Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coefficient matrix that accoun…
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48 results for “Conditional Sparse Regression”
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.
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated…
New algorithms find conditions and linear rules with high probability and loss.
problem Finding conditions and rules with high probability and loss in conditional sparse regression.
method Efficient algorithms for identifying conditions and rules with optimal probability and loss.
result Achieved algorithms that nearly match the probability of the ideal condition and improve the approximation to the target loss.
New algorithm reduces sample complexity for sparse linear regression.
problem Sparse linear regression with correlated covariates and approximate dependencies.
method Polynomial-time algorithm that adapts the Lasso to tolerate approximate dependencies.
result Achieves near-optimal sample complexity for constant sparsity and ill-conditioned covariates.
Relaxed Sparse Eigenvalue Conditions for Sparse Estimation via Non-convex Regularized Regressioncs.LG
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…
The paper tackles identifying a small segment of a population with sparse linear regression.
problem Identifying a small segment of a population with a sparse linear regression fit.
method Algorithms for joint identification of a significant segment of a population with a sparse linear regression fit under the sup norm, using k-DNF conditions and s-sparse regression fits.
result Preliminary algorithms and challenges for future work in non-sparse regression and expected error.
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…
Proposes a model selection procedure for high-dimensional binary classification using sparse logistic regression.
problem High-dimensional binary classification with sparse logistic regression.
method Penalized maximum likelihood with complexity penalty on model size, Slope estimator for logistic regression.
result Proposed complexity penalty is rate-optimal in the minimax sense.
Sharp rates for prediction error in high-dimensional sparse models.
problem High-dimensional sparse linear models with limited predictive power.
method Forward regression for model selection and least squares estimation.
result Sharp convergence rates without beta-min or irrepresentability conditions.
Proposes a nonconvex optimization method for sparse logistic regression.
problem Sparse logistic regression with weakly convex regularization.
method Proximal gradient descent for solving nonconvex optimization problem.
result Proves local optimality conditions and convergence of the method.
Study improves error bounds for sparse regression with heavy-tailed covariates.
problem Estimating sparse coefficients in linear regression with heavy-tailed covariates.
method Employed an -penalized Huber regression method.
result Error bound identical to Gaussian case for -subexponential covariates.
Paper proposes robust and sparse GLM regression using stochastic optimization.
problem Sparse GLM's lack robustness against outliers in high-dimensional data.
method Robust and sparse linear regression based on -divergence with stochastic optimization.
result The proposed method outperforms existing methods in numerical experiments and real data analysis.
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of computationally tractable sparse regression algorithms---such as the Lasso, Orthogonal Matchi…
New method constructs matrices satisfying Restricted Eigenvalue condition for sparse recovery.
problem Sparse recovery in high-dimensional settings with limited data.
method Constructs matrices from a fixed deterministic matrix and a subgaussian random matrix.
result New matrices satisfy Restricted Eigenvalue condition with high probability.
SLR tackles sparse linear regression problems, showing hardness for efficient algorithms.
problem Sparse linear regression with noisy data and k-sparse solutions.
method Reduction from lattice problems to SLR instances, showing hardness.
result Hardness of SLR instances, even for isotropic Gaussian design matrices.
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterat…
The paper analyzes optimization methods for high-dimensional linear regression.
problem Estimating sparse parameters from noisy observations in high-dimensional settings.
method Introduces and analyzes optimization methods for sparse estimation.
result Shows stable recovery properties and bounds for minimization and regularization methods.
Sparsistent Model Discoverystat.ML
New method recovers PDEs from noisy data, even when conditions are violated.
problem Discovering PDEs from noisy, limited data.
method Randomized adaptive Lasso integrated into DeepMod.
result Recovery of PDEs with higher noise-to-sample ratios and single hyperparameters.
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.
Improved CRT for sparse logistic regression in high dimensions.
problem Accurate inference in high-dimensional sparse logistic regression.
method Variable-distillation and decorrelation steps in CRT-logit.
result CRT-logit provides a more powerful solution with theoretical guarantees.
Combines regularization and optimal scaling for better regression models.
problem Improving regression models with categorical and continuous data.
method Integrates optimal scaling and regularization methods.
result Enhances model performance and condition of predictor correlation matrix.
AIHT improves online high-dimensional quantile regression by separating support discovery and refinement.
problem Online high-dimensional quantile regression with structural sparsity.
method Adaptive Iterative Hard Thresholding (AIHT) alternates stochastic updates with adaptive hard-thresholding steps.
result AIHT achieves logarithmic regret for the sliding-window objective in high-dimensional settings.
Wavelet regression method handles irregular data efficiently.
problem Nonparametric regression with irregularly spaced data.
method Wavelet regression using proximal gradient descent.
result Adaptive minimax convergence rates for non-equispaced data.
