Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis.

Factor analysis provides a canonical framework for imposing lower-dimensional structure such as sparse covariance in high-dimensional data. High-dimensional data on the same set of variables are often collected under different conditions, for instance in reproducing studies across research groups. In such cases, it is natural to seek to learn the shared versus condition-specific structure.

Product Centred Dirichlet Processes for Bayesian Multiview Clustering.

While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables.

Nonparametric IPSS: fast, flexible feature selection with false discovery control.

Motivation: Feature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery control, or (iii) identify few true positives.

Results: We introduce a general feature selection method with finite-sample false discovery control based on applying integrated path stability selection (IPSS) to arbitrary feature importance scores.

LOW-RANK LONGITUDINAL FACTOR REGRESSION WITH APPLICATION TO CHEMICAL MIXTURES.

Developmental epidemiology commonly focuses on assessing the association between multiple early life exposures and childhood health. Statistical analyses of data from such studies focus on inferring the contributions of individual exposures, while also characterizing time-varying and interacting effects. Such inferences are made more challenging by correlations among exposures, nonlinearity, and the curse of dimensionality.

Radial Neighbors for Provably Accurate Scalable Approximations of Gaussian Processes.

In geostatistical problems with massive sample size, Gaussian processes can be approximated using sparse directed acyclic graphs to achieve scalable computational complexity. In these models, data at each location are typically assumed conditionally dependent on a small set of parents which usually include a subset of the nearest neighbors. These methodologies often exhibit excellent empirical performance, but the lack of theoretical validation leads to unclear guidance in specifying the underlying graphical model and sensitivity to graph choice.

Bayesian semiparametric inference in longitudinal metabolomics data.

The article is motivated by an application to the EarlyBird cohort study aiming to explore how anthropometrics and clinical and metabolic processes are associated with obesity and glucose control during childhood. There is interest in inferring the relationship between dynamically changing and high-dimensional metabolites and a longitudinal response. Important aspects of the analysis include the selection of the important set of metabolites and the accommodation of missing data in both response and covariate values.

Brain network fingerprints of Alzheimer's disease risk factors in mouse models with humanized APOE alleles.

Alzheimer's disease (AD) presents complex challenges due to its multifactorial nature, poorly understood etiology, and late detection. The mechanisms through which genetic and modifiable risk factors influence disease susceptibility are under intense investigation, with APOE being the major genetic risk factor for late onset AD. Yet the impact of unique risk factors on brain networks is difficult to disentangle, and their interactions remain unclear.

APOE, Immune Factors, Sex, and Diet Interact to Shape Brain Networks in Mouse Models of Aging.

Unlabelled: Alzheimer's disease (AD) presents complex challenges due to its multifactorial nature, poorly understood etiology, and late detection. The mechanisms through which genetic, fixed and modifiable risk factors influence susceptibility to AD are under intense investigation, yet the impact of unique risk factors on brain networks is difficult to disentangle, and their interactions remain unclear. To model multiple risk factors including APOE genotype, age, sex, diet, and immunity we leveraged mice expressing the human APOE and NOS2 genes, conferring a reduced immune response compared to mouse Nos2.

Spatial meshing for general Bayesian multivariate models.

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial dependence is encoded as a latent Gaussian process (GP) in the increasingly common large scale data settings on which we focus. The scenario worsens in non-Gaussian models because the reduced analytical tractability leads to additional hurdles to computational efficiency. In this article, we introduce Bayesian models of spatially referenced data in which the likelihood or the latent process (or both) are not Gaussian.

Ellipsoid fitting with the Cayley transform.

We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always returns elliptic solutions, and can fit arbitrary ellipsoids. It also significantly outperforms other fitting methods when data are not uniformly distributed over the surface of an ellipsoid.

Bayesian inference on high-dimensional multivariate binary responses.

It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algorithms for fitting such models face issues in scaling up to high dimensions due to the intractability of the likelihood, involving an integral over a multivariate normal distribution having no analytic form.

A generalized Bayes framework for probabilistic clustering.

Loss-based clustering methods, such as k-means clustering and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative approach, but such methods face computational problems and are highly sensitive to the choice of kernel.

Explaining transmission rate variations and forecasting epidemic spread in multiple regions with a semiparametric mixed effects SIR model.

