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Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
We propose one-at-a-time knockoffs (OATK), a new methodology for detecting important explanatory variables in linear regression models while controlling the false discovery rate (FDR). For each explanatory variable, OATK generates a…
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for…
An important problem in machine learning and statistics is to identify features that causally affect the outcome. This is often impossible to do from purely observational data, and a natural relaxation is to identify features that are…
We tackle the problem of selecting from among a large number of variables those that are 'important' for an outcome. We consider situations where groups of variables are also of interest in their own right. For example, each variable might…
More than 10.7% of people aged 65 and older are affected by Alzheimer's disease. Early diagnosis and treatment are crucial as most Alzheimer's patients are unaware of having it until the effects become detrimental. AI has been known to use…
Alzheimer's disease detection requires expensive neuroimaging or invasive procedures, limiting accessibility. This study explores whether deep learning can enable non-invasive Alzheimer's disease detection through handwriting analysis.…
The current state-of-the-art deep neural networks (DNNs) for Alzheimer's Disease diagnosis use different biomarker combinations to classify patients, but do not allow extracting knowledge about the interactions of biomarkers. However, to…
Large-scale hypothesis testing is central to modern science, where controlling the False Discovery Rate (FDR) has become the standard approach to managing false positives across many simultaneous tests. Hypotheses rarely exist in isolation;…
The recent proliferation of high-dimensional data, such as electronic health records and genetics data, offers new opportunities to find novel predictors of outcomes. Presented with a large set of candidate features, interest often lies in…
Thalamic alterations are relevant to many neurological disorders including Alzheimer's disease, Parkinson's disease and multiple sclerosis. Routine interventions to improve symptom severity in movement disorders, for example, often consist…
Although Alzheimer's disease detection via MRIs has advanced significantly thanks to contemporary deep learning models, challenges such as class imbalance, protocol variations, and limited dataset diversity often hinder their generalization…
We consider problems where many, somewhat redundant, hypotheses are tested and we are interested in reporting the most precise rejections, with false discovery rate (FDR) control. This is the case, for example, when researchers are…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
The knockoff filter is a recent false discovery rate (FDR) control method for high-dimensional linear models. We point out that knockoff has three key components: ranking algorithm, augmented design, and symmetric statistic, and each…
Multiple hypothesis testing has been widely applied to problems dealing with high-dimensional data, e.g., selecting significant variables and controlling the selection error rate. The most prevailing measure of error rate used in the…
The knockoffs is a recently proposed powerful framework that effectively controls the false discovery rate (FDR) for variable selection. However, none of the existing knockoff solutions are directly suited to handle multivariate or…
We consider controlling the false discovery rate for testing many time series with an unknown cross-sectional correlation structure. Given a large number of hypotheses, false and missing discoveries can plague an analysis. While many…
Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been…