arXiv subjects

Till Hoffmann

Publications and source records attributed to Till Hoffmann.

18 recordsLinked to original sources

arXiv2025

Information is localized in growing network models

Mechanistic network models can capture salient characteristics of empirical networks using a small set of domain-specific, interpretable mechanisms. Yet inference remains challenging because the likelihood is often intractable. We show that, for a broad class of growing network models, information about model parameters is localized in the network, i.e., the likelihood can be expressed in terms of small subgraphs. We take a Bayesian perspective to inference and develop neural density estimators (NDEs) to approximate the posterior distribution of model parameters using graph neural networks (GNNs) with limited receptive size, i.e., the GNN can only "see" small subgraphs. We characterize nine growing network models in terms of their localization and demonstrate that localization predictions agree with NDEs on simulated data. Even for non-localized models, NDEs can infer high-fidelity posteriors matching model-specific inference methods at a fraction of the cost. Our findings establish information localization as a fundamental property of network growth, theoretically justifying the analysis of local subgraphs embedded in larger, unobserved networks and the use of GNNs with limited receptive field for likelihood-free inference.

cs.SI↗

arXiv2025

Approximate Bayesian Inference on Mechanisms of Network Growth and Evolution

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may be designed to facilitate the appearance of certain network motifs. In the formation of real-world networks, multiple mechanisms may be simultaneously involved; it is then important to understand the relative contribution of each of these mechanisms. In this paper, we propose the use of a conditional density estimator, augmented with a graph neural network, to perform inference on a flexible mixture of network-forming mechanisms. This event-wise mixture-of-mechanisms model assigns mechanisms to each edge formation event rather than stipulating node-level mechanisms, thus allowing for an explanation of the network generation process, as well as the dynamic evolution of the network over time. We demonstrate that our approximate Bayesian approach yields valid inferences for the relative weights of the mechanisms in our model, and we utilize this method to investigate the mechanisms behind the formation of a variety of real-world networks.

cs.SI↗

arXiv2025

Bayesian Inference for Sexual Contact Networks Using Longitudinal Survey Data

Characterizing sexual contact networks is essential for understanding sexually transmitted infections, but principled parameter inference for mechanistic network models remains challenging. We develop a discrete-time simulation framework that enables parameter estimation using approximate Bayesian computation. The interpretable model incorporates relationship formation, dissolution, concurrency, casual contacts, and population turnover. Applying our framework to survey data from 403 men who have sex with men in Stockholm, we provide principled uncertainty quantification for key network dynamics. Our analysis estimates the timescale for seeking a new steady relationship at 25 weeks and for relationship dissolution at 42 weeks. Casual contacts occur more frequently for single individuals (every 1.8 weeks) than for partnered individuals (every 4.5 weeks). However, while cross-sectional data constrains these parameters, migration rates remain poorly identified. We demonstrate that simple longitudinal data can resolve this issue. Tracking participant retention between survey waves directly informs migration rates, though survey dropout is a potential confounder. Furthermore, simple binary survey questions can outperform complex timeline follow-back methods for estimating contact frequencies. This framework provides a foundation for uncertainty quantification in network epidemiology and offers practical strategies to improve inference from surveys, the primary data source for studying sexual behavior.

stat.ME↗

arXiv2024

Network Layout Algorithm with Covariate Smoothing

Network science explores intricate connections among objects, employed in diverse domains like social interactions, fraud detection, and disease spread. Visualization of networks facilitates conceptualizing research questions and forming scientific hypotheses. Networks, as mathematical high-dimensional objects, require dimensionality reduction for (planar) visualization. Visualizing empirical networks present additional challenges. They often contain false positive (spurious) and false negative (missing) edges. Traditional visualization methods don't account for errors in observation, potentially biasing interpretations. Moreover, contemporary network data includes rich nodal attributes. However, traditional methods neglect these attributes when computing node locations. Our visualization approach aims to leverage nodal attribute richness to compensate for network data limitations. We employ a statistical model estimating the probability of edge connections between nodes based on their covariates. We enhance the Fruchterman-Reingold algorithm to incorporate estimated dyad connection probabilities, allowing practitioners to balance reliance on observed versus estimated edges. We explore optimal smoothing levels, offering a natural way to include relevant nodal information in layouts. Results demonstrate the effectiveness of our method in achieving robust network visualization, providing insights for improved analysis.

cs.SI↗

arXiv2024

Approximate Inference for Longitudinal Mechanistic HIV Contact Networks

Network models are increasingly used to study infectious disease spread. Exponential Random Graph models have a history in this area, with scalable inference methods now available. An alternative approach uses mechanistic network models. Mechanistic network models directly capture individual behaviors, making them suitable for studying sexually transmitted diseases. Combining mechanistic models with Approximate Bayesian Computation allows flexible modeling using domain-specific interaction rules among agents, avoiding network model oversimplifications. These models are ideal for longitudinal settings as they explicitly incorporate network evolution over time. We implemented a discrete-time version of a previously published continuous-time model of evolving contact networks for men who have sex with men (MSM) and proposed an ABC-based approximate inference scheme for it. As expected, we found that a two-wave longitudinal study design improves the accuracy of inference compared to a cross-sectional design. However, the gains in precision in collecting data twice, up to 18%, depend on the spacing of the two waves and are sensitive to the choice of summary statistics. In addition to methodological developments, our results inform the design of future longitudinal network studies in sexually transmitted diseases, specifically in terms of what data to collect from participants and when to do so.

stat.ME↗

arXiv2023

Latent space approaches to aggregate network data

Large-scale network data can pose computational challenges, be expensive to acquire, and compromise the privacy of individuals in social networks. We show that the locations and scales of latent space cluster models can be inferred from the number of connections between groups alone. We demonstrate this modelling approach using synthetic data and apply it to friendships between students collected as part of the Add Health study, eliminating the need for node-level connection data. The method thus protects the privacy of individuals and simplifies data sharing. It also offers performance advantages over node-level latent space models because the computational cost scales with the number of clusters rather than the number of nodes.

cs.SI↗

arXiv2023

Scalable Gaussian Process Inference with Stan

Gaussian processes (GPs) are sophisticated distributions to model functional data. Whilst theoretically appealing, they are computationally cumbersome except for small datasets. We implement two methods for scaling GP inference in Stan: First, a general sparse approximation using a directed acyclic dependency graph; second, a fast, exact method for regularly spaced data modeled by GPs with stationary kernels using the fast Fourier transform. Based on benchmark experiments, we offer guidance for practitioners to decide between different methods and parameterizations. We consider two real-world examples to illustrate the package. The implementation follows Stan's design and exposes performant inference through a familiar interface. Full posterior inference for ten thousand data points is feasible on a laptop in less than 20 seconds. Details on how to get started using the popular interfaces cmdstanpy for Python and cmdstanr for R are provided.

stat.ME↗

arXiv2022

Unifying Summary Statistic Selection for Approximate Bayesian Computation

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize three different classes of summaries and demonstrate their importance for correctly analyzing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model provides a unifying principle that subsumes many existing methods; they are shown to be equivalent to, or special or limiting cases of, minimizing the EPE. We offer a unifying framework for obtaining informative summaries and propose a practical method using conditional density estimation to learn high-fidelity summaries automatically. We evaluate this approach on diverse problems, including a challenging benchmark model with a multi-modal posterior, a population genetics model, and a dynamic network model of growing trees. The results show that EPE-minimizing summaries can lead to posterior inference that is competitive with, and in some cases superior to, dedicated likelihood-based approaches, providing a powerful and general tool for practitioners.

stat.ME↗

arXiv2021

Thematic recommendations on knowledge graphs using multilayer networks

We present a framework to generate and evaluate thematic recommendations based on multilayer network representations of knowledge graphs (KGs). In this representation, each layer encodes a different type of relationship in the KG, and directed interlayer couplings connect the same entity in different roles. The relative importance of different types of connections is captured by an intuitive salience matrix that can be estimated from data, tuned to incorporate domain knowledge, address different use cases, or respect business logic. We apply an adaptation of the personalised PageRank algorithm to multilayer models of KGs to generate item-item recommendations. These recommendations reflect the knowledge we hold about the content and are suitable for thematic and/or cold-start recommendation settings. Evaluating thematic recommendations from user data presents unique challenges that we address by developing a method to evaluate recommendations relying on user-item ratings, yet respecting their thematic nature. We also show that the salience matrix can be estimated from user data. We demonstrate the utility of our methods by significantly improving consumption metrics in an AB test where collaborative filtering delivered subpar performance. We also apply our approach to movie recommendation using publicly-available data to ensure the reproducibility of our results. We demonstrate that our approach outperforms existing thematic recommendation methods and is even competitive with collaborative filtering approaches.

cs.IR↗

arXiv2021

Cost-based feature selection for network model choice

Selecting a small set of informative features from a large number of possibly noisy candidates is a challenging problem with many applications in machine learning and approximate Bayesian computation. In practice, the cost of computing informative features also needs to be considered. This is particularly important for networks because the computational costs of individual features can span several orders of magnitude. We addressed this issue for the network model selection problem using two approaches. First, we adapted nine feature selection methods to account for the cost of features. We show for two classes of network models that the cost can be reduced by two orders of magnitude without considerably affecting classification accuracy (proportion of correctly identified models). Second, we selected features using pilot simulations with smaller networks. This approach reduced the computational cost by a factor of 50 without affecting classification accuracy. To demonstrate the utility of our approach, we applied it to three different yeast protein interaction networks and identified the best-fitting duplication divergence model.

stat.ME↗

arXiv2020

Inference of a universal social scale and segregation measures using social connectivity kernels

How people connect with one another is a fundamental question in the social sciences, and the resulting social networks can have a profound impact on our daily lives. Blau offered a powerful explanation: people connect with one another based on their positions in a social space. Yet a principled measure of social distance, allowing comparison within and between societies, remains elusive. We use the connectivity kernel of conditionally-independent edge models to develop a family of segregation statistics with desirable properties: they offer an intuitive and universal characteristic scale on social space (facilitating comparison across datasets and societies), are applicable to multivariate and mixed node attributes, and capture segregation at the level of individuals, pairs of individuals, and society as a whole. We show that the segregation statistics can induce a metric on Blau space (a space spanned by the attributes of the members of society) and provide maps of two societies. Under a Bayesian paradigm, we infer the parameters of the connectivity kernel from eleven ego-network datasets collected in four surveys in the United Kingdom and United States. The importance of different dimensions of Blau space is similar across time and location, suggesting a macroscopically stable social fabric. Physical separation and age differences have the most significant impact on segregation within friendship networks with implications for intergenerational mixing and isolation in later stages of life.

cs.SI↗

arXiv2020

Community detection in networks without observing edges

We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection as well as the selection of an optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of the S&P100 index as well as climate data from US cities.

cs.SI↗

arXiv2016

Bayesian hierarchical modelling of weak lensing - the golden goal

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.

astro-ph.CO↗

arXiv2016

Hierarchical Cosmic Shear Power Spectrum Inference

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models \emph{a posteriori} without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear $E$-mode, $B$-mode and $EB$-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coefficients recover the underlying simulated power spectra for both $E$- and $B$-modes.

astro-ph.CO↗

arXiv2015

Unified treatment of the asymptotics of asymmetric kernel density estimators

We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density estimators which are subsumed under these two general classes of kernel density estimators. We demonstrate our method by deriving the asymptotic bias, variance, and mean (integrated) squared error of density estimators with gamma, log-normal, Birnbaum-Saunders, inverse Gaussian and reciprocal inverse Gaussian kernels. We propose two new density estimators for positive random variables that yield properly-normalised density estimates. Plugin expressions for bandwidth estimation are provided to facilitate easy exploratory data analysis.

stat.ME↗

arXiv2013

Decentralized Routing on Spatial Networks with Stochastic Edge Weights

We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual simplifying assumptions: (1) we allow edge weights to be stochastic rather than deterministic; and (2) we do not assume that global knowledge of a network is available. We develop a decentralized routing algorithm that provides en route guidance for travelers on a spatial network with stochastic edge weights without the need to rely on global knowledge about the network. To guide a traveler, our algorithm uses an estimation function that evaluates cumulative arrival probability distributions based on distances between pairs of nodes. The estimation function carries a notion of proximity between nodes and thereby enables routing without global knowledge. In testing our decentralized algorithm, we define a criterion that allows one to discriminate among arrival probability distributions, and we test our algorithm and this criterion using both synthetic and real networks.

cs.SI↗

arXiv2013

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.

physics.soc-ph↗

arXiv2011

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

physics.soc-ph↗