The transmission rate is a central parameter in mathematical models of infectious disease. Its pivotal role in outbreak dynamics makes estimating the current transmission rate and uncovering its dependence on relevant covariates a core challenge in epidemiological research as well as public health policy evaluation. Here, we develop a method for flexibly inferring a time-varying transmission rate parameter, modeled as a function of covariates and a smooth Gaussian process (GP).

PPA: Principal parcellation analysis for brain connectomes and multiple traits.

Our understanding of the structure of the brain and its relationships with human traits is largely determined by how we represent the structural connectome. Standard practice divides the brain into regions of interest (ROIs) and represents the connectome as an adjacency matrix having cells measuring connectivity between pairs of ROIs. Statistical analyses are then heavily driven by the (largely arbitrary) choice of ROIs.

Bayesian matrix completion for hypothesis testing.

We aim to infer bioactivity of each chemical by assay endpoint combination, addressing sparsity of toxicology data. We propose a Bayesian hierarchical framework which borrows information across different chemicals and assay endpoints, facilitates out-of-sample prediction of activity for chemicals not yet assayed, quantifies uncertainty of predicted activity, and adjusts for multiplicity in hypothesis testing. Furthermore, this paper makes a novel attempt in toxicology to simultaneously model heteroscedastic errors and a nonparametric mean function, leading to a broader definition of activity whose need has been suggested by toxicologists.

Mutual information: Measuring nonlinear dependence in longitudinal epidemiological data.

Given a large clinical database of longitudinal patient information including many covariates, it is computationally prohibitive to consider all types of interdependence between patient variables of interest. This challenge motivates the use of mutual information (MI), a statistical summary of data interdependence with appealing properties that make it a suitable alternative or addition to correlation for identifying relationships in data. MI: (i) captures all types of dependence, both linear and nonlinear, (ii) is zero only when random variables are independent, (iii) serves as a measure of relationship strength (similar to but more general than R2), and (iv) is interpreted the same way for numerical and categorical data.

Escaping The Curse of Dimensionality in Bayesian Model-Based Clustering.

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too few clusters. This article explains this behavior by studying the random partition posterior in a non-standard setting with a fixed sample size and increasing data dimensionality.

Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data.

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters.

Bayesian Modeling of Sequential Discoveries.

We aim at modeling the appearance of distinct tags in a sequence of labeled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarized via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects.

Corrigendum: Absolute winding number differentiates mouse spatial navigation strategies with genetic risk for Alzheimer's disease.

[This corrects the article DOI: 10.3389/fnins.2022.

BAYESIAN SEMIPARAMETRIC LONG MEMORY MODELS FOR DISCRETIZED EVENT DATA.

We introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed methodology is motivated by a study of bird vocalizations in the Amazon rain forest; the timings of vocalizations exhibit self-similarity and long range dependence. This rules out Poisson process based models where the rate function itself is not long range dependent.

EXTENDED STOCHASTIC BLOCK MODELS WITH APPLICATION TO CRIMINAL NETWORKS.

Reliably learning group structures among nodes in network data is challenging in several applications. We are particularly motivated by studying covert networks that encode relationships among criminals. These data are subject to measurement errors, and exhibit a complex combination of an unknown number of core-periphery, assortative and disassortative structures that may unveil key architectures of the criminal organization.

Identifying vulnerable brain networks associated with Alzheimer's disease risk.

The selective vulnerability of brain networks in individuals at risk for Alzheimer's disease (AD) may help differentiate pathological from normal aging at asymptomatic stages, allowing the implementation of more effective interventions. We used a sample of 72 people across the age span, enriched for the APOE4 genotype to reveal vulnerable networks associated with a composite AD risk factor including age, genotype, and sex. Sparse canonical correlation analysis (CCA) revealed a high weight associated with genotype, and subgraphs involving the cuneus, temporal, cingulate cortices, and cerebellum.

Spatial Multivariate Trees for Big Data Bayesian Regression.

High resolution geospatial data are challenging because standard geostatistical models based on Gaussian processes are known to not scale to large data sizes. While progress has been made towards methods that can be computed more efficiently, considerably less attention has been devoted to methods for large scale data that allow the description of complex relationships between several outcomes recorded at high resolutions by different sensors. Our Bayesian multivariate regression models based on spatial multivariate trees (SpamTrees) achieve scalability via conditional independence assumptions on latent random effects following a treed directed acyclic graph.