Exploring the dynamic co-evolution of multiplex graphs and nodal attributes is a compelling question in criminal and terrorism networks. This article is motivated by the study of dynamically evolving interactions among prominent terrorist organizations, considering various organizational attributes like size, ideology, leadership, and operational capacity. Statistically principled integration of multiplex graphs with nodal attributes is significantly challenging due to the need to leverage shared information within and across layers, account for uncertainty in predicting unobserved links, and capture temporal evolution of node attributes. These difficulties increase when layers are partially