Paper develops methods for estimating GLMs and SNR under proportional asymptotics.
problem Estimation of regression coefficients and SNR in high-dimensional GLMs.
method Method-of-Moments type estimators that bypass nuisance function estimation.
result Consistent and asymptotically normal estimators derived for targets of inference.
The paper analyzes how generated data improves adversarial training in high-dimensional regression.
problem Improving adversarial training in high-dimensional regression.
method Theoretical analysis of a two-stage training approach with generated data and pseudo-labels.
result Two-stage adversarial training achieves better performance than ridgeless training in high-dimensional linear regression.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
The paper provides guarantees for high-dimensional DML estimators in observational studies.
problem Estimating treatment effects in observational settings with many covariates.
method Debiased machine learning (DML) with finite-sample guarantees.
result Bounding the deviation of finite-sample distribution from asymptotic Gaussian approximation.
The paper develops methods to estimate the high-dimensional efficient frontier without distributional assumptions.
problem Estimating the mean-variance efficient frontier in high-dimensional settings.
method Random matrix theory and asymptotic analysis for high-dimensional data.
result Developed consistent estimators for the mean, variance, and covariance of the efficient frontier.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
A framework to compare federated learning algorithms in high-dimensional settings.
problem Comparing the performance of federated learning algorithms in high-dimensional settings.
method Formulating federated learning as a multi-criterion objective and analyzing a linear regression model.
result Federated Averaging with simple client fine-tuning achieves the same asymptotic risk as more intricate approaches and outperforms without personalization.
Study on sensor fusion algorithms under high dimensional noise.
problem Behavior of sensor fusion algorithms under high dimensional noise.
method Analysis of NCCA and AD algorithms using Gaussian kernel.
result Robustness of NCCA and AD to high dimensional noise depends on SNR and bandwidth selection.
New test for comparing high-dimensional text data.
problem Testing equality of multinomial distributions in high dimensions.
method Proposed a test statistic with asymptotic normality under null.
result Achieves optimal detection boundary across parameter space.
Study shows double descent curve in high-dimensional linear regression with random projections.
problem Understanding the generalization performance in high-dimensional settings with random projections.
method Fixed prediction problem, ridge regression estimator, minimum norm least-squares fit, random matrix theory, asymptotic equivalents.
result Exhibit a double descent curve for high-dimensional linear regression with random projections.
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…
The paper calculates the value of information in high-dimensional decision making.
problem Determining the value of acquiring new information in high-dimensional decision problems.
method Using tools from sub-Gaussian processes and generic chaining for asymptotic analysis.
result Asymptotic results on the expected value of information as dimensionality increases.
Develops a new method for uncertainty quantification in high-dimensional learning.
problem Challenges in uncertainty quantification in high-dimensional regression or learning problems.
method Data-driven approach for UQ that corrects bias terms from training data.
result Non-asymptotic confidence intervals that avoid overestimating uncertainty.
Paper generalizes Gaussian universality and CGMT to dependent data, impacting data augmentation in high-dimensional logistic regression.
problem Limitation of Gaussian universality and CGMT in handling dependent data.
method Generalizes Gaussian universality and CGMT to dependent data (block dependence, m-dependence, mixing). Establishes a novel CGMT framework.
result Gaussian universality holds for high-dimensional logistic regression under various types of dependence.
Analyzes high-dimensional SGD dynamics using DMFT.
problem Understanding the high-dimensional behavior of multi-pass SGD with small batch sizes.
method Derives DMFT equations for high-dimensional SGD dynamics.
result Proves DMFT equations characterize the asymptotic distribution of SGF parameters.
The paper proves asymptotic normality for multinomial logistic regression on null covariates.
problem Classical asymptotic normality results fail in high-dimensional multinomial logistic models.
method Developed asymptotic normality and chi-square results for multinomial logistic MLE on null covariates.
result Validated new methodology to test feature significance in high-dimensional classification problems.
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.
The paper develops methods to accurately locate change points in high-dimensional mean shift models.
problem Locating change points in high-dimensional mean shift models.
method Locally refitted least squares estimator, component-wise and simultaneous rates of estimation.
result Asymptotic validity of component-wise and simultaneous confidence intervals for change point parameters.
This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.
problem Measurement errors in high-dimensional regression models involving compositional covariates.
method Calibration approach for the linear log-contrast model under lenient sparsity conditions.
result Established asymptotic normality of the estimator for inference.
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al.…
Study examines Lasso performance in high-dimensional MoE models.
problem Estimating MoE models in high-dimensional settings with Lasso.
method Investigates SGMoE models with Lasso regularization under mild assumptions.
result Provides non-asymptotic bounds for Lasso regularization parameter.
High-dimensional inference for sparse spectral precision matrices
problem Inference on the spectral precision matrix at a fixed frequency
method Full likelihood-based inference using neighboring discrete Fourier transforms
result Simultaneous control of regularization, finite-sample truncation, and smoothing biases
Paper addresses high-dimensional linear regression with missing data, proposing efficient and nearly unbiased estimators.
problem High-dimensional linear regression with blockwise missing covariates and partially observed responses.
method Proposes a computationally efficient estimator and nearly unbiased debiased estimators using blockwise imputation and estimating equations.
result Asymptotically valid confidence intervals and statistical tests constructed based on debiased estimators.
