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We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function…
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…
A variety of interesting parameters may depend on high dimensional regressions. Machine learning can be used to estimate such parameters. However estimators based on machine learners can be severely biased by regularization and/or model…
We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, a multivariate non-linearity is…
Remote sensing imagery offers rich spectral data across extensive areas for Earth observation. Many attempts have been made to leverage these data with transfer learning to develop scalable alternatives for estimating socio-economic…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
The widespread adoption of mobile communication technology has led to a severe shortage of spectrum resources, driving the development of cognitive radio technologies aimed at improving spectrum utilization, with spectrum sensing being the…
Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…
We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
Category imbalance is one of the most popular and important issues in the domain of classification. Emotion classification model trained on imbalanced datasets easily leads to unreliable prediction. The traditional machine learning method…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
Two-phase sampling designs are frequently employed in epidemiological studies and large-scale health surveys. In such designs, certain variables are exclusively collected within a second-phase random subsample of the initial first-phase…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…