arXiv subjects

Shangsi Wang

Publications and source records attributed to Shangsi Wang.

4 recordsLinked to original sources

arXiv2024

Statistical Analysis of Data Repeatability Measures

The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the characteristics of the data which are repeatable -- the aspects of the data that are able to be identified under a duplicated analysis. Conflictingly, the utility of traditional repeatability measures, such as the intraclass correlation coefficient, under these settings is limited. In recent work, novel data repeatability measures have been introduced in the context where a set of subjects are measured twice or more, including: fingerprinting, rank sums, and generalizations of the intraclass correlation coefficient. However, the relationships between, and the best practices among these measures remains largely unknown. In this manuscript, we formalize a novel repeatability measure, discriminability. We show that it is deterministically linked with the correlation coefficient under univariate random effect models, and has desired property of optimal accuracy for inferential tasks using multivariate measurements. Additionally, we overview and systematically compare repeatability statistics using both theoretical results and simulations. We show that the rank sum statistic is deterministically linked to a consistent estimator of discriminability. The power of permutation tests derived from these measures are compared numerically under Gaussian and non-Gaussian settings, with and without simulated batch effects. Motivated by both theoretical and empirical results, we provide methodological recommendations for each benchmark setting to serve as a resource for future analyses. We believe these recommendations will play an important role towards improving repeatability in fields such as functional magnetic resonance imaging, genomics, pharmacology, and more.

stat.AP↗

arXiv2024

Discovering the Signal Subgraph: An Iterative Screening Approach on Graphs

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.

stat.ME↗

arXiv2019

Joint Embedding of Graphs

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.

stat.AP↗

arXiv2012

On individual neutrality and collective decision making

We derive a simple mathematical "theory" to show that two decision-making entities can work better together only if at least one of them is occasionally willing to stay neutral. This provides a mathematical "justification" for an age-old cliche among marriage counselors.

stat.OT↗