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A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
Model averaging is an important alternative to model selection with attractive prediction accuracy. However, its application to high-dimensional data remains under-explored. We propose a high-dimensional model averaging method via…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are…
We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
As medical devices become more complex, they routinely collect extensive and complicated data. While classical regressions typically examine the relationship between an outcome and a vector of predictors, it becomes imperative to identify…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is crucial for variable selection and interpretability of deep…