Related papers: Root Cause Analysis of Outliers in Unknown Cyclic …
A subcycle of an Eulerian circuit is a sequence of edges that are consecutive in the circuit and form a cycle. We characterise the quartic planar graphs that admit Eulerian circuits avoiding 3-cycles and 4-cycles. From this, it follows that…
We study distribution-free root cause analysis in multi-stream data, where an evolving underlying system is observed through multiple data streams that may each undergo distributional changes at unknown timepoints. In such settings, the…
We present in this paper a new tool for outliers detection in the context of multiple regression models. This graphical tool is based on recursive estimation of the parameters. Simulations were carried out to illustrate the performance of…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…
Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate…
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical…
Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic…
Suppose that a cascade (e.g., an epidemic) spreads on an unknown graph, and only the infection times of vertices are observed. What can be learned about the graph from the infection times caused by multiple distinct cascades? Most of the…
Understanding the laws that govern a phenomenon is the core of scientific progress. This is especially true when the goal is to model the interplay between different aspects in a causal fashion. Indeed, causal inference itself is…
Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when…
Estimating the location and scale parameters is common in statistics, using, for instance, the well-known sample mean and standard deviation. However, inference can be contaminated by the presence of outliers if modeling is done with…
Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…
In this paper, we investigate the ratio of the numbers of odd and even cycles in outerplanar graphs. We verify that the ratio generally diverges to infinity as the order of a graph diverges to infinity. We also give sharp estimations of the…
Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and…
We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…
Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the…
We describe a formal approach based on graphical causal models to identify the "root causes" of the change in the probability distribution of variables. After factorizing the joint distribution into conditional distributions of each…