Related papers: High-dimensional Adaptive Minimax Sparse Estimatio…
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear…
If error distribution has heteroscedasticity, it voliates the assumption of linear regression. Expectile regression is a powerful tool for estimating the conditional expectiles of a response variable in this setting. Since multiple levels…
Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…
We propose and analyze a variant of Sparse Polyak for high dimensional M-estimation problems. Sparse Polyak proposes a novel adaptive step-size rule tailored to suitably estimate the problem's curvature in the high-dimensional setting,…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications including, e.g. heritability estimation in bioinformatics. One commonly used estimator, usually referred to as…
Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…
This paper considers the sample-efficiency of preference learning, which models and predicts human choices based on comparative judgments. The minimax optimal estimation error rate $\Theta(d/n)$ in classical estimation theory requires that…
Many areas of research are characterised by the deluge of large-scale highly-dimensional time-series data. However, using the data available for prediction and decision making is hampered by the current lag in our ability to uncover and…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…
Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as…
We propose an approach to better inform treatment decisions at an individual level by adapting recent advances in average treatment effect estimation to conditional average treatment effect estimation. Our work is based on doubly robust…
During an epidemic outbreak, individuals often modify their behavior in response to global prevalence cues, using spatially mediated adaptations such as reduced mobility or transmission range. In this work, we investigate the impact of…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
Existing high-dimensional statistical methods are largely established for analyzing individual-level data. In this work, we study estimation and inference for high-dimensional linear models where we only observe "proxy data", which include…