The paper improves machine learning for heavy-tailed panel data.
problem Improving estimates for financial and economic data with fat tails.
method Sparse-group LASSO regularization and Fuk-Nagaev concentration inequality.
result Oracle inequalities for panel data estimators.
Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and β-mixing condition to establish consistency of lasso when data comes from a $β…
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of in…
Paper introduces machine learning for time series data, improving nowcasting accuracy.
problem Improving accuracy in nowcasting US GDP growth using machine learning.
method Sparse-group LASSO estimator for high-dimensional time series data, considering different sampling frequencies and financial/macroeconomic data tail properties.
result Sparse-group LASSO outperforms unstructured LASSO in nowcasting US GDP growth.
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
problem Sparse learning for high-dimensional heavy-tailed locally stationary time series.
method Additive modeling with kernel smoothing, sparsity-inducing penalized estimation.
result Prediction-error bounds and convergence rates for different sparsity structures.
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.
problem Challenges of classical Lasso in handling heavy-tailed noise and outliers.
method Data-augmented soft-thresholding with Student's t-distribution loss.
result Heavy Lasso achieves comparable rates to Huber loss under theoretical bounds.
The paper proves concentration inequalities for diffusion processes.
problem Proving concentration inequalities for diffusion processes.
method Analysis via the Poisson equation for a broad class of subexponentially ergodic processes.
result Demonstrates power of concentration inequalities in validating conditions for Lasso estimation and sampling algorithms.
Study high-dimensional Granger causality tests for VIX and financial news.
problem Testing Granger causality in high-dimensional time series data.
method Regularized regressions, sparse-group LASSO, HAC estimation of variance.
result Valid time series inference for Granger causality tests in high dimensions.
New concentration inequalities for tensors with heavy-tailed coefficients.
problem Developing bounds for Euclidean functions of tensors with sub-Weibull distributions.
method Extending concentration inequalities to sub-Weibull random tensors, using new inequalities for heavy-tailed random variables and martingale analysis.
result Established a phase transition between sub-gaussian and heavy-tailed regimes for Euclidean functions of tensors.
Study LASSO for high-dimensional VAR models with weakly dependent innovations.
problem Understanding sparse regularization in high-dimensional VAR models with weakly dependent innovations.
method LASSO estimation for weakly sparse VAR models with heavy tailed innovations, under L1 mixingale condition. result Oracle properties of LASSO estimation in high-dimensional VAR models with weakly dependent innovations.
Predictive analytics uses proxy data when true data is scarce, but this can lead to errors.
problem Bias in using proxy data for predictive analytics.
method Proposes a two-step estimator using high-dimensional statistics to combine proxy and true data.
result Achieves better predictive accuracy with less true data.
New weighted Lasso estimates improve logistic regression performance with measurement error.
problem Improper Lasso estimates in sparse logistic regression with equal penalties.
method Proposed weighted Lasso estimates using McDiarmid inequality for non-asymptotic oracle inequalities.
result Finite sample behavior illustrated by non-asymptotic oracle inequalities for estimation and prediction errors.
New clustering method handles heavy-tailed, asymmetric data.
problem Robust clustering of high-dimensional, heavy-tailed data.
method Sparse mixture of generalized hyperbolic distributions with gamma-lasso penalty.
result Improved clustering performance on heavy-tailed data.
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample …
Upper bounds for CV errors apply to lasso and other models.
problem Bounding CV errors for lasso and similar models.
method Rademacher complexity and Orlicz-Ψν norm. result Upper bounds are tight and stable for lasso.
New tail inequalities for sums of random matrices without matrix-dimension terms.
problem Tail behavior of matrix functions in high-dimensional settings.
method Developed new tail inequalities for matrix sums, independent of matrix dimension.
result Tail inequalities for various matrix functions without matrix-dimension terms.
The paper improves count data regression models for overdispersed data.
problem Improving regression models for overdispersed count data.
method Double ℓ1-regularized negative binomial regressions. result Oracle inequalities and consistency for Lasso estimators of partial regression coefficients.
Proposes a robust method for high-dimensional linear models.
problem Inference in high-dimensional settings with heavy-tailed errors and clustered data.
method Residual randomization procedure for Lasso-based inference.
result Outperforms state-of-the-art methods in challenging settings.
Paper supports robust estimation in regression with heavy-tailed errors.
problem Support estimation in high-dimensional heteroscedastic mean regression.
method Use of Huber loss function and adaptive LASSO penalty for robust estimation.
result Sign-consistency and optimal rates of convergence in ℓ∞ norm. We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…
We consider the problem of binary classification where one can, for a particular cost, choose not to classify an observation. We present a simple proof for the oracle inequality for the excess risk of structural risk minimizers using a lasso type penalty.