Study on estimating parameters in sparse nonlinear regression models.
problem Parameter estimation and asymptotic inference for sparse nonlinear regression models.
method Proposes an ℓ1-regularized least-squares estimator to handle nonlinearity and nonconvexity.
result Proves that every stationary point of the objective enjoys an optimal statistical rate of convergence.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
New research shows how preconditioning can solve sparse linear regression problems efficiently.
problem Efficiently solving sparse linear regression problems without restrictive conditions.
method Preconditioned Lasso approach to solve sparse linear regression problems.
result Preconditioning can solve a large class of sparse linear regression problems nearly optimally.
Study variational Bayes for high-dimensional linear regression with sparse priors.
problem Sparse high-dimensional linear regression model selection.
method Mean-field spike and slab variational Bayes approximation, oracle inequalities, coordinate-ascent variational inference (CAVI), prioritized updating scheme.
result Mean-field VB approximation converges to the sparse truth at optimal rate and gives optimal prediction.
Investigates FITC and VFE approximations for Gaussian Processes.
problem Efficient inference in Gaussian Processes for large datasets.
method Analytical and illustrative examples of FITC and VFE approximations.
result Different theoretical properties and practical behaviors of FITC and VFE.
PROBE algorithm efficiently solves sparse high-dimensional linear regression.
problem Sparse high-dimensional linear regression models with complex parameter spaces.
method Partitioned empirical Bayes ECM algorithm for computationally efficient MAP estimation.
result PROBE algorithm provides robust and efficient coordinate-wise optimization.
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
Sparse Regression for Discovery of Constitutive Models from Oscillatory Shear Measurementscond-mat.soft
Sparse regression models CMs from oscillatory shear data efficiently.
problem Discovering parsimonious constitutive models from oscillatory shear experiments.
method Sparse regression with tensor basis functions, l1 regularization, and greedy two-stage algorithm.
result Inferred CMs extrapolate well beyond training data and flow conditions.
A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.
problem Sparse-penalized quantile regression with non-convex penalties.
method Single-loop smoothing ADMM (SIAD) algorithm for faster convergence.
result SIAD method outperforms existing approaches in solving sparse-penalized quantile regression.
Proposes a convex method for high-dimensional sparse sliced inverse regression.
problem Difficulty in interpreting results and variability in high-dimensional settings.
method Convex formulation and linearized alternating direction methods of multiplier algorithm.
result Upper bound on the subspace distance between estimated and true subspaces.
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.
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior…
Efficiently estimates sparse functionals robustly in high dimensions.
problem Statistical procedures are sensitive to minor deviations in high-dimensional settings.
method Proposes a computationally and statistically efficient algorithm for robust estimation of sparse functionals.
result Guarantees accurate recovery of sparse functionals under certain deterministic conditions.
Proposes SHORE model for efficient MOR with sparsity and scalability.
problem Challenges of interpretability and scalability in MOR with high-dimensional outputs.
method Incorporates sparsity requirements and a two-stage optimization framework for efficient compression.
result Theoretical and empirical validation of the proposed framework's efficiency and accuracy.
Proposes FARM model combining latent factor and sparse regression.
problem Testing adequacy of latent factor and sparse regression models.
method Factor Augmented sparse linear Regression Model (FARM) with FabTest and ANOVA type tests.
result Model robustness and effectiveness validated through experiments.
New algorithms learn GGMs without condition number bounds, even with strong dependencies.
problem Learning Gaussian Graphical Models without condition number bounds.
method Polynomial-time algorithms for attractive and walk-summable GGMs.
result Efficient recovery of graph structure with logarithmic number of samples.
Paper analyzes IHT's performance in sparse recovery problems.
problem Generalization performance of Iterative Hard Thresholding (IHT).
method Sparse generalization theory under algorithmic stability.
result IHT achieves convergence rates in sparse excess risk.
Graph-Sparse Logistic Regression for sparse and connected support classification.
problem Sparse and connected support classification problems.
method Introduces Graph-Sparse Logistic Regression algorithm.
result Validated and benchmarked against L1-regularized Logistic Regression.
New method outperforms standard procedures in heavy-tailed problems.
problem Regression function estimation under heavy-tailed conditions.
method Regularized risk minimization procedure based on median-of-means tournaments.
result The new procedure achieves near optimal accuracy and confidence in heavy-tailed problems.
TSN improves sparse signal recovery with less complexity.
problem Sparse regression problem of recovering sparse signals from measurements.
method Tree search algorithm driven by deep neural network with pruning.
result TSN outperforms conventional methods in various sensing matrices.
Paper presents a new method for solving sparse learning problems.
problem Sparse learning challenges in high-dimensional data analysis.
method Parametric Simplex Method (PSM) for solving linear programs parametrized by a regularization factor.
result PSM offers advantages over competing methods in terms of solution path, precision, and computational efficiency.