New insights into simple kernel smoothing reveal surprising asymptotics.
problem Understanding precise asymptotics of Nadaraya-Watson kernel smoothing.
method Using ideas from the random energy model in statistical physics.
result Sharp asymptotics for the NW predictor on the sphere.
New algorithms improve sampling from complex distributions.
problem Sampling from high-dimensional target distributions with super-linearly growing potentials.
method Proposed aHOLA and aHOLLA algorithms with non-asymptotic convergence bounds.
result Achieved state-of-the-art rates of convergence in non-convex settings.
The paper develops methods for high-dimensional inference in Markov random fields.
problem Statistical inference for high-dimensional Markov random fields.
method Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization.
result The proposed methods achieve ℓ1-consistency and false discovery rate control. Javanmard and Montanari propose a debiased estimator for high-dimensional regression.
problem Bias in high-dimensional regression models.
method Debiased LASSO estimator.
result Debiased LASSO yields asymptotically normal estimators and valid hypothesis tests.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.
The paper analyzes how combining samples from two tasks can improve performance, especially in high dimensions.
problem Understanding when combining samples from two related tasks outperforms learning with one task alone.
method Applying random matrix theory to high-dimensional linear regression, focusing on proportional sample size increases.
result Precise high-dimensional asymptotics for bias and variance of HPS estimator, showing phase transitions in transfer performance.
The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.
problem Understanding the behavior of PLS-SVD in high-dimensional data integration.
method Analysis using random matrix theory and singular value decomposition.
result PLS-SVD exhibits counter-intuitive or limiting behavior in certain regimes and outperforms PCA when detecting common latent subspace.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Transfer learning improves prediction quality in high-dimensional sparse regression.
problem Selecting hyperparameters for Lasso-based transfer learning algorithms.
method Asymptotic analysis using the replica method.
result Ignoring one type of transferred information has minimal impact on performance.
Estimates change point in high-dimensional dynamic graphical models.
problem Detecting change points in high-dimensional graphical models.
method Developed an estimator with Op(ψ−2) rate of convergence, established asymptotic distribution under high-dimensional scaling. result Asymptotic distribution characterized under vanishing and non-vanishing jump size regimes.
Proposes an EM algorithm for high-dimensional Markov-switching VAR models.
problem Estimating regime shifts in high-dimensional time series data.
method Approximate EM algorithm for Markov-switching VAR models.
result Established consistency of the proposed EM algorithm in high dimensions.
Study reveals how high-dimensional models are vulnerable to consistent adversarial attacks.
problem Understanding the vulnerability of high-dimensional linear classifiers to adversarial attacks.
method Introducing a new error metric to quantify model vulnerability, and rigorously characterizing these metrics in asymptotic settings.
result As models become more overparameterized, their vulnerability to label-preserving perturbations increases.
The paper analyzes an ensemble of randomly projected linear discriminants for high-dimensional data.
problem Classification issues in small samples of high-dimensional data.
method Asymptotic analysis using random matrix theory.
result The ensemble offers a performance advantage under certain conditions.
CP-factorization for high-dimensional tensor time series and double projection iterations
problem Identifying and estimating factor loadings in CP decomposition for high-dimensional tensor time series
method One-pass estimation procedure using standard eigen-analysis for matrix constructed based on serial dependence
result Asymptotic properties established under general settings, adapt to sparsity, accommodates weak factors
The study uncovers the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
problem Understanding the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
method Extending the Convex Gaussian Min-Max Theorem to non-Gaussian settings, deriving asymptotic min-max characterizations, and proving asymptotic equivalence of regularizers.
result The projection of the ERM estimator onto a test covariate approximately follows a Gaussian convolution under certain conditions.
Study examines robust regression in high dimensions with heavy-tailed data.
problem Analyzing robust regression in high-dimensional settings with heavy-tailed data.
method Sharp asymptotic characterisation of M-estimators and ridge regression in elliptical distributions.
result Ridge regression is optimal and universal for finite second moments but can decay faster without them.
Study SGD dynamics in high-dimensional models, revealing consistent behavior across different batch sizes and learning rates.
problem Understanding SGD dynamics in high-dimensional multi-index models.
method Asymptotic analysis of SGD, developing mean-field equations and Gaussian diffusion approximations.
result Consistent SGD dynamics across different batch sizes and learning rates, distinct from gradient flow and online SGD.
Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an ℓ1-penalization (Lasso and Adaptive Lasso). …
In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by simultaneously solving two estimating equations---one imposing a zero-bias constrain…
Study on kernel tests for high-dimensional data, focusing on MMD and CLT.
problem Asymptotic behavior of kernel two-sample tests in high dimensions and large samples.
method Maximum mean discrepancy (MMD) with isotropic kernels, deriving asymptotic expansions and CLT.
result Interplay between moment discrepancy and dimension-and-sample orders in kernel tests.
Unified derivation of high-dimensional linear models using stochastic gradient descent.
problem Performance analysis of high-dimensional linear models trained with stochastic gradient descent.
method Derivation of a deterministic equivalence for the two-point function of a random matrix resolvent.
result Unified understanding of model performance including previously known and novel results.
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its imp…
Study examines influence diagnostics in high-dimensional M-estimation.
problem Understanding influence diagnostics in high-dimensional settings.
method Characterized the distribution of leave-one-out influences in high-dimensional Gaussian M-estimation.
result The distribution of influences converges to a limiting measure in high-dimensional settings.
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…