Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1704.06017

PAFit: an R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks

Thong Pham·Paul Sheridan·Hidetoshi Shimodaira
View original source ↗Read source document ↗Export metadata ↓

Abstract

Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are statistical packages for estimating various parametric forms of the preferential attachment function, there is no such package implementing non-parametric estimation procedures. The non-parametric approach to the estimation of the preferential attachment function allows for comparatively finer-grained investigations of the `rich-get-richer' phenomenon that could lead to novel insights in the search to explain certain nonstandard structural properties observed in real-world networks. This paper introduces the R package PAFit, which implements non-parametric procedures for estimating the preferential attachment function and node fitnesses in a growing network, as well as a number of functions for generating complex networks from these two mechanisms. The main computational part of the package is implemented in C++ with OpenMP to ensure scalability to large-scale networks. We first introduce the main functionalities of PAFit through simulated examples, and then use the package to analyze a collaboration network between scientists in the field of complex networks. The results indicate the joint presence of `rich-get-richer' and `fit-get-richer' phenomena in the collaboration network. The estimated attachment function is observed to be near-linear, which we interpret as meaning that the chance an author gets a new collaborator is proportional to their current number of collaborators. Furthermore, the estimated author fitnesses reveal a host of familiar faces from the complex networks community among the field's topmost fittest network scientists.

Explore related subjects

physics.data-ancs.SIphysics.soc-phstat.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thong Pham, Paul Sheridan, Hidetoshi Shimodaira. 2018-10-24. PAFit: an R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks. https://doi.org/10.18637/jss.v092.i03

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Learning to bin: differentiable and Bayesian optimization for multi-dimensional discriminants in high-energy physics

Categorizing events using discriminant observables is central to many high-energy physics analyses. Yet, bin boundaries are often chosen manually. A simple, popular choice in multi-classification tasks is to assign events according to the largest per-class score ("argmax") and to apply equidistant binning to the resulting one-dimensional discriminants. We propose a binning optimization for signal significance directly in multi-dimensional discriminants. We use a Gaussian Mixture Model (GMM) to define flexible regions in the score space, which can be interpreted either as bins or as analysis categories. While this GMM-based strategy is applicable in both one and multiple dimensions, we also study a direct bin-boundary optimization in one dimension as a simpler alternative for binary discriminants. On this binning model, we study two optimization strategies: a differentiable and a Bayesian optimization approach. We study two toy setups: a binary classification and a three-class problem with two signals and backgrounds. In the one-dimensional case, both approaches achieve similar gains in signal sensitivity compared to equidistant binning for a given number of bins, while in the multi-dimensional case the differentiable approach performs best. We show that the GMM-based optimization can outperform argmax classification even after optimized binning is applied to the one-dimensional projections. We further study the performance of our methods on the FAIR Universe $H\rightarrowττ$ dataset, where the GMM-based optimization gives the highest signal significance. Both methods are released as lightweight Python plugins intended for straightforward integration into existing analyses.

physics.data-an↗
arXiv2026

When Should Team KPIs Be Absolute or Relative for Match-Outcome Prediction?

In rugby union and association football, team key performance indicators (KPIs) can be represented in absolute terms or relative to the opponent. Relativisation sometimes improves match-outcome prediction and sometimes harms it. There has been no general account of when each occurs. The answer depends on how much the two teams differ in variability and how strongly their KPI values rise and fall together. We combine these properties into the Paired Efficiency Factor (PEF), which generalises Fisher's paired-efficiency result to the unequal-variance conditions typical of competitive sport. The PEF also connects a KPI's statistical efficiency to how much information its relative form carries about the outcome. Combined KPIs can interact in complex ways, so we analyse each indicator on its own. Across 86 team KPIs from professional rugby union and association football, the PEF places every metric in one of four regimes. Anti-correlation is common, especially for high-volume competitive counts, and absolute measures are then usually preferable. Relativisation can still improve prediction when a noisier difference carries more outcome information. An idealised simulation and one representative KPI from each regime confirm both signs under team-blocked cross-validation. The same pairing geometry appears in healthcare, genomics, finance, and manufacturing. The PEF turns an ad hoc feature-engineering choice into a transparent, data-informed diagnostic for when to relativise performance metrics and when not to.

physics.data-an↗
arXiv2026

Comparison of Image Processing Models in Quark Gluon Jet Classification

Quark-gluon discrimination provides a useful test case for studying how different machine-learning architectures learn the spatial structure of QCD radiation. In this work, we compare convolutional neural network (CNN), Vision Transformers (ViT), and hierarchical Swin Transformers using the same three-channel jet-image representation, consisting of charged-particle momentum, neutral-particle momentum, and charged-particle multiplicity from PYTHIA 8 jets. We study their performance for different training-set sizes and fine-tuning configurations, with particular attention to the role of local and global information in the jet images. CNN and Swin models consistently perform better than ViT in the cases studied. Since both CNN and Swin retain a strong local component in their architectures, this suggests that local jet substructure plays an important role in quark-gluon discrimination. The performance of the hierarchical Swin model also suggests that combining local features over larger spatial scales is useful. Block-wise fine-tuning improves the performance of the Transformer models, although the improvement becomes smaller and the training less stable as more blocks are unfrozen. We also find that self-supervised Momentum Contrast (MoCo) pretraining improves the model initialization, particularly when the amount of labeled training data is limited. Based on these observations, we developed a smaller Swin model adopted to the jet-image representation used in this study. It achieves comparable performance with substantially fewer parameters. The results show that it is important to adapt the model architecture and training procedure to the specific input characteristics of High Energy Physics (HEP) data when applying vision models in HEP.

physics.data-an↗