New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
This paper explores how entropic regularization improves Wasserstein estimators' performance.
problem Improving the approximation and estimation properties of Wasserstein estimators.
method Entropic regularization of optimal transport costs to smooth Wasserstein estimators.
result Entropic regularization can achieve comparable statistical performance to un-regularized estimators at lower computational cost.
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 analyzes the risk of bagging regularized M-estimators under proportional asymptotics.
problem Characterizing the risk of ensemble estimators trained with subsamples and regularizers.
method Developed a consistent estimator for the risk of ensemble estimators under proportional asymptotics.
result Optimal subsample size k⋆ tends to be in the overparameterized regime for the full-ensemble estimator. New method resolves density ratio estimation saturation issues.
problem Error saturation in density ratio estimation methods.
method Iterated regularization to improve kernel methods.
result Achieves fast error rates on regular learning problems.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
problem Selecting an appropriate regularization parameter for sparse precision matrix estimation.
method Developed a closed-form matrix-valued regularization parameter based on the sampling distribution of optimality conditions.
result The proposed method achieves comparable estimation accuracy and superior support recovery to cross-validation, with significant runtime improvements.
The paper proves diameter bounds and finiteness for amply regular graphs.
problem Proving diameter bounds and finiteness for amply regular graphs.
method Improved curvature estimates and new Bakry-Émery curvature estimates.
result There are only finitely many amply regular graphs with specific parameters.
Statistical analysis of regularization in continual learning tasks.
problem Understanding how regularization affects model performance in sequential learning.
method Derivation of convergence rates, iterative update formula, and optimal hyperparameters for generalized ℓ2-regularization.
result Optimal hyperparameters balance forward and backward knowledge transfer, improving model performance.
We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust estimator of the class probability P(y∣x). The regularization term meas…
Proposes a method to adapt models in nonstationary environments using ℓ1 regularization.
problem Adapting models to nonstationary environments in machine learning.
method Integrates ℓ1 regularization of differences between source and target parameters.
result Effective balance of stability and plasticity in model adaptation.
Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects or location effects), treatment effects for many groups, and prediction models wi…
Improved covariance matrix estimation for multiple classes with limited data.
problem Estimating covariance matrices for multiple classes with scarce data.
method Coupled regularized sample covariance matrix estimator (RSCM) that combines pooled SCM and scaled identity matrix for regularization.
result The coupled RSCM estimators outperform cross-validation in classification tasks with comparable accuracy but faster computation.
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on E=[0,∞]d\{(0,0,...,0)} and models another regular variation on the sub-cone E(2)=E\∪i=1dLi, where Li is the $i…
We estimate Radon-Nikodym derivatives using regularization in reproducing kernel Hilbert spaces.
problem Estimating Radon-Nikodym derivatives in various applications.
method General regularization scheme in reproducing kernel Hilbert spaces.
result High order accuracy in reconstructing Radon-Nikodym derivatives at any point.
Unified DICE estimators as regularized Lagrangians for improved off-policy evaluation.
problem Improving off-policy evaluation from behavior-agnostic data.
method Unified derivation of DICE estimators as regularized Lagrangians of a linear program.
result Dual solutions offer greater flexibility and provide superior estimates in practice.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
problem Jointly estimate multiple related zero-mean Gaussian distributions.
method Laplacian regularized stratified model fitting with hyper-parameters to encourage covariance closeness.
result The method performs well, especially in low data regimes, as demonstrated in finance, radar, and weather.
Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
problem Local elliptic regularity for operators with low regularity coefficients in Sobolev-type spaces.
method Rescaling estimates and multiplication results for function spaces.
result Unified set of interior estimates and regularity inference for operators with Sobolev-type coefficients.
The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.
problem Identifying low-order linear systems from limited data.
method Hankel nuclear norm regularization to encourage low-rankness of the Hankel matrix.
result Hankel regularization enables optimal system recovery with fewer observations and better estimation rates.
Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.
DONUT improves treatment effect estimation by enforcing orthogonality constraints.
problem Estimating treatment effects from observational data is challenging due to unobserved outcomes.
method DONUT uses a regularization framework that formalizes unconfoundedness as orthogonality, leading to deep orthogonal networks.
result DONUT outperforms state-of-the-art methods in estimating average treatment effects.
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoye…
Study improves regularity estimates for harmonic maps into ellipsoids.
problem Independence of regularity estimates on harmonic maps with varying target dimensions.
method Analyzes harmonic maps into ellipsoids, uses Palais-Smale sequences, and critical metrics.
result Enhanced regularity estimates for Laplace harmonic eigenmaps.
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that…
A framework for analyzing regularizers to ensure trustworthy theory-driven model estimation.
problem Uncertain choice of regularizers can compromise the interpretability of deep grey-box models.
method Adapting neural net architecture and training objective to analyze regularizer behavior empirically.
result Empirical analysis of regularizers helps in making a justified choice for trustworthy theory-driven model estimation.
