arXiv subjects

Peter W. MacDonald

Publications and source records attributed to Peter W. MacDonald.

9 recordsLinked to original sources

arXiv2026

Group-regularized matrix factorization for fast and reliable module discovery in pan-omics pan-cancer studies

In pan-omics pan-cancer studies, it is critical to identify latent sources of variation that are shared across particular subsets. This task often requires bidimensionally linked data matrices to be decomposed into a sum of block-sparse, low-rank modules. Existing approaches often rely on pre-specified module numbers, ranks, or post-hoc thresholding and can be sensitive to model specification when the underlying sharing structure is complex. To address these issues, we propose GL-BIDIFAC+, a group-regularized matrix factorization framework for discovering partially shared modules. It requires only an upper bound on the latent dimension and encourages module selection through group regularization with theoretically-motivated tuning parameter selection and local support recovery analysis, providing both scalability and principled guidance for module discovery. It also admits a probabilistic interpretation that enables model-based imputation of missing data. Simulation studies demonstrate accurate module recovery and favorable computational performance relative to existing approaches. We further apply GL-BIDIFAC+ to analyze the Cancer Genome Atlas data, where well-established molecular structure provides interpretable biological references. Our analysis distinguishes broad pan-cancer variation, cancer-specific subtype structure, and variation shared across cancers with related tissue origins or histologic features.

stat.AP↗

arXiv2026

Inference for subgraph densities in noisy dynamic networks

In this work we develop statistical methodology to estimate and perform inference on subgraph densities using time-indexed, or dynamic network sequences. These estimates explicitly adjust for observation errors for the network edges, and have good theoretical properties as the size of the network grows. By specifying a stochastically evolving hidden Markov network model, we address two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots. These new methods vastly expand the analysis of noisy networks to new data settings, as network replicates are commonly observed dynamically. The methodology is also extended to consider joint inference for subgraph densities at multiple time points, to facilitate formal statistical comparison of dynamic network snapshots.

stat.ME↗

arXiv2026

Autoregressive networks with dependent edges

We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network data. By assuming the edges of networks at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal ERGMs, facilitate both simulation and the maximum likelihood estimation in a straightforward manner. Due to the possibly large number of parameters in the models, the natural MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration employing projection, which mitigates the impact of the other parameters (Chang et al., 2021; Chang et al., 2023). Leveraging a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the assumption of stationarity. The limiting distribution is not normal in general, although it reduces to normal when the underlying process satisfies some mixing conditions. Illustration with a transitivity model was carried out in both simulation and a real network data set.

math.ST↗

arXiv2026

Mesoscale two-sample testing for networks

Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests.

stat.ME↗

arXiv2026

Latent space models for grouped multiplex networks

Complex multilayer network datasets have become ubiquitous in various applications, including neuroscience, social sciences, economics, and genetics. Notable examples include brain connectivity networks collected across multiple patients or trade networks between countries collected across multiple goods. Existing statistical approaches to such data typically focus on modeling the structure shared by all networks; some go further by accounting for individual, layer-specific variation. However, real-world multilayer networks often exhibit additional patterns shared only within certain subsets of layers, which can represent treatment and control groups, or patients grouped by a specific trait. Identifying these group-level structures can uncover systematic differences between groups of networks and influence many downstream tasks, such as testing and low-dimensional visualization. To address this gap, we introduce the GroupMultiNeSS model, which enables the simultaneous extraction of shared, group-specific, and individual latent structures from a sample of networks on a shared node set. For this model, we establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared, group-specific, and individual latent subspaces. We compare the model with MultiNeSS and other models for multiplex networks in various synthetic scenarios and observe an apparent improvement in the modeling accuracy when the group component is accounted for. Experiment with the Parkinson's disease brain connectivity dataset demonstrates the superiority of GroupMultiNeSS in highlighting node-level insights on biological differences between the treatment and control patient groups.

cs.SI↗

arXiv2025

Minority representation and fairness in network ranking: An application to school contact diary data

Considerations of bias, fairness and representation are a prerequisite of responsible modern statistics. In statistical network analysis, observed networks are often incomplete or systematically biased, which can lead to systematic underrepresentation of protected groups, and affect any downstream ranking or decision based on the observed network. In this paper, we study a high school contact network constructed from self-reported contact diaries and introduce a formal measure of minority representation, defined as the proportion of minority nodes among the top-ranked individuals. We model systematic bias through group-dependent missing edge mechanisms and develop statistical methods to estimate and test for such bias. When bias is detected, we propose a re-ranking procedure based on an asymptotic approximation that improves group representation. Applying the framework to the high school contact network reveals systematic underreporting of cross-group contacts consistent with recall bias. These findings highlight the importance of modeling and correcting systematic bias in social networks with heterogeneous groups.

stat.ME↗

arXiv2024

Latent process models for functional network data

Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network analysis are traditionally designed for a single network, and can be applied to an aggregated network in this setting, but that approach can miss important functional structure. Here we develop an approach to estimating the expected network explicitly as a function of a continuous index, be it time or another indexing variable. We parameterize the network expectation through low dimensional latent processes, whose components we represent with a fixed, finite-dimensional functional basis. We derive a gradient descent estimation algorithm, establish theoretical guarantees for recovery of the low dimensional structure, compare our method to competitors, and apply it to a data set of international political interactions over time, showing our proposed method to adapt well to data, outperform competitors, and provide interpretable and meaningful results.

stat.ME↗

arXiv2022

Approximate Post-Selective Inference for Regression with the Group LASSO

After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), inference for the selected parameters is unreliable in the absence of adjustments for selection bias. In the penalized Gaussian regression setup, existing approaches provide adjustments for selection events that can be expressed as linear inequalities in the data variables. Such a representation, however, fails to hold for selection with the Group LASSO and substantially obstructs the scope of subsequent post-selective inference. Key questions of inferential interest -- for example, inference for the effects of selected variables on the outcome -- remain unanswered. In the present paper, we develop a consistent, post-selective, Bayesian method to address the existing gaps by deriving a likelihood adjustment factor and an approximation thereof that eliminates bias from the selection of groups. Experiments on simulated data and data from the Human Connectome Project demonstrate that our method recovers the effects of parameters within the selected groups while paying only a small price for bias adjustment.

stat.ME↗

arXiv2021

Latent space models for multiplex networks with shared structure

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex network structures, which are becoming increasingly common in practice. Here we propose a new latent space model for multiplex networks: multiple, heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of our model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared and the individual latent subspaces. We compare the model to competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.

stat.ME↗