Bayesian Approximate Kernel Regression with Variable Selection

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coefficients. In this paper, we propose a novel framework that provides an effect size analog of each explanatory variable for Bayesian kernel regression models when the kernel is shift-invariant --- for example, the Gaussian kernel. We use function analytic properties of shift-invariant reproducing kernel Hilbert spaces (RKHS) to define a linear vector space that: (i) captures nonlinear structure, and (ii) can be projected onto the original explanatory variables. The projection onto the original explanatory variables serves as an analog of effect sizes. The specific function analytic property we use is that shift-invariant kernel functions can be approximated via random Fourier bases. Based on the random Fourier expansion we propose a computationally efficient class of Bayesian approximate kernel regression (BAKR) models for both nonlinear regression and binary classification for which one can compute an analog of effect sizes. We illustrate the utility of BAKR by examining two important problems in statistical genetics: genomic selection (i.e. phenotypic prediction) and association mapping (i.e. inference of significant variants or loci). State-of-the-art methods for genomic selection and association mapping are based on kernel regression and linear models, respectively. BAKR is the first method that is competitive in both settings.Comment: 22 pages, 3 figures, 3 tables; theory added; new simulations presented; references adde

Stem Cells and Extracellular Vesicles: Biological Regulators of Physiology and Disease

This is an extraordinary time in cell biology with evolving data pushing a reconsideration of the stability of cell systems and the regulatory mechanisms underlying cell phenotypes, especially the functional cell phenotypes. In this chapter, we will explore new insights into stem cell and extracellular vesicle biology with a focus on the role of extracellular vesicles in normal stem cell physiology as well as in various disease states. Extracellular vesicles (EVs) are being recognized as influential mediators of cellular function and potential experimental therapeutic strategies for a number of disorders outlined in this review. An evolving paradigm indicates a dynamic flux of EV populations within these disease states. We conclude our discussion of EV by extending our knowledge of robust EV biology toward disease detection and prognostication. Characterizing the biophysical and functional changes of vesicles amid disease progression or regression enables investigators to merge this information flux with existing deep learning computational and statistical techniques—allowing knowledge to be abstracted from large data sets profiling the biology of EVs within various disease states. Understanding how EV population shifts represent disease regression or progression creates paramount potential for EVs as salient and clinically relevant diagnostic and prognosticating tools

Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two parametric algorithms for testing hypotheses on random shapes. Simulation studies are presented to validate our mathematical derivations and to compare our algorithms with state-of-the-art methods to demonstrate the utility of our proposed framework. As real applications, we analyze a data set of mandibular molars from four genera of primates and show that our algorithms have the power to detect significant shape differences that recapitulate known morphological variation across suborders. Altogether, our discussions bridge the following fields: algebraic and computational topology, probability theory and stochastic processes, Sobolev spaces and functional analysis, statistical inference, and geometric morphometrics.Comment: 99 page

Should I Stop or Should I Go: Early Stopping with Heterogeneous Populations

Randomized experiments often need to be stopped prematurely due to the treatment having an unintended harmful effect. Existing methods that determine when to stop an experiment early are typically applied to the data in aggregate and do not account for treatment effect heterogeneity. In this paper, we study the early stopping of experiments for harm on heterogeneous populations. We first establish that current methods often fail to stop experiments when the treatment harms a minority group of participants. We then use causal machine learning to develop CLASH, the first broadly-applicable method for heterogeneous early stopping. We demonstrate CLASH's performance on simulated and real data and show that it yields effective early stopping for both clinical trials and A/B tests.Comment: NeurIPS 2023 (spotlight

An Open-Access Model for Parkinson's Disease Progression

Using machine learning, we developed a statistical progression model of early Parkinson’s disease that accounts for medication effects and variability within and between subjects and medication effects. The resulting personalized model can be used to quantitatively describe clinical visits and will be made public, enabling replication and reproducibility

A preliminary analysis of educational needs for Navy health care executives

The Bureau of Medicine and Surgery and the Naval Postgraduate School have initiated the development of an innovative program in management education for senior Naval health care executives. The first phase of the development was based on interviews with 80 executives to determine their perceptions of the skills needed to effectively manage military treatment facilities. The interview findings became the basis of a survey-based needs analysis, which is the focus of this report. Data analyses were focused on the requirements for specific management skill areas, needs for education in these domanins, and how these perceptions differ as a function of rank, position, and corps of the respondents.Bureau of Medicine and Surgery, Department of the Navyhttp://archive.org/details/preliminaryanaly00crawN0619A93P000014Approved for public release; distribution is unlimited