Simultaneous analysis of Lasso and Dantzig selector

Abstract

We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ${\ell }_p$ estimation loss for $1\le p\le 2$ in the linear model when the number of variables can be much larger than the sample size.

Noramlization factor corrected

References in corpus (8)

• Pathwise coordinate optimization
• The sparsity and bias of the Lasso selection in high-dimensional linear regression
• Lasso-type recovery of sparse representations for high-dimensional data
• High-dimensional generalized linear models and the lasso
• Sparsity oracle inequalities for the Lasso
• Aggregation for Gaussian regression
• The Dantzig selector and sparsity oracle inequalities
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$

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• On the Exponentially Weighted Aggregate with the Laplace Prior
• Alternating Estimation for Structured High-Dimensional Multi-Response Models
• Optimal Statistical Inference for Individualized Treatment Effects in High-dimensional Models
• Conjugate gradient acceleration of iteratively re-weighted least squares methods
• A concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise
• Sparse Sliced Inverse Regression Via Lasso
• Asymptotic properties of adaptive group Lasso for sparse reduced rank regression
• Least Squares with Error in Variables
• Scalable Interpretable Learning for Multi-Response Error-in-Variables Regression
• Transfer Learning via ${\ell }_1$ Regularization
• Structure-Blind Signal Recovery
• Simultaneous support recovery in high dimensions: Benefits and perils of block ${\ell }_1/{\ell }_{\infty }$-regularization
• Aggregation of supports along the Lasso path
• Bayesian high-dimensional linear regression with generic spike-and-slab priors
• Sequential scaled sparse factor regression
• Compound Poisson Point Processes, Concentration and Oracle Inequalities
• Robust Reduced Rank Regression
• Doubly robust estimators for the average treatment effect under positivity violations: introducing the $e$-score
• Uncertainty Quantification Under Group Sparsity
• Grouped Variable Selection via Nested Spike and Slab Priors
• Online Convex Matrix Factorization with Representative Regions
• Detection and estimation of parameters in high dimensional multiple change point regression models via ${\ell }_1/{\ell }_0$ regularization and discrete optimization
• High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis
• Estimating Network Structure from Incomplete Event Data
• Nonsparse learning with latent variables
• Path Thresholding: Asymptotically Tuning-Free High-Dimensional Sparse Regression
• Selection consistency of Lasso-based procedures for misspecified high-dimensional binary model and random regressors
• Single Point Transductive Prediction
• Optimal estimation of functionals of high-dimensional mean and covariance matrix
• Regularization for supervised learning via the "hubNet" procedure
• Computing Estimators of Dantzig Selector type via Column and Constraint Generation
• Efficient regularization with wavelet sparsity constraints in PAT
• Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery
• Sparse Recovery with Coherent Tight Frames via Analysis Dantzig Selector and Analysis LASSO
• Causal aggregation: estimation and inference of causal effects by constraint-based data fusion
• Sparse Group Selection Through Co-Adaptive Penalties
• Chi-square and normal inference in high-dimensional multi-task regression
• Sharp Support Recovery from Noisy Random Measurements by L1 minimization
• Blending search queries with social media data to improve forecasts of economic indicators
• Keeping greed good: sparse regression under design uncertainty with application to biomass characterization
• The greedy side of the LASSO: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit
• Variance Estimation Using Refitted Cross-validation in Ultrahigh Dimensional Regression
• A local stochastic Lipschitz condition with application to Lasso for high dimensional generalized linear models
• Adaptive Feature Selection: Computationally Efficient Online Sparse Linear Regression under RIP
• Statistical inference for high dimensional regression via Constrained Lasso
• An analysis of the SPARSEVA estimate for the finite sample data case
• An error bound for Lasso and Group Lasso in high dimensions
• Bayesian Inference using the Proximal Mapping: Uncertainty Quantification under Varying Dimensionality
