arXiv subjects

Ravi Goyal

Publications and source records attributed to Ravi Goyal.

8 recordsLinked to original sources

arXiv2026

CCMnet: A Software Package for Network Generation with Congruence Class Models

We introduce CCMnet, an R package designed to generate network ensembles that accurately reflect the uncertainty inherent in empirical data. While traditional network modeling often results in ensembles with fixed property values or model-determined levels of variability, CCMnet enables a continuous spectrum of variability for network properties, including edge counts, degree distribution, and mixing patterns. By defining probability distributions directly over congruence classes of networks, the package allows researchers to specify the uncertainty in network properties across the generated ensemble to match a specific sampling design or empirical distribution. Furthermore, this formulation provides a principled framework that encompasses several classic models (e.g., Erd\H{o}s--R\'{e}nyi model, stochastic block models, and certain exponential random graph models) that implicitly share this structural basis, while offering the flexibility to specify arbitrary, even non-parametric, distributions for network properties. CCMnet implements a Markov chain Monte Carlo (MCMC) framework to sample from these models. The utility of the package is illustrated by generating posterior predictive network ensembles representing school friendship networks.

stat.CO↗

arXiv2026

Early warning of Mpox outbreaks in U.S. jurisdictions using Lasso Vector Autoregression models with cross-jurisdictional lags

Mpox is an orthopoxvirus that infects humans and animals and is transmitted primarily through close physical contact. The episodic and spatially heterogeneous dynamics of Mpox transmission underscores the need for timely, area-specific forecasts to support targeted public health responses in the U.S. We develop a Vector Autoregression model with Lasso regularization (VAR-Lasso) to generate rolling two-week-ahead forecasts of weekly Mpox cases for eight high-incidence U.S. jurisdictions using national surveillance data from the Centers for Disease Control and Prevention (CDC). The VAR-Lasso model identifies significant long-lag, cross-jurisdictional predictors. For a case study in San Diego County (SDC), these statistical predictors align with phylogenetic analysis that traces a 2023 cluster in SDC to an outbreak in Illinois six months earlier. As the need for public health action is often greatest when incidence is increasing, our performance evaluation focuses on positive-slope weighted error metrics. Forecast performance of the VAR-Lasso model is compared to a uni-variate Auto-Regressive (AR) Lasso model and a naive moving-average estimate. The models are compared using slope-weighted Root Mean Squared Error (RMSE), slope-weighted Mean Absolute Error (MAE), and slope-weighted bias. Across all observations, the VAR-Lasso model reduces slope-weighted RMSE, MAE, and bias by 12%, 7%, and 66% relative to the AR model, and by 16%, 13%, and 76% relative to the naive benchmark. Our findings highlight the value of sparse multivariate time-series models that leverage cross-jurisdictional case data for early forecasting of Mpox outbreaks. Such forecasting can aid health departments in proactively providing timely resources and messaging to mitigate the risks of a future outbreak.

stat.AP↗

arXiv2024

Investigating the HIV Epidemic in Miami Using a Novel Approach for Bayesian Inference on Partially Observed Networks

Molecular HIV Surveillance (MHS) has been described as key to enabling rapid responses to HIV outbreaks. It operates by linking individuals with genetically similar viral sequences, which forms a network. A major limitation of MHS is that it depends on sequence collection, which very rarely covers the entire population of interest. Ignoring missing data by conducting complete case analysis--which assumes that the observed network is complete--has been shown to result in significantly biased estimates of network properties. We use MHS to investigate disease dynamics of the HIV epidemic in Miami-Dade County (MDC) among men who have sex with men (MSM)--only 30.1% have a reported sequence. To do so, we present an approach for making Bayesian inferences on partially observed networks. Through a simulation study, we demonstrate a reduction in error of 43%-63% between our estimates and complete case analyses. We estimate increased mixing between MSM communities in MDC, defined by race and transmission risk compared to the results based on complete case analysis. Our approach makes use of a flexible network model--congruence class model--to overcome the high computational burden of previously reported Bayesian approaches to estimate network properties from partially observed networks.

