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.
Proposes an L1-regularized functional SVM for binary classification with functional covariates.
problem Binary classification with multivariate functional covariates.
method L1-regularized functional support vector machine (SVM) with an accompanying algorithm.
result The proposed classifier performs well in prediction and feature selection.
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.
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
Study optimal ridge regularization for out-of-distribution prediction.
problem Optimal ridge regularization for predicting out-of-distribution data.
method Established conditions for optimal regularization under covariate and regression shifts, proving monotonic risk in data aspect ratio.
result Negative regularization can be optimal under shifts, even with isotropic or underparameterized training features.
Improved LDA method for better classification and dimensionality reduction.
problem Improving linear discriminant analysis for better classification performance.
method Integrates spectrally-corrected covariance matrix and regularized discriminant analysis.
result SRLDA has a linear classification global optimal solution under spiked model assumption.
The paper defines conditions for Gaussian process sample path regularity.
problem Lack of understanding of Gaussian process sample path regularity.
method Analyzes covariance kernels to determine sample path regularity.
result Necessary and sufficient conditions for Hölder regularity are provided.
Regularized EM algorithm improves clustering performance with small sample sizes.
problem Performance reduction in EM algorithm due to small sample size and poorly conditioned covariance matrices.
method Regularized EM algorithm that uses prior knowledge to ensure positive definiteness of covariance matrices.
result The regularized EM algorithm outperforms standard EM in clustering tasks with small sample sizes.
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.
Regularized EM algorithm improves GMM clustering in low sample settings.
problem Numerical instability and convergence issues in EM-GMM for low sample support.
method Regularized EM algorithm that maximizes penalized GMM likelihood, ensuring positive definiteness and structured covariance matrices.
result The regularized EM algorithm leads to better performing EM for structured covariance matrix models or low sample settings.
Statistical characteristics of deep network representations, such as sparsity and correlation, are known to be relevant to the performance and interpretability of deep learning. When a statistical characteristic is desired, often an adequate regularizer can be designed and applied during the training phase. Typically, …
Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case
problem Adaptation to misspecified covariate shift
method Regularized Nyström subsampling with Tikhonov regularization
result Upper bounds on excess risk
Estimates linear model from noisy covariates and instruments using spectral regularization.
problem Estimating a linear model from many noisy covariates and instruments.
method Two-stage least squares with spectral regularization of canonical correlations.
result Upper and lower bounds on estimation error, proving optimality of the method with noisy data.
A new QDA classifier for high-dimensional data with spiked covariance.
problem Classifying high-dimensional data with distinct covariance matrices.
method Proposes a novel quadratic classification technique with parameters chosen to maximize the fisher-discriminant ratio.
result The proposed classifier outperforms classical R-QDA and requires lower computational complexity.
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.
Two new regularization methods improve neural network performance and complexity control.
problem Improving neural network performance and complexity control with correlated or high-dimensional features.
method Two regularization strategies: covariance-aware ridge and covariance-aware lasso.
result Improves predictive performance and complexity control over standard penalties.
Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is critical to the interpretability of a learned model. Much of the current literature…
Generative models improve MRI reconstruction by learning image structure.
problem Improving MRI image quality from undersampled data.
method Using variational autoencoders (VAEs) to learn image structure and covariance.
result The proposed method outperforms other regularization techniques on MRI datasets.
Proposes a method to improve regression model performance with limited target data using fused-regularizer.
problem Model shifts and covariate shifts in high-dimensional regression.
method Two-step method with fused-regularizer to leverage source data for target task.
result Robust to covariate shifts, minimax-optimal under certain conditions, and validated by numerical tests.
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter ρ. Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at ρ is decomposed into connected components. We show that the vertex-partition induced by the thresh…
Method regularizes Cholesky factors to detect nonstationarity in longitudinal data.
problem Detecting nonstationarity in large covariance matrices of longitudinal data.
method Fused-Lasso regularization on Cholesky factors.
result Regularization leads to smooth subdiagonals, indicating nonstationarity.
Enhances GBDT robustness with one-hot encoding and regularization.
problem Low robustness of GBDT models against covariate perturbation.
method One-hot encoding to linear framework, risk decomposition, L1 or L2 regularization. result Regularization enhances GBDT robustness.