• A Probabilistic Framework for Discriminative Dictionary Learning
• Sparse regression and marginal testing using cluster prototypes
• Adaptive Estimation and Statistical Inference for High-Dimensional Graph-Based Linear Models
• Restricted eigenvalue property for corrupted Gaussian designs
• Robust learning and complexity dependent bounds for regularized problems
• Aggregation of Affine Estimators
• Inferring serial correlation with dynamic backgrounds
• The Finite Sample Performance of Treatment Effects Estimators based on the Lasso
• Sparse Density Estimation with Measurement Errors
• Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approach
• High-dimensional Adaptive Minimax Sparse Estimation with Interactions
• Multiple Hypotheses Testing For Variable Selection
• The Function-on-Scalar LASSO with Applications to Longitudinal GWAS
• Learning Generative Prior with Latent Space Sparsity Constraints
• Greedy Forward Regression for Variable Screening
• L1 penalized LAD estimator for high dimensional linear
• Some exercises with the Lasso and its compatibility constant
• On Quadratic Convergence of DC Proximal Newton Algorithm for Nonconvex Sparse Learning in High Dimensions
• On Regularized Square-root Regression Problems: Distributionally Robust Interpretation and Fast Computations
• Low-rank matrix estimation in multi-response regression with measurement errors: Statistical and computational guarantees
• Oracle inequalities for sign constrained generalized linear models
• Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties
• SOFAR: large-scale association network learning
• Outlier-robust sparse/low-rank least-squares regression and robust matrix completion
• High-dimensional Inference for Dynamic Treatment Effects
• Constraints and Conditions: the Lasso Oracle-inequalities
• A Provable Smoothing Approach for High Dimensional Generalized Regression with Applications in Genomics
• Adaptive elastic net and Separate Selection from Least Squares for ultra-high dimensional regression models
• Extreme Eigenvalues of Nonlinear Correlation Matrices with Applications to Additive Models
• Rapid mixing of a Markov chain for an exponentially weighted aggregation estimator
• Distributed Sparse Regression via Penalization
• Adaptive Huber Regression on Markov-dependent Data
• Sorted Concave Penalized Regression
• Sparse recovery based on q-ratio constrained minimal singular values
• Directional FDR Control for Sub-Gaussian Sparse GLMs
• The $l_q$ consistency of the Dantzig Selector for Cox's Proportional Hazards Model
• Context-dependent self-exciting point processes: models, methods, and risk bounds in high dimensions
• Stochastic Lipschitz continuity for high dimensional Lasso with multiple linear covariate structures or hidden linear covariates
• Tuning-Free Heterogeneity Pursuit in Massive Networks
• Simultaneous Heterogeneity and Reduced-rank Learning for Multivariate Response Regression
• Submodularity in Statistics: Comparing the Success of Model Selection Methods
• High-Dimensional Semiparametric Selection Models: Estimation Theory with an Application to the Retail Gasoline Market
• Imputation for High-Dimensional Linear Regression
• Structural Change in Sparsity
• Error bounds for sparse classifiers in high-dimensions
• Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data
• A Unified Dynamic Approach to Sparse Model Selection
• Post Selection Shrinkage Estimation for High Dimensional Data Analysis
• Honest confidence sets for high-dimensional regression by projection and shrinkage
• Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculations
• Necessary moment conditions for exact reconstruction via basis pursuit
• New Computational and Statistical Aspects of Regularized Regression with Application to Rare Feature Selection and Aggregation
• Kernel-based estimation for partially functional linear model: Minimax rates and randomized sketches
• Learning the Dynamics of Sparsely Observed Interacting Systems
• Optimal prediction for sparse linear models? Lower bounds for coordinate-separable M-estimators
• Generalization error minimization: a new approach to model evaluation and selection with an application to penalized regression
• A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity
• Censored linear model in high dimensions
• Ultra-high Dimensional Multiple Output Learning With Simultaneous Orthogonal Matching Pursuit: A Sure Screening Approach
• Relaxed Sparse Eigenvalue Conditions for Sparse Estimation via Non-convex Regularized Regression