stat.AP↗

arXiv2020

Framework for Converting Mechanistic Network Models to Probabilistic Models

There are two prominent paradigms to the modeling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models are scalable and, in select cases, allow for analytical solutions for some of their properties, whereas probabilistic models have inferential tools available. Mechanistic models are appealing because they capture scientific processes that are hypothesized to be responsible for network generation. We introduce a generic framework for converting a mechanistic network model to a probabilistic network model. The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for mechanistic network models, which enables addressing questions such as whether two mechanistic models generate networks with identical distributions of properties of interest, or whether a network property, such as clustering, is over- or under- represented in the generated networks compared to a reference model. The proposed framework is intended to bridge some of the gap that currently exists between mechanistic and probabilistic network models.

physics.soc-ph↗

arXiv2020

Investigation of Patient-sharing Networks Using a Bayesian Network Model Selection Approach for Congruence Class Models

A Bayesian approach to conduct network model selection is presented for a general class of network models referred to as the congruence class models (CCMs). CCMs form a broad class that includes as special cases several common network models, such as the Erdős-Rényi-Gilbert model, stochastic block model and many exponential random graph models. Due to the range of models able to be specified as a CCM, investigators are better able to select a model consistent with generative mechanisms associated with the observed network compared to current approaches. In addition, the approach allows for incorporation of prior information. We utilize the proposed Bayesian network model selection approach for CCMs to investigate several mechanisms that may be responsible for the structure of patient-sharing networks, which are associated with the cost and quality of medical care. We found evidence in support of heterogeneity in sociality but not selective mixing by provider type nor degree.

stat.AP↗

arXiv2019

Recursive Formula for Labeled Graph Enumeration

This manuscript presents a general recursive formula to estimate the size of fibers associated with algebraic maps from graphs to summary statistics of importance for social network analysis, such as number of edges (graph density), degree sequence, degree distribution, mixing by nodal covariates, and degree mixing. That is, the formula estimates the number of labeled graphs that have given values for network properties. The proposed approach can be extended to additional network properties (e.g., clustering) as well as properties of bipartite networks. For special settings in which alternative formulas exist, simulation studies demonstrate the validity of the proposed approach. We illustrate the approach for estimating the size of fibers associated with the Barabási--Albert model for the properties of degree distribution and degree mixing. In addition, we demonstrate how the approach can be used to assess the diversity of graphs within a fiber.

stat.CO↗

arXiv2018

Dynamic Network Prediction

We present a statistical framework for generating predicted dynamic networks based on the observed evolution of social relationships in a population. The framework includes a novel and flexible procedure to sample dynamic networks given a probability distribution on evolving network properties; it permits the use of a broad class of approaches to model trends, seasonal variability, uncertainty, and changes in population composition. Current methods do not account for the variability in the observed historical networks when predicting the network structure; the proposed method provides a principled approach to incorporate uncertainty in prediction. This advance aids in the designing of network-based interventions, as development of such interventions often requires prediction of the network structure in the presence and absence of the intervention. Two simulation studies are conducted to demonstrate the usefulness of generating predicted networks when designing network-based interventions. The framework is also illustrated by investigating results of potential interventions on bill passage rates using a dynamic network that represents the sponsor/co-sponsor relationships among senators derived from bills introduced in the US Senate from 2003-2016.

cs.SI↗

arXiv2016

A New Characterisation of Total Graphs

Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a vertex colouring problem of the transformed graph. In this paper, we obtain a new characterisation of total graphs of simple graphs. We also design algorithms to compute the inverse total graphs when the input graph is a total graph. These results improve over the work of Behzad, by using novel observations on the properties of the local structure in the neighbourhood of each vertex. The earlier algorithm was based on bfs and distances. Our theorems result in partitioning the vertex set of the total graph into the original graph and the line graph efficiently. We obtain constructive results for special classes, most notably for total graph of complete graphs.

math.GM↗