Transformers excel at sparse token selection, surpassing FCNs in both worst and average cases.
problem Sparse token selection task
method One-layer transformer trained with gradient descent
result Transformers learn sparse token selection and exhibit strong out-of-distribution length generalization
Sparse PCA selects variables with FDR control for improved performance.
problem Sparse PCA selects irrelevant variables when maximizing explained variance.
method Proposes FDR-controlled selection using T-Rex selector.
result Significant performance improvement over traditional sparse PCA.
Sparse GEMINI selects relevant features for clustering without assumptions.
problem Feature selection in clustering with relevant clusters and variables.
method Discriminative clustering model maximizing GEMINI with l1 penalty.
result Sparse GEMINI selects relevant subsets of variables without prior hypotheses.
Efficiently selects predictors in sparse regression without approximations.
problem High computational cost in subset selection for sparse regression.
method Conditional uncorrelation formula and efficient non-approximate method.
result Significant reduction in computational complexity for subset selection.
The paper uses TDA to select stocks for a sparse portfolio, improving performance across market scenarios.
problem Sparse portfolio selection in financial markets.
method Topological data analysis (TDA) for clustering stock price movements.
result The TDA-based clustering strategy significantly enhances sparse portfolio performance.
A new knot selection method speeds up sparse Gaussian process approximations.
problem Efficiently selecting knots for sparse Gaussian processes.
method One-at-a-time Bayesian optimization for knot selection.
result Competitive performance with reduced computational cost.
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 feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and parameter estimation. In this paper, we expand a nonconvex paradigm to sparse group …
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
A new method selects features efficiently for high-dimensional data.
problem High computational costs and memory requirements in high-dimensional data.
method QuickSelection uses the strength of neurons in sparse autoencoders to select features.
result QuickSelection achieves the best trade-off of accuracy, speed, and memory usage.
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By co…
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
Improves Group Lasso for categorical data by reducing dimensionality and selecting models.
problem Sparse modelling of categorical data is challenging, especially for high dimensions.
method Two-step procedure: first, reduce dimensionality using Group Lasso; second, select final model using an information criterion on clustered levels.
result The method produces a sparse solution and performs better than state-of-the-art algorithms in prediction accuracy and model dimension.
Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.
problem Functional predictor selection and estimation of smooth functional coefficients in high-dimensional multivariate functional data.
method Functional group-sparse regression methods in a generic Hilbert space of infinite dimension.
result Consistency of estimation and selection (oracle property) under infinite-dimensional Hilbert spaces.
Proposes a Bayesian approach for automatic node selection in sparse neural networks.
problem Reduces structural complexity and computational speedup in large-scale predictive models.
method Uses spike-and-slab Gaussian priors and variational Bayes approach for node selection.
result Establishes variational posterior consistency and optimal contraction rates for sparse networks.
Proposes a more efficient knot selection method for sparse Gaussian processes.
problem Optimizing marginal likelihood for knot selection leads to suboptimal and inefficient placement of knots.
method Uses Bayesian optimization to propose knots one at a time, avoiding multimodal surface issues.
result Improves both accuracy and speed of knot selection compared to current methods.
New insights into variable selection with different model assumptions.
problem Sparse recovery with ℓ∞ error guarantees in variable selection. method Separation between oblivious and adaptive models of ℓ∞ sparse recovery. result Proves a surprising contrast between oblivious and adaptive models in ℓ∞ sparse recovery. ControlBurn selects few features from tree ensembles for better model interpretability.
problem Improving model interpretability in machine learning models.
method Sparse tree ensembles with lasso optimization.
result ControlBurn selects feature-sparse subsets for better model interpretability.
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.
New regularization scheme for FMs improves feature interaction selection.
problem Feature selection in FMs leads to loss of feature interactions.
method Proposes a new regularization scheme for FMs with upper bound of ℓ1 regularizer. result Improves feature interaction selection without restricting sparsity patterns.
Unified framework for sparse logistic regression with nonconvex regularization.
problem Sparse logistic regression with nonconvex regularization.
method Unified framework, line search criteria for nonconvex terms.
result Effective classification and feature selection at lower computational cost.
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning (SGL), for variable selection and dimension reduction via learning the gradients of t…
Picasso is a new library for sparse learning problems in R and Python.
problem Sparse learning problems in high-dimensional data analysis.
method Unified framework of pathwise coordinate optimization with efficient active set selection strategies.
result picasso can efficiently handle large-scale problems.