• Estimation and inference for high-dimensional non-sparse models
• Doubly robust matching estimators for high dimensional confounding adjustment
• Quantile universal threshold: model selection at the detection edge for high-dimensional linear regression
• Interaction Pursuit Biconvex Optimization
• Near Oracle Performance and Block Analysis of Signal Space Greedy Methods
• High-dimensional instrumental variables regression and confidence sets -- v2/2012
• Oracle approach and slope heuristic in context tree estimation
• Sparse Recovery from Extreme Eigenvalues Deviation Inequalities
• Convergence Rates of Empirical Bayes Posterior Distributions: A Variational Perspective
• Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oracle
• Bayesian High-dimensional Semi-parametric Inference beyond sub-Gaussian Errors
• Convergence rate of Bayesian tensor estimator: Optimal rate without restricted strong convexity
• Lasso-type estimators for Semiparametric Nonlinear Mixed-Effects Models Estimation
• Survival Analysis with Graph-Based Regularization for Predictors
• A Bernstein-type Inequality for High Dimensional Linear Processes with Applications to Robust Estimation of Time Series Regressions
• Parallelism, Uniqueness, and Large-Sample Asymptotics for the Dantzig Selector
• On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model
• A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem
• Sliding window strategy for convolutional spike sorting with Lasso : Algorithm, theoretical guarantees and complexity
• Generic chaining and the l1-penalty
• Sparse Trace Norm Regularization
• A Smoothed Analysis of Online Lasso for the Sparse Linear Contextual Bandit Problem
• High Dimensional Logistic Regression Under Network Dependence
• Rank-Constrained Least-Squares: Prediction and Inference
• Boosting with Structural Sparsity: A Differential Inclusion Approach
• GenMod: A generative modeling approach for spectral representation of PDEs with random inputs
• Weak convergence of the regularization path in penalized M-estimation
• Scaling Multiple-Source Entity Resolution using Statistically Efficient Transfer Learning
• Predicting Future Cognitive Decline with Hyperbolic Stochastic Coding
• The Stability of Low-Rank Matrix Reconstruction: a Constrained Singular Value View
• Structure learning for CTBN's via penalized maximum likelihood methods
• Comments on Leo Breiman's paper 'Statistical Modeling: The Two Cultures' (Statistical Science, 2001, 16(3), 199-231)
• A Significance Test for Graph-Constrained Estimation
• II. High Dimensional Estimation under Weak Moment Assumptions: Structured Recovery and Matrix Estimation
• Statistical inference and feasibility determination: a nonasymptotic approach
• On Cross-validation for Sparse Reduced Rank Regression
• Smooth Adjustment for Correlated Effects
• Sparse estimation for case-control studies with multiple subtypes of cases
• Bayesian Factor-adjusted Sparse Regression
• Errors-in-variables models with dependent measurements
• A problem dependent analysis of SOCP algorithms in noisy compressed sensing
• Dantzig Selector with an Approximately Optimal Denoising Matrix and its Application to Reinforcement Learning
• High-Dimensional Varying Coefficient Models with Functional Random Effects
• Selective Inference via Marginal Screening for High Dimensional Classification
• Logistic regression and Ising networks: prediction and estimation when violating lasso assumptions
• Large scale Lasso with windowed active set for convolutional spike sorting
• A Simple Homotopy Proximal Mapping for Compressive Sensing
• Consistency of modified versions of Bayesian Information Criterion in sparse linear regression with subgaussian errors
• A Convex Approach to Sparse H infinity Analysis & Synthesis
• Fast Sparse Least-Squares Regression with Non-Asymptotic Guarantees
• Network-Based Pathway Enrichment Analysis with Incomplete Network Information
• Signal extraction approach for sparse multivariate response regression
• Coherence of high-dimensional random matrices in a Gaussian case : application of the Chen-Stein method
• Estimation of matrices with row sparsity
• A comprehensive study of sparse representation techniques for offline signature verification
• A Bayesian approach for the segmentation of series corrupted by a functional part
• Adaptive Estimation In High-Dimensional Additive Models With Multi-Resolution Group Lasso
• Scalable simultaneous inference in high-dimensional linear regression models
