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The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysis-of-variance dimensional…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
Alzheimer's disease (AD) is known as one of the major causes of dementia and is characterized by slow progression over several years, with no treatments or available medicines. In this regard, there have been efforts to identify the risk of…
An important line of research in the field of explainability is to extract a small subset of crucial rationales from the full input. The most widely used criterion for rationale extraction is the maximum mutual information (MMI) criterion.…
In our contemporary era, meteorological weather forecasts increasingly incorporate ensemble predictions of visibility - a parameter of great importance in aviation, maritime navigation, and air quality assessment, with direct implications…
The proliferation of healthcare data has brought the opportunities of applying data-driven approaches, such as machine learning methods, to assist diagnosis. Recently, many deep learning methods have been shown with impressive successes in…
Regressions are commonly used in environmental science and economics to identify causal or associative relationships between variables. In these settings, remote sensing-derived map products increasingly serve as sources of variables,…
Data augmentation is essential when applying Machine Learning in small-data regimes. It generates new samples following the observed data distribution while increasing their diversity and variability to help researchers and practitioners…
Multiple imputation (MI) is a method for repairing and analyzing data with missing values. MI replaces missing values with a sample of random values drawn from an imputation model. The most popular form of MI, which we call posterior draw…
Biomedical researchers usually study the effects of certain exposures on disease risks among a well-defined population. To achieve this goal, the gold standard is to design a trial with an appropriate sample from that population. Due to the…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
Clinical prediction models must be developed using sufficiently large datasets to minimise overfitting and ensure robust predictive performance. Existing sample size calculations assume complete predictor data for all included participants,…
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…
Missing data is a major challenge in clinical research. In electronic medical records, often a large fraction of the values in laboratory tests and vital signs are missing. The missingness can lead to biased estimates and limit our ability…
Prediction-Powered Inference (PPI) is a powerful framework for enhancing statistical estimates by combining limited gold-standard data with machine learning (ML) predictions. While prior work has demonstrated PPI's benefits for individual…
Predictive mean matching (PMM) is a popular imputation strategy that imputes missing values by borrowing observed values from other cases with similar expectations. We show that, unlike other imputation strategies, PMM is not guaranteed to…
Machine Learning (ML) has emerged as a promising approach in healthcare, outperforming traditional statistical techniques. However, to establish ML as a reliable tool in clinical practice, adherence to best practices regarding data…
In multivariate nonparametric regression the additive models are very useful when a suitable parametric model is difficult to find. The backfitting algorithm is a powerful tool to estimate the additive components. However, due to complexity…
Climate change impact studies inform policymakers on the estimated damages of future climate change on economic, health and other outcomes. In most studies, an annual outcome variable is observed, e.g. agricultural yield, along with a…
Fueled by the call for formative assessments, diagnostic classification models (DCMs) have recently gained popularity in psychometrics. Despite their potential for providing diagnostic information that aids in classroom instruction and…