New method improves PCA for high-dimensional data with n < p.
problem PCA struggles in high-dimensional settings with n < p.
method Pairwise differences covariance estimation with four regularized versions.
result Proposed methods outperform existing estimators in high-dimensional data settings.
Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
New method groups similar functional covariates for better modeling.
problem Analyzing functional covariates with similar shapes.
method Coefficient shape alignment regularization approach.
result True grouping structure can be accurately identified under certain conditions.
Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs require the …
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Current adoption of machine learning in industrial, societal and economical activities has raised concerns about the fairness, equity and ethics of automated decisions. Predictive models are often developed using biased datasets and thus retain or even exacerbate biases in their decisions and recommendations. Removing …
KMRCD detects outliers in non-elliptical data using kernel trick.
problem Outlier detection in non-elliptical data.
method KMRCD estimator that uses kernel trick to compute robust covariance matrix in a feature space.
result KMRCD performs well in simulations and real-life data.
Study on linear regression with dependent covariates, proving universality and error characterization.
problem Linear regression with dependent covariates in high-dimensional settings.
method Analysis of ridge regression performance, Gaussian universality theorem, spectral properties of covariance matrices.
result Asymptotic performance of ridge regression is invariant under non-Gaussian covariates with preserved mean and covariance.
The graphical lasso (glasso) is a widely-used fast algorithm for estimating sparse inverse covariance matrices. The glasso solves an L1 penalized maximum likelihood problem and is available as an R library on CRAN. The output from the glasso, a regularized covariance matrix estimate a sparse inverse covariance matrix e…
The paper refines classical covariance asymptotics using geometric information geometry.
problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.
Proposes FarmHazard model for hazard regression with correlated covariates.
problem Model selection challenges in high-dimensional data with correlated covariates.
method Factor-Augmented Regularized Model for Hazard Regression (FarmHazard) that learns latent factors and idiosyncratic components.
result Proves model selection and estimation consistency under mild conditions.
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multil…
Paper introduces Floer theory for field theories, proving periodic solutions for particle-field systems.
problem Defining Hamiltonian Floer theory for covariant field theories, especially those with degenerate action functionals.
method Regularization procedure to handle degeneracy, leading to Floer curves that converge to periodic solutions.
result Existence of Floer curves and space-time periodic solutions for coupled particle-field systems.
The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distribution…
The paper develops methods to reduce deployment risk under dynamic covariate shifts.
problem Reduction of deployment risk under dynamic covariate shifts.
method Time-domain Poincare inequality and Jacobian-velocity theorem to identify and control directional tangent energy.
result Drift-aligned tangent regularization (DTR) reduces risk volatility and directional gain in low-rank drift regimes.
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.
New method for valid prediction sets in high-dimensional covariate shifts.
problem Valid prediction sets in high-dimensional covariate shifts.
method Likelihood-ratio regularized quantile regression (LR-QR) algorithm.
result LR-QR constructs valid prediction sets with desired coverage in target domain.
Paper estimates GMMs with unknown covariances using sparse regularization.
problem Estimating GMMs with unknown diagonal covariances from samples.
method Employed Beurling-LASSO (BLASSO) for sparse estimation of component means, covariances, and weights.
result Established non-asymptotic recovery guarantees with nearly parametric convergence rates.
Optimally tackles covariate shift in RKHS-based nonparametric regression.
problem Covariate shift in nonparametric regression over RKHS.
method Two families of covariate shift problems defined using likelihood ratios. Minimax rate-optimal estimators for KRR and reweighted KRR.
result KRR is minimax rate-optimal and strictly sub-optimal compared to naive estimator under covariate shift.
New method encodes function preferences into neural nets for better generalization.
problem Challenges in encoding explicit function preferences in neural network training.
method Function-space empirical Bayes (FSEB) regularization.
result FSEB leads to near-perfect semantic shift detection and improved generalization.
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…
We quantify causal bias in continuous treatment settings.
problem Identifying and quantifying causal bias in continuous treatment scenarios.
method Developed a novel characterization of causal bias in structural causal models, proving conditions for zero bias and efficient estimation.
result Causal bias can be estimated efficiently under certain structural equation restrictions, allowing for causal regularization of predictive models.
Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this estimation problem, leading to a tractable class of regularized estimators. Speci…
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample cov…
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…