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…
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48 results for “smooth penalties”
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…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…
New nonconvex penalty smooths at origin for deep learning.
problem Improving variable selection and bias in high-dimensional statistical learning.
method Developed a new nonconvex penalty function smooth at origin.
result Asymptotic bias of new penalty function vanishes exponentially fast.
New method approximates sampling from smooth potential distributions using a vanishing penalty.
problem Sampling from smooth potential distributions on high-dimensional spaces.
method Penalized Langevin dynamics (PLD) with vanishing penalty.
result Established upper bound on Wasserstein-2 distance for PLD approximation.
Gradient-based Regularization Parameter Selection for Problems with Non-smooth Penalty Functionsstat.ML
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…
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.
Curvature penalties improve interpretability of KANs without sacrificing accuracy.
problem Pathologically high-curvature oscillations in KANs activations make them hard to interpret.
method Derived a curvature penalty and proved an upper bound on model curvature.
result KANs with curvature penalties achieve substantially smoother activations while maintaining accuracy.
Efficient Penalty-Based Bilevel Methods: Improved Analysis, Novel Updates, and Flatness Conditionmath.OC
Improved penalty-based methods for bilevel optimization with reduced complexity.
problem Suboptimal complexity in solving bilevel optimization problems with large penalty terms.
method Novel penalty reformulation that decouples upper and lower-level variables, enabling larger step sizes and reduced iteration complexity.
result PBGD-Free algorithm that avoids inner loops for coupled constraint BLO problems, with reduced iteration complexity.
A new spline method for manifold learning using Hessian-based curvature penalties.
problem Learning manifolds with curvature penalties in high dimensions.
method Generalizes thin-plate splines to flat manifolds using Hessian matrices, minimizing square error with curvature constraints.
result Existence and uniqueness of the spline solution, expressed as Green's functions and Hessian approximations.
Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.
problem Minimizing loss and constraint violations in online convex optimization with smooth penalties.
method Projected gradient descent over a set around the current action.
result Both dynamic regret and constraint violation are bounded by the path-length.
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…
Motivated by manifold learning techniques, we give an explicit lower bound for how far a smoothly embedded compact submanifold in can move in a normal direction and remain an embedding. In addition, given a penalty function on the space of embeddi…
Proposes a new ridge estimator for smooth covariates with adaptive centering.
problem Estimating coefficients and center function for smooth covariates in linear models.
method SACR framework with convex formulation, roughness penalty, and adaptive centering.
result Improves prediction and variable selection for smooth covariates.
Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the nonconvex penalized SVMs due to their nondifferentiability, nonsmoothness and nonconve…
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 …
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cas…
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical K-means. However, solving the ONMF model is a challenging optimization problem becau…
Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off. This paper introduces an impulse response estimator which relies on an -type regularization including a rank-penalty derive…
New calibration measure SSCE ensures truthful prediction, unlike existing measures.
problem Ensuring truthful calibration measures in sequential prediction.
method Introduced a new calibration measure, Subsampled Smooth Calibration Error (SSCE).
result SSCE ensures truthful prediction, while existing measures are far from truthful.
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The proposed approach combines appealing features of finite basis representation and smoot…
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems. We propose a…
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.
New iterative regularization method tackles non-smooth, non-strongly convex functionals.
problem Tackles non-smooth, non-strongly convex functionals in regularization problems.
method Primal-dual algorithm with convergence and stability analysis.
result First iterative regularization procedure for non-smooth, non-strongly convex functionals.
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…
Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lassostat.ML
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regressio…
Unified framework for fair regression in aware and unaware settings.
problem Lack of principled methods for fair regression in unawareness settings.
method Formulated as an optimal transport problem, unifying aware and unaware settings.
result Characterizes optimal prediction functions via optimal transport maps under different penalties.
A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted -norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed to approximate the -norm. The convergence of the global minimum points o…
Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.
problem Selecting optimal tree structure and ranks for high-dimensional function approximation.
method Proposes a complexity-based model selection method for tree tensor networks in empirical risk minimization.
result Demonstrates near-minimax adaptive performance across various smoothness classes.
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
problem Understanding the implicit bias of gradient descent in neural networks.
method Analysis of gradient descent training for wide neural networks, focusing on the curvature penalty and initialization schemes.
result The solutions of gradient descent training are polyharmonic splines for certain initialization schemes.
Paper proves robust M-estimators' coordinates' normality in high dimensions.
problem High-dimensional robust M-estimators' asymptotic normality.
method Develops Stein formulae for high-dimensional random vectors on the sphere.
result Asymptotic normality holds for most coordinates of robust M-estimators with convex penalty.
Deep weight factorization improves neural network training through smooth optimization of sparse penalties.
problem Challenges in applying sparse regularization in neural networks due to non-differentiability of penalties.
method Introduces deep weight factorization, decomposing weights into multiple factors for smooth optimization of -penalized networks.
result Deep weight factorization outperforms shallow factorization and pruning methods consistently across various architectures and datasets.
Recent contributions have framed linear system identification as a nonparametric regularized inverse problem. Relying on -type regularization which accounts for the stability and smoothness of the impulse response to be estimated, these approaches have been shown to be competitive w.r.t classical parametric met…
fastkqr speeds up kernel quantile regression by up to 10x.
problem Huge computational demands of kernel quantile regression.
method A novel finite smoothing algorithm and spectral technique.
result Significantly faster computation of quantile regression.
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingstat.ML
New algorithms improve sampling from constrained distributions.
problem Sampling from distributions constrained to convex bodies.
method Penalized Langevin Dynamics and Underdamped Monte Carlo methods.
result Improved convergence rates for constrained sampling problems.
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a conv…
Modified ReLU networks improve regression estimation rates.
problem Regression estimation with smooth functions.
method Using modified ReLU neural networks with specific weight modifications.
result Empirical risk minimizers achieve minimax rate of prediction.
Kronecker trend filtering improves lattice data smoothing.
problem Estimating smooth functions on lattice data.
method Penalized least squares with Kronecker products of univariate trend filtering penalties.
result Kronecker trend filtering outperforms linear smoothers in high dimensions.
While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on th…
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…
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of co…
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
Multivariate boosted trees improve forecasting and control by capturing correlated predictions.
problem Capturing multivariate target cross-correlations and applying structured penalties to predictions.
method A computationally efficient algorithm for fitting multivariate boosted trees.
result Multivariate trees outperform univariate counterparts in correlated prediction scenarios.
This paper improves adversarial robustness of deep learning models.
problem Vulnerability of machine learning models to adversarial perturbations.
method Analyzes adversarial training for linear regression and neural networks, incorporating L1 penalty.
result Incorporating L1 penalty leads to consistent adversarially robust estimation in high-dimensional settings.