• Inference Without Compatibility
• Sharp Oracle Inequalities for Low-complexity Priors
• Cox's proportional hazards model with a high-dimensional and sparse regression parameter
• Decision Triggered Data Transmission and Collection in Industrial Internet of Things
• Estimating the Penalty Level of ${\ell }_1$-minimization via Two Gaussian Approximation Methods
• Phase Transition in Limiting Distributions of Coherence of High-Dimensional Random Matrices
• Sparse and Efficient Estimation for Partial Spline Models with Increasing Dimension
• Robust Elastic Net Regression
• Limiting Laws of Coherence of Random Matrices with Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices
• Statistical Inference for Data-adaptive Doubly Robust Estimators with Survival Outcomes
• Minimum Description Length Principle in Supervised Learning with Application to Lasso
• Variable selection and structure identification for varying coefficient Cox models
• Consistency of ${\ell }_1$ Penalized Negative Binomial Regressions
• On the uniform convergence of empirical norms and inner products, with application to causal inference
• A proximal dual semismooth Newton method for computing zero-norm penalized QR estimator
• Two step estimations via the Dantzig selector for models of stochastic processes with high-dimensional parameters
• High-dimensional Statistical Inference and Variable Selection Using Sufficient Dimension Association
• Sparse Empirical Bayes Analysis (SEBA)
• A Knowledge Transfer Framework for Differentially Private Sparse Learning
• Improved error rates for sparse (group) learning with Lipschitz loss functions
• Sharp Convergence Rate and Support Consistency of Multiple Kernel Learning with Sparse and Dense Regularization
• A Global Homogeneity Test for High-Dimensional Linear Regression
• On the Conditions of Sparse Parameter Estimation via Log-Sum Penalty Regularization
• Sharp Threshold for Multivariate Multi-Response Linear Regression via Block Regularized Lasso
• Estimating high-dimensional Markov-switching VARs
• Asymptotic Minimaxity, Optimal Posterior Concentration and Asymptotic Bayes Optimality of Horseshoe-type Priors Under Sparsity
• High-dimensional inference robust to outliers with l1-norm penalization
• Worst possible sub-directions in high-dimensional models
• A provable two-stage algorithm for penalized hazards regression
• Testing Mediation Effects Using Logic of Boolean Matrices
• Oracle inequalities for ranking and U-processes with Lasso penalty
• A note on sharp oracle bounds for Slope and Lasso
• Non-separable Models with High-dimensional Data
• Best subset selection in linear regression via bi-objective mixed integer linear programming
• Deviation bound for non-causal machine learning
• Predicting sparse circle maps from their dynamics
• Ultra High Dimensional Change Point Detection
• Column normalization of a random measurement matrix
• Characterization of Excess Risk for Locally Strongly Convex Population Risk
• Efficient Predictor Ranking and False Discovery Proportion Control in High-Dimensional Regression
• Learning the intensity of time events with change-points
• Cox process functional learning
• An \ell_1-oracle inequality for the Lasso in finite mixture of multivariate Gaussian regression models
• Forward variable selection for sparse ultra-high dimensional varying coefficient models
• High Dimensional Tests for Functional Networks of Brain Anatomic Regions
• Minimax Estimation of Partially-Observed Vector AutoRegressions
• Mean and variance estimation in high-dimensional heteroscedastic models with non-convex penalties
• Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models
• Improved bounds for Square-Root Lasso and Square-Root Slope
• On prediction with the LASSO when the design is not incoherent
• On The Sparse Bayesian Learning Of Linear Models
• On sure early selection of the best subset
• Robust Lasso with missing and grossly corrupted observations
• Low noise sensitivity analysis of Lq-minimization in oversampled systems
• Structured Sparse Aggregation
• Optimal Estimation of Slope Vector in High-dimensional Linear Transformation Model
• Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference
• Non-Asymptotic Bounds for the ${\ell }_{\infty }$ Estimator in Linear Regression with Uniform Noise
• High-dimensional regression with unknown variance
• New Error Analysis for Lasso
• Inference for biased models: a quasi-instrumental variable approach