arXiv subjects

Simon Lunagomez

Publications and source records attributed to Simon Lunagomez.

8 recordsLinked to original sources

arXiv2026

Decision-Theoretic Robustness for Network Models

Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit higher-order dependence. How stable are network-based decisions, model selection, and policy recommendations to small model misspecification? We study local decision-theoretic robustness by allowing the posterior to vary within a small Kullback-Leibler neighborhood and choosing actions that minimize worst-case posterior expected loss. Exploiting low-dimensional functionals available under exchangeability, we (i) adapt decision-theoretic robustness to exchangeable graphs via graphon limits and derive sharp small-radius expansions of robust posterior risk; under squared loss the leading inflation is controlled by the posterior variance of the loss, and for robustness indices that diverge at percolation/fragmentation thresholds we obtain a universal critical exponent describing the explosion of decision uncertainty near criticality. (ii) Develop a nonparametric minimax theory for robust model selection between sparse Erdos-Renyi and block models, showing-via robustness error exponents-that no Bayesian or frequentist method can uniformly improve upon the decision-theoretic limits over configuration models and sparse graphon classes for percolation-type functionals. (iii) Propose a practical algorithm based on entropic tilting of posterior or variational samples, and demonstrate it on functional brain connectivity and Karnataka village social networks.

math.ST↗

arXiv2023

Bayesian model-based clustering for populations of network data

There is increasing appetite for analysing populations of network data due to the fast-growing body of applications demanding such methods. While methods exist to provide readily interpretable summaries of heterogeneous network populations, these are often descriptive or ad hoc, lacking any formal justification. In contrast, principled analysis methods often provide results difficult to relate back to the applied problem of interest. Motivated by two complementary applied examples, we develop a Bayesian framework to appropriately model complex heterogeneous network populations, whilst also allowing analysts to gain insights from the data, and make inferences most relevant to their needs. The first application involves a study in Computer Science measuring human movements across a University. The second analyses data from Neuroscience investigating relationships between different regions of the brain. While both applications entail analysis of a heterogeneous population of networks, network sizes vary considerably. We focus on the problem of clustering the elements of a network population, where each cluster is characterised by a network representative. We take advantage of the Bayesian machinery to simultaneously infer the cluster membership, the representatives, and the community structure of the representatives, thus allowing intuitive inferences to be made. The implementation of our method on the human movement study reveals interesting movement patterns of individuals in clusters, readily characterised by their network representative. For the brain networks application, our model reveals a cluster of individuals with different network properties of particular interest in Neuroscience. The performance of our method is additionally validated in extensive simulation studies.

stat.AP↗

arXiv2022

Wrapped Distributions on homogeneous Riemannian manifolds

We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions that are straightforward to sample from, suitable for use within Monte Carlo algorithms and latent variable models, such as autoencoders. As an illustration, we empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model. Finally, we take advantage of the generalized description of this framework to posit questions for future work.

math.ST↗

arXiv2022

Latent Space Network Modelling with Hyperbolic and Spherical Geometries

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is typical to assume that the underlying geometry is Euclidean. Recent work has explored the consequences of this choice and has motivated the study of models which rely on non-Euclidean latent geometries, with a primary focus on spherical and hyperbolic geometry. In this paper, we examine to what extent latent features can be inferred from the observable links in the network, considering network models which rely on spherical and hyperbolic geometries. For each geometry, we describe a latent space network model, detail constraints on the latent coordinates which remove the well-known identifiability issues, and present Bayesian estimation schemes. Thus, we develop computational procedures to perform inference for network models in which the properties of the underlying geometry play a vital role. Finally, we assess the validity of these models on real data.

stat.ME↗

arXiv2021

Bayesian modelling and computation utilising directed cycles in multiple network data

Modelling multiple network data is crucial for addressing a wide range of applied research questions. However, there are many challenges, both theoretical and computational, to address. Network cycles are often of particular interest in many applications; for example in ecology a largely unexplored area has been how to incorporate network cycles within the inferential framework in an explicit way. The recently developed Spherical Network Family of models (SNF) offers a flexible formulation for modelling multiple network data that permits any type of metric. This has opened up the possibility to formulate network models that focus on network properties hitherto not possible or practical to consider. In this article we propose a novel network distance metric that measures similarities between networks with respect to their cycles, and incorporates this within the SNF model to allow inferences that explicitly capture information on cycles. These network motifs are of particular interest in ecological studies aimed at understanding competitive and hierarchical interactions. We further propose a novel computational framework to allow posterior inferences from the intractable SNF model for moderate-sized networks. Lastly, we apply the resulting methodology to a set of ecological network data studying aggressive interactions between species of fish. We show our model is able to make cogent inferences concerning the cycle behaviour amongst the species, and beyond those possible from a model that does not consider this network motif.

stat.AP↗

arXiv2020

Robustness on Networks

We adopt the statistical framework on robustness proposed by Watson and Holmes in 2016 and then tackle the practical challenges that hinder its applicability to network models. The goal is to evaluate how the quality of an inference for a network feature degrades when the assumed model is misspecified. Decision theory methods aimed to identify model missespecification are applied in the context of network data with the goal of investigating the stability of optimal actions to perturbations to the assumed model. Here the modified versions of the model are contained within a well defined neighborhood of model space. Our main challenge is to combine stochastic optimization and graph limits tools to explore the model space. As a result, a method for robustness on exchangeable random networks is developed. Our approach is inspired by recent developments in the context of robustness and recent works in the robust control, macroeconomics and financial mathematics literature and more specifically and is based on the concept of graphon approximation through its empirical graphon.

stat.ME↗

arXiv2020

Lasso for hierarchical polynomial models

In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy and to extend existing work in the literature, which at the moment is only concerned with models of degree two. We discuss how to estimate parameters in lasso using standard quadratic programming techniques and apply our proposal to both simulated data and examples from the literature. The proposed methodology compares favorably with existing techniques in terms of low validation error and model size.

stat.CO↗

arXiv2016

Bayesian Inference from Non-Ignorable Network Sampling Designs

Consider a population of individuals and a network that encodes social connections among them. We are interested in making inference on finite population and super-population estimands that are a function of both individuals' responses and of the network, from a sample. Neither the sampling frame nor the network are available. However, the sampling mechanism implicitly leverages the network to recruit individuals, thus partially revealing social interactions among the individuals in the sample, as well as their responses. This is a common setting that arises, for instance, in epidemiology and healthcare, where samples from hard-to-reach populations are collected using link-tracing mechanisms, including respondent-driven sampling. In this paper, we study statistical properties of popular network sampling mechanisms. We formulate the estimation problem in terms of Rubin's inferential framework to explicitly account for social network structure. We then identify key modeling elements that lead to inferences with good frequentist properties when dealing with data collected through non-ignorable network sampling mechanisms. We demonstrate these methods on a study of the incidence of HIV in Brazil

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