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Multivariable Mendelian Randomization (MVMR) estimates the direct causal effects of multiple risk factors on an outcome using genetic variants as instruments. The growing availability of summary-level genetic data has created opportunities…

A major limitation of machine learning (ML) prediction models is that they recover associational, rather than causal, predictive relationships between variables. In high-stakes automation applications of ML this is problematic, as the model…

Sparse Discrete Empirical Interpolation Method (S-DEIM) was recently proposed for state estimation in dynamical systems when only a sparse subset of the state variables can be observed. The S-DEIM estimate involves a kernel vector whose…

Mendelian randomization (MR) uses genetic variants as instrumental variables to make causal claims. Standard MR approaches typically report a single population-averaged estimate, limiting their ability to explore effect heterogeneity or…

Sensitivity analysis is important to assess the impact of unmeasured confounding in causal inference from observational studies. The marginal sensitivity model (MSM) provides a useful approach in quantifying the influence of unmeasured…

Multiscale entropy (MSE) is a widely-used tool to analyze biomedical signals. It was proposed to overcome the deficiencies of conventional entropy methods when quantifying the complexity of time series. However, MSE is undefined for very…

The estimation of causal effects with observational data continues to be a very active research area. In recent years, researchers have developed new frameworks which use machine learning to relax classical assumptions necessary for the…

Several works have proven that finetuning is an applicable approach for debiasing contextualized word embeddings. Similarly, discrete prompts with semantic meanings have shown to be effective in debiasing tasks. With unfixed mathematical…

In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation…

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Micro-randomized trials (MRTs) are increasingly used to evaluate mobile health interventions with binary proximal outcomes. Standard inverse probability weighting (IPW) estimators are unbiased but unstable in small samples or under extreme…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Mendelian randomization (MR) is a powerful approach to examine the causal relationships between health risk factors and outcomes from observational studies. Due to the proliferation of genome-wide association studies (GWASs) and abundant…

In modern large-scale observational studies, data collection constraints often result in partially labeled datasets, posing challenges for reliable causal inference, especially due to potential labeling bias and relatively small size of the…

Structural Nested Mean Models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at pre-fixed time points for all subjects, which,…

Unlike parametric regression, machine learning (ML) methods do not generally require precise knowledge of the true data generating mechanisms. As such, numerous authors have advocated for ML methods to estimate causal effects.…

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…

In many observational studies, researchers are often interested in studying the effects of multiple exposures on a single outcome. Standard approaches for high-dimensional data such as the lasso assume the associations between the exposures…

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…