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of ℓ0-regularized estimation. In this note, we show that ℓ1-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …
Unified framework for analyzing pessimism in off-policy learning with regularized importance sampling.
problem High variance in importance weighting for off-policy learning.
method Unified PAC-Bayesian study of pessimism with regularized importance sampling.
result Derivation of a tractable PAC-Bayesian generalization bound for common importance weight regularizations.
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of prediction accuracy. We assume only that the densities have a convex parametrization …
Study geodesics on spherical polyhedra, estimating their number.
problem Counting simple closed geodesics on spherical polyhedra.
method Examined regular spherical octahedra, cubes, and tetrahedra.
result Estimated the number of simple closed geodesics on spherical polyhedra.
This work improves trace norm regularization for multi-task learning with limited data.
problem Learning from few samples across multiple tasks.
method Trace norm regularization for a linear shared representation model.
result First estimation error bound for trace norm regularized estimator with scarce data.
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by divergence minimization principles. We derive the estimator by a Poisson process appr…
Unified approach to linear regression using covariance fitting for optimal weights.
problem Finding optimal weights for linear regression models when weights are unknown.
method Covariance fitting SPICE-methodology to obtain data-adaptive weights.
result Tuned versions of known regularized estimators are unified under a common approach.
Dynamic CBDT improves treatment effect estimation in clinical data.
problem Estimating heterogeneous treatment effects in observational data with high accuracy and interpretability.
method Dynamic Regularized Causal Boosted Decision Trees (CBDT) integrating variance regularization and calibration.
result Significantly improved estimation accuracy and reliable coverage of true treatment effects.
Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data than traditional regularization. The reason stems from the fact that the ordered…
Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.
problem Injectivity for tensor fields on negatively curved manifolds with low regularity metrics.
method Pestov energy estimates for transport equation on non-smooth unit sphere bundle, keeping track of regularity, and using functions with more vertical than horizontal regularity.
result Proves solenoidal injectivity for tensor fields on simple Riemannian manifolds with C1,1 metrics and non-positive sectional curvature. Gradient matching method estimates implicit regularization in complex deep learning systems.
problem Estimating implicit regularization in modern deep learning systems with complex modifications.
method Gradient matching methods to empirically estimate implicit regularization.
result Empirical estimation of implicit regularization in arbitrary networks, including dropout.
We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our met…
We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family. Our theory reveals that if the Tikhonov regularizers share the same penalty matrix wit…
DRIVE improves IV estimation by accounting for distributional uncertainties.
problem Challenges in IV estimation due to untestable model assumptions and poor finite sample properties.
method DRIVE is a distributionally robust IV estimation method that minimizes a square root TSLS objective with a Wasserstein ambiguity set.
result DRIVE achieves consistency without requiring regularization parameter to vanish, ensuring robustness to distributional uncertainties.
This paper analyzes M-estimators under infinite-variance noise in high dimensions.
problem High-dimensional M-estimation with infinite-variance noise.
method Study of the Fenchel conjugate domain and its impact on risk.
result Exact risk of M-estimators under infinite-variance noise is derived.
Deep learning method improves myelin water fraction estimation.
problem Estimating myelin water fraction in the brain using magnetic resonance relaxometry.
method Combines input layer regularization with automated regularization hyperparameter tuning.
result Proposed method outperforms classical methods and multi-layer perceptrons on in vivo brain data.
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…
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 ℓ2-type regularization including a rank-penalty derive…
Method estimates parameters of complex nonlinear systems.
problem Parameter estimation for nonlinear systems with derivative states.
method Regularized linear regression using differentiation filtering and least squares.
result Finite-sample bound on mean absolute error of estimation.
A new method for faster estimation of Wasserstein distance using Sinkhorn divergence.
problem Estimating the squared Wasserstein distance between probability distributions.
method Proposes a new estimator based on the Sinkhorn divergence with debiasing terms, and analyzes its sample complexity and computational efficiency.
result The proposed estimator allows higher regularization levels, leading to improved computational complexity and speedup in practice.
This paper identifies a problem with the usual procedure for L2-regularization parameter estimation in a domain adaptation setting. In such a setting, there are differences between the distributions generating the training data (source domain) and the test data (target domain). The usual cross-validation procedure requ…
Improved LDA using a nonlinear covariance estimator for better performance.
problem Inefficient LDA when data covariance is ill-conditioned.
method Regularized LDA with a positive semidefinite ridge-type estimator of the inverse covariance matrix.
result The proposed NL-RLDA classifier outperforms state-of-the-art methods across multiple datasets.
New estimate for Curve Shortening Flow improves graphical solutions.
problem Improving regularity estimates for Curve Shortening Flow.
method Generalizing delayed parabolic regularity for Curve Shortening Flow.
result Interior graphical estimate for Curve Shortening Flow.