More for less: predicting and maximizing genomic variant discovery via Bayesian nonparametrics
以更少资源发现更多基因变异:贝叶斯非参数预测与优化AI 解读 ↓
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以更少资源发现更多基因变异:贝叶斯非参数预测与优化AI 解读 ↓
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Summary While the cost of sequencing genomes has decreased dramatically in recent years, this expense often remains nontrivial. Under a fixed budget, scientists face a natural trade-off between quantity and quality: spending resources to sequence a greater number of genomes or spending resources to sequence genomes with increased accuracy. Our goal is to find the optimal allocation of resources between quantity and quality. Optimizing resource allocation promises to reveal as many new variations in the genome as possible. We introduce a Bayesian nonparametric methodology to predict the number of new variants in a follow-up study based on a pilot study. When experimental conditions are kept constant between the pilot and follow-up, we find that our prediction is competitive with the best existing methods. Unlike current methods, though, our new method allows practitioners to change experimental conditions between the pilot and the follow-up. We demonstrate how this distinction allows our method to be used for more realistic predictions and for optimal allocation of a fixed budget between quality and quantity. We validate our method on cancer and human genomics data.
Principal stratification (PS) is a commonly used approach for understanding the mechanisms through which a treatment affects an outcome. The goal of this work is to extend the PS framework to studies with continuous treatments, which introduces a number of both challenges and opportunities in terms of defining causal effects and performing inference. This manuscript provides multiple key methodological contributions: 1) we introduce principal causal estimands for continuous…
多元Lévy自适应B样条回归
We propose Multivariate Lévy Adaptive B-Spline Regression (MLABS), a Bayesian nonparametric regression model designed to capture nonlinear effects, interactions, and locally varying features of multivariate functions. MLABS represents the regression function as a random sum of low-order tensor-product B-spline basis functions under a finite Lévy random measure prior. The resulting representation adapts to the complexity and local structure of the regression function while…
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
估计纵向因果剂量反应关系的贝叶斯框架
Existing causal methods for time-varying exposure and time-varying confounding focus on estimating the average causal effect of a time-varying binary treatment on an end-of-study outcome, offering limited tools for characterizing marginal causal dose-response relationships under continuous exposures. We propose a scalable, nonparametric Bayesian framework for estimating marginal longitudinal causal dose-response functions with repeated outcome measurements. Our approach…
贝叶斯算子学习:高斯先验下后验存在性与点估计收敛
We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map $g_0:\mathcal{X}\to\mathcal{Y}$ between separable Hilbert spaces, we study the recovery of $g_0$ from $n\in\mathbb{N}$ noisy input-output pairs $(\boldsymbol{X},\boldsymbol{Z})=(X_i,Z_i)_{i=1}^n$ with $Z_i= g_0 (X_i ) + E_i$. Here the $X_i\in\mathcal{X}$ are randomly drawn 'design' points in a compact subset of $\mathcal X$, and the $E_i$ are assumed to be i.i.d.…
面向高维数据的残差树高斯过程建模框架
With the advance of measurement technologies and increasing computing power, large spatial data with heterogeneous structures are often collected over high-dimensional domains. Existing Gaussian process (GP) models and computational strategies are often inadequate for analyzing such datasets in multi-dimensional domains. To address these challenges, we develop a Bayesian residual tree GP methodology called ResTGP for large spatial data with potentially heterogeneous…