contrastive learning.
method Introduces minimum-volume covering sets with learnable constraints.
result Improves inclusion-exclusion trade-offs in positive and negative samples.
Improves unsupervised feature learning with an exclusivity concept.
problem Overfitting in AE-based unsupervised feature learning.
method Integrates exclusivity concept to enhance AE's latent feature representation.
result Significant improvement in performance compared to other methods.
Model predicts firms likely to be added to investment exclusion lists.
problem Identifying firms likely to be added to investment exclusion lists.
method Constructed a heterogeneous information network from curated and open datasets.
result Predictive accuracy improved substantially using the network.
MUSIC learns coupled systems with sparse data and incomplete physics.
problem Learning coupled systems with incomplete physical constraints and missing data.
method Sparsity induced multitask neural network framework integrating partial physical constraints with data-driven learning.
result MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions.
The paper studies super metrics and their local isometry groups.
problem Understanding the structure of super metrics and their isometry groups.
method Deriving canonical forms, computing covering groups, and applying Rogers' Theorem.
result For certain super metrics, the simply connected covering groups are super Lie groups with conventional super Lie algebras.
Proposes mutual exclusivity loss for semi-supervised deep learning.
problem Improving object recognition with unlabeled data.
method Introduces an unsupervised regularization term to force mutually-exclusive predictions.
result Improves ConvNet object recognition performance using unlabeled data.
Optimal PCA formulation for sparse loadings.
problem Sparse loadings in PCA with optimal variance.
method New variance definition, group-ℓ1 regularization, analytical solution. result GSMV formulation produces better and more robust results.
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.
New method sets explicit sparsity for groups of vectors in deep learning and NMF.
problem Tackles the challenge of achieving a desired average sparsity level in vector groups.
method Designs a new sparse projection method that sets the sparsity level for the whole set explicitly and automatically tunes the sparsity of each vector.
result Shows significant improvements in accuracy and reconstruction errors compared to existing methods in deep learning and NMF.
A new method for differentiable structured sparsity improves neural network performance and sparsity.
problem Non-differentiability of structured sparsity penalties in neural networks.
method Introducing D-Gating, a differentiable approach to structured overparameterization. result The D-Gating objective converges to the L2,2/D-regularized loss and induces sparse learning dynamics. Dagma-DCE improves causal discovery with interpretable measures and open-source code.
problem Arbitrary proxy measures of causal strength in non-parametric causal discovery.
method Uses weighted adjacency matrices based on an interpretable measure of causal strength.
result Achieves state-of-the-art performance in simulated datasets.
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the indivi…