Optimizes subset selection in sparse learning problems.
problem Sparse learning problems, particularly best subset selection.
method Developed an efficient primal-dual algorithm leveraging dual range estimation and incremental strategy.
result Improves solutions of best subset selection with reduced redundant computation.
Paper optimizes sparse feature selection for cancer detection using GSVP and SVM.
problem Sparse feature selection for cancer detection.
method Regularized GSVP with proximal gradient descent, feature selection via SVM.
result Near-perfect balanced accuracy with few selected features.
Paper proposes a sparse synthetic control method to select important predictors.
problem Choosing and weighting predictors affects synthetic control estimator performance.
method Sparse synthetic control procedure that penalizes predictors, derived in a linear factor model.
result Sparse synthetic control achieves lower bias and better post-treatment performance.
This paper considers portfolio construction in a dynamic setting. We specify a loss function comprised of utility and complexity components with an unknown tradeoff parameter. We develop a novel regret-based criterion for selecting the tradeoff parameter to construct optimal sparse portfolios over time.
Sparse text alignments learned via optimal transport improve model explainability.
problem Building self-explaining models by selecting relevant text pieces.
method Employing optimal transport to find minimal cost alignments, introducing constrained variants for sparsity.
result Sparse and interpretable alignments achieved, preserving prediction accuracy.
We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this …
Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since ea…
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.
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be v…
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.
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-…
In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-fre…
This work improves SINDy-type algorithms for system identification using score-guided dictionary selection.
problem Improving accuracy and interpretability in dynamical system identification.
method Score-guided library selection to refine dictionary terms in sparse regression.
result Score-guided methods enhance SINDy's robustness in discovering governing equations.
VC-PCR improves prediction by clustering correlated variables.
problem Decreased prediction accuracy due to cluster structure in predictor variables.
method Supervised variable selection and clustering to integrate cluster information into a sparse modeling process.
result VC-PCR achieves better prediction, variable selection, and clustering performance.
Proposes a method to learn sparse deep neural networks with theoretical guarantees.
problem Over-parameterized deep neural networks cause training, prediction, and interpretation difficulties.
method Frequentist-like method for sparse DNNs under Bayesian framework.
result Consistent sparse DNNs with at most O(n/log(n)) connections. Sparse multinomial logistic regression for multiclass classification with feature selection.
problem High-dimensional multiclass classification with a focus on sparse models.
method Penalized maximum likelihood with complexity penalty, feature selection using group Lasso and Slope classifiers.
result Achievement of minimax order in both small and large number of classes regimes.
Introduces top-k regularization for better feature selection in machine learning.
problem Limited ability of existing feature selection methods to reconcile feature representativeness and inter-correlations.
method Top-k regularization, which induces a sub-architecture on the model's architecture to select informative features and model complex relationships. result Uniform approximation error bound for top-k regularization approximating high-dimensional sparse functions. New approach selects sparse features without validation.
problem Overfitting and high storage/compute costs in AI models.
method Phase transition in probability of feature retrieval.
result Flexible approach for various models and loss functions.
ARGEN method improves variable selection and regularization in high-dimensional sparse models.
problem Constrained variable selection and regularization in high-dimensional sparse linear models.
method ARGEN penalty method, variable selection and regularization.
result ARGEN method has variable selection and estimation consistency under certain conditions.
Sparse feature selection improves batch RL efficiency.
problem High-dimensional batch RL with many features.
method Sparse linear function approximation, Lasso, group Lasso, fitted Q-evaluation, fitted Q-iteration.
result Sparse feature selection makes batch RL more sample efficient.
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse representation. There have been several studies for improving this problem such…
New method selects variables for GP regression using sparse projection.
problem Identifying environmental factors affecting metal corrosion.
method Sparse projection of input variables, gradient descent optimization, non-convex marginal likelihood.
result Proposed method outperforms benchmarks in variable selection accuracy.
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In th…
sBayFDNN bridges deep learning and functional data analysis for complex, structured data.
problem Challenges in functional data analysis, especially for complex, continuously structured data.
method Sparse Bayesian functional deep neural network (sBayFDNN) that learns adaptive functional embeddings and interpretable region selection.
result First theoretical guarantees for a Bayesian deep functional model, ensuring reliability and statistical rigor.