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Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…
We develop estimators that improve precision of heterogeneous treatment effect estimates that allow borrowing information from observational studies when the available covariates in each data source do not perfectly match. Standard…
When conducting a randomized controlled trial, it is common to specify in advance the statistical analyses that will be used to analyze the data. Typically these analyses will involve adjusting for small imbalances in baseline covariates.…
Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation…
Causal inference is vital for informed decision-making across fields such as biomedical research and social sciences. Randomized controlled trials (RCTs) are considered the gold standard for internal validity of inferences, whereas…
The Kaczmarz and Gauss-Seidel methods aim to solve a linear $m \times n$ system $\boldsymbol{X} \boldsymbol{\beta} = \boldsymbol{y}$ by iteratively refining the solution estimate; the former uses random rows of $\boldsymbol{X}$ {to update…
Precision medicine is of considerable interest in clinical, academic and regulatory parties. The key to precision medicine is the optimal treatment regime. Recently, Zhou et al. (2017) developed residual weighted learning (RWL) to construct…
Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability…
We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are…
Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying…
Due to spurious correlations, machine learning systems often fail to generalize to environments whose distributions differ from the ones used at training time. Prior work addressing this, either explicitly or implicitly, attempted to find a…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
In this paper, we identify the criteria for the selection of the minimal and most efficient covariate adjustment sets for the regression calibration method developed by Carroll, Rupert and Stefanski (CRS, 1992), used to correct bias due to…
Most of previous machine learning algorithms are proposed based on the i.i.d. hypothesis. However, this ideal assumption is often violated in real applications, where selection bias may arise between training and testing process. Moreover,…
Personalized medicine aims to tailor treatments to individual patients, especially when people respond heterogeneously to therapies. A key objective is to learn individualized treatment rules that recommend optimal treatments from patient…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes…
Learning low-dimensional latent representations is a central topic in statistics and machine learning, and rotation methods have long been used to obtain sparse and interpretable representations. Despite nearly a century of widespread use…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…