New RDP guarantees for heavy-tailed SDEs and SGD.
problem Characterizing differential privacy for heavy-tailed noise in learning algorithms.
method Rényi flow computations and fractional Poincaré inequalities.
result First RDP guarantees for heavy-tailed SDEs with weaker dependence on dimension.
We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We p…
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a deterministic choice of the regularization parameter. These bounds tend to zero if …
Paper simplifies concentration inequalities for easier probabilistic analysis.
problem Complexity in probabilistic analysis of random variables.
method Compact notations for concentration inequalities.
result Simplified expressions for typical sizes and tails of random variables.
A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is …
Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for a certain value of the regularization parameter, is a technique for improving t…
The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such…
Proposes a method to improve pWCET estimation for heavy-tailed distributions.
problem Improving pWCET estimation for heavy-tailed distributions in real-time systems.
method Incorporates saturating functions into Chebyshev's inequality to mitigate the influence of large outliers.
result Achieves safe and tighter bounds for heavy-tailed distributions.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…
Improves robustness of high-dimensional regression with rank objective and group lasso regularization.
problem Heavy-tailed noise and outliers in high-dimensional regression.
method Non-smooth Wilcoxon score based rank objective, group lasso regularization, data-driven tuning rule, proximal augmented Lagrangian method.
result Robust estimator with finite-sample error bound and efficient computational method.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
problem Sampling from heavy-tailed distributions efficiently.
method Transformed Unadjusted Langevin Algorithm on specific transformations.
result Polynomial-order oracle complexities for certain heavy-tailed densities.
This paper extends the convergence analysis of Langevin Monte Carlo beyond Poincaré inequalities.
problem Analyzing convergence of Langevin Monte Carlo under various functional inequalities.
method Establishing upper and lower bounds for Langevin diffusions and LMC under weak Poincaré inequalities.
result Explicitly quantifies the effect of the initializer on the performance of LMC algorithm.
Soft diamond regularizers improve deep learning performance and sparsity.
problem Improving deep learning performance and sparsity of trained weights.
method New soft diamond synaptic weight priors based on thick-tailed symmetric alpha stable probability curves.
result Soft diamond regularizers outperform state-of-the-art methods in deep learning tasks.
Sharp concentration inequalities for sub-Orlicz random variables with phase transition at α=2.
problem Developing concentration inequalities for sub-Orlicz random variables with phase transition.
method New theoretical analysis framework involving variance and min/max functions of Orlicz tails.
result Sharp concentration inequalities with phase transition at α=2 for sub-Orlicz random variables.
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
problem Heavy-tailed data in modern learning pipelines.
method Tail-dependent information-theoretic framework for sub-Weibull data.
result Sharp generalization bounds for heavy-tailed data.
We improve bounds for stochastic processes, especially those with heavy tails.
problem Bounding the concentration of sub-ψ processes with heavy tails. method Variational approach to concentration, focusing on sub-Gaussian and other tail conditions.
result First dimension-free self-normalized empirical Bernstein inequality.
Sharp concentration results for sums of heavy-tailed random variables.
problem Analyzing sums of independent heavy-tailed random variables.
method Using concentration inequalities and large deviation principles for distributions satisfying specific tail bounds.
result Sharp concentration inequalities and large deviation results for sums of heavy-tailed random variables.
Ridge regression performs optimally in noisy environments with heavy-tailed distributions.
problem Performance of ridge regression in noisy environments with heavy-tailed noise.
method Established excess risk bounds using integral operator framework and Fuk-Nagaev inequality.
result Ridge regression achieves optimal convergence rates under heavy-tailed noise, demonstrating robustness.
PANDA augments data to regularize GLM estimation and inference.
problem Regularizing estimation and inference in GLMs with noisy data.
method Iteratively optimizes augmented noise data to converge to regularized model estimates.
result Established convergence and asymptotic distributions for regularized parameters.
The paper examines how to protect LASSO-based feature selection from adversarial attacks.
problem Adversarial attacks on LASSO-based feature selection.
method Formulated as a bi-level optimization problem, reformulated LASSO with linear inequality constraints, solved using interior-point method, and modified using projected gradient descent.
result Demonstrated the effectiveness of the proposed method in protecting LASSO-based feature selection from adversarial attacks.
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate to each other. The restricted eigenvalue condition (Bickel et al., 2009) or the…
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.
New method corrects selection bias in post-selective inference for Group LASSO.
problem Inference after Group LASSO selection is unreliable.
method Develops a consistent, post-selective Bayesian method to adjust for selection bias.
result Corrects bias in recovering effects of selected variables.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
New proof shows faster convergence rate for robust estimation with Lasso in adversarially contaminated outputs.
problem Robust estimation of parameters in the presence of adversarial output contamination.
method Extended Lasso with Huber loss function and L1 penalty, focusing on specific properties of the Huber function. result Same convergence rate as Dalalyan and Thompson (2019), but with a different proof.