Caterina De Bacco

Dhanya Sridhar, Caterina De Bacco, David Blei

We consider the problem of estimating social influence, the effect that a person's behavior has on the future behavior of their peers. The key challenge is that shared behavior between friends could be equally explained by influence or by two other confounding factors: 1) latent traits that caused people to both become friends and engage in the behavior, and 2) latent preferences for the behavior. This paper addresses the challenges of estimating social influence with three contributions. First, we formalize social influence as a causal effect, one which requires inferences about hypothetical interventions. Second, we develop Poisson Influence Factorization (PIF), a method for estimating social influence from observational data. PIF fits probabilistic factor models to networks and behavior data to infer variables that serve as substitutes for the confounding latent traits. Third, we develop assumptions under which PIF recovers estimates of social influence. We empirically study PIF with semi-synthetic and real data from Last.fm, and conduct a sensitivity analysis. We find that PIF estimates social influence most accurately compared to related methods and remains robust under some violations of its assumptions.

Andrea Della Vecchia, Kibidi Neocosmos, Daniel B. Larremore et al.

We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each node is real-valued and varies in time as each new edge, encoding an outcome like a win or loss, raises or lowers the node's estimated strength or prestige, as is often observed in real scenarios including sequences of games, tournaments, or interactions in animal hierarchies. Our method works by solving a linear system of equations and requires only one parameter to be tuned. As a result, the corresponding algorithm is scalable and efficient. We test our method by evaluating its ability to predict interactions (edges' existence) and their outcomes (edges' directions) in a variety of applications, including both synthetic and real data. Our analysis shows that in many cases our method's performance is better than existing methods for predicting dynamic rankings and interaction outcomes.

Alessandro Lonardi, Diego Baptista, Caterina De Bacco

In classification tasks, it is crucial to meaningfully exploit the information contained in data. While much of the work in addressing these tasks is devoted to building complex algorithmic infrastructures to process inputs in a black-box fashion, less is known about how to exploit the various facets of the data, before inputting this into an algorithm. Here, we focus on this latter perspective, by proposing a physics-inspired dynamical system that adapts Optimal Transport principles to effectively leverage color distributions of images. Our dynamics regulates immiscible fluxes of colors traveling on a network built from images. Instead of aggregating colors together, it treats them as different commodities that interact with a shared capacity on edges. The resulting optimal flows can then be fed into standard classifiers to distinguish images in different classes. We show how our method can outperform competing approaches on image classification tasks in datasets where color information matters.

Michela Lapenna, Caterina De Bacco

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured data, but their inherent functioning is different. The question is how do they compare in capturing the information contained in networked datasets? We address this objective by solving a link prediction task and we conduct three main experiments, on both synthetic and real networks: one focuses on how PGMs and GNNs handle input features, while the other two investigate their robustness to noisy features and increasing heterophily of the graph. PGMs do not necessarily require features on nodes, while GNNs cannot exploit the network edges alone, and the choice of input features matters. We find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, mimicking many real scenarios where node attributes might be scalar or noisy. Then, we find that PGMs are more robust than GNNs when the heterophily of the graph is increased. Finally, to assess performance beyond prediction tasks, we also compare the two frameworks in terms of their computational complexity and interpretability.

Laura Iacovissi, Caterina De Bacco

Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstrate our method on synthetic and real-world data and compare performance with two standard approaches for community detection and ranking extraction. We find that the algorithm accurately retrieves the overall node's preference in different scenarios, and we show that it can distinguish small subsets of nodes that behave differently than the majority. As a consequence, the model can recognize whether a network has an overall preferred interaction mechanism. This is relevant in situations where there is no clear "a priori" information about what structure explains the observed network datasets well. Our model allows practitioners to learn this automatically from the data.

Abdullahi Adinoyi Ibrahim, Alessandro Lonardi, Caterina De Bacco

Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and computationally efficient methods to address this problem, but they are mainly focused on modeling single-layer networks. Here we adapt these results to study how optimal flows distribute on multilayer networks. We propose a model where optimal flows on different layers contribute differently to the total cost to be minimized. This is done by means of a parameter that varies with layers, which allows to flexibly tune the sensitivity to traffic congestion of the various layers. As an application, we consider transportation networks, where each layer is associated to a different transportation system and show how the traffic distribution varies as we tune this parameter across layers. We show an example of this result on the real 2-layer network of the city of Bordeaux with bus and tram, where we find that in certain regimes the presence of the tram network significantly unburdens the traffic on the road network. Our model paves the way to further analysis of optimal flows and navigability strategies in real multilayer networks.

Diego Baptista, Caterina De Bacco

Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that is scalable and efficient. We map this goal into solving a routing optimization problem where the solution is a network that minimizes an energy function which can be interpreted in terms of an operational and infrastructural cost. Our method relies on recent results from optimal transport theory and is a principled alternative to standard image-processing techniques that are based on heuristics. We test our model on real images of the retinal vascular system, slime mold and river networks and compare with routines combining image-processing techniques. Results are tested in terms of a similarity measure related to the amount of information preserved in the extraction. We find that our model finds networks from retina vascular network images that are more similar to hand-labeled ones, while also giving high performance in extracting networks from images of rivers and slime mold for which there is no ground truth available. While there is no unique method that fits all the images the best, our approach performs consistently across datasets, its algorithmic implementation is efficient and can be fully automatized to be run on several datasets with little supervision.

Caterina De Bacco, Daniel B. Larremore, Cristopher Moore

We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including datasets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions.

Thibault Lesieur, Caterina De Bacco, Jess Banks et al.

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $α= m/n$ stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of $α$ and the distance between the clusters at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. We also determine the accuracy achievable by the Bayes-optimal estimation algorithm. In particular, we find that when the number of clusters is sufficiently large, $r > 4 + 2 \sqrtα$, there is a gap between the threshold for information-theoretically optimal performance and the threshold at which known algorithms succeed.