arXiv subjects

Sergio Buttazzo

Publications and source records attributed to Sergio Buttazzo.

3 recordsLinked to original sources

arXiv2026

Exact Likelihood Inference for Snowball-Sampled Erd\H{o}s-R\'enyi Networks

Network data obtained through link-tracing designs, such as snowball sampling, are collected through a mechanism that depends on the very structure the analysis seeks to estimate. Ignoring this dependence and treating the observed sample as though it were itself a complete network can lead to substantially biased inference. While the resulting selection problem is intractable in general, we show that it admits an exact solution for $r$-wave snowball samples, with full-neighbourhood recruitment, drawn from an Erd\H{o}s--R\'{e}nyi population. We derive the exact likelihood of such a sample and show that it defines a curved exponential family in the edge probability $\pi$, with a low-dimensional sufficient statistic. Building on this result, we obtain the maximum likelihood estimator of $\pi$ that correctly accounts for the sampling design and, as a function of the minimal sufficient statistic, makes full use of the information in the sample. Simulation studies show that this correction substantially reduces bias relative to the naive estimator, remaining effectively unbiased even when the sample covers as little as 0.1\% of the network. We further construct valid confidence intervals for $\pi$ by inverting a test built on the exact sampling distribution, approximated via Monte Carlo simulation. Simulation studies confirm that these confidence intervals attain the nominal coverage level within Monte Carlo error across a range of edge probabilities and numbers of waves.

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arXiv2026

Maximum Likelihood Estimation for Network Models with Latent Geometry under Snowball Sampling

Snowball sampling is a widely used design for collecting network data from large or hard-to-reach populations, yet naive inference that ignores the sampling mechanism produces systematically biased parameter estimates. We derive the exact likelihood of a multi-wave snowball sample for the class of continuous latent space (CLS) models, in which edges form independently conditional on latent vertex-level quantities, and show that conditional edge independence reduces the marginalization over unobserved network configurations to a closed-form expression portable across the entire CLS class. We develop a stochastic Expectation-Maximization algorithm for the Euclidean latent distance model as a concrete implementation, and apply the framework to the large-scale co-inventor network of German semiconductor patent applicants by drawing multiple snowball samples. We find that the naive procedure severely underestimates latent space variance, produces networks with nearly twice the observed edge count, and achieves a spectral goodness-of-fit nine times worse than the corrected model, which directly affects the quantitative interpretation of covariate effects.

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arXiv2024

Using LASSO for Variable Selection in Exponential Random Graph models

The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify the (sufficient) statistics, that define the model structure. This includes both, endogenous network statistics (e.g. twostars, triangles, etc.) as well as statistics involving exogenous covariates; on the node as well as on the edge level. LASSO estimation is a penalized estimation that shrinks some of the parameter estimates to be equal to zero. As such it allows for model selection by modifying the amount of penalty. The concept is well established in standard regression and we demonstrate its usage in network data analysis, with the advantage of automatically providing a model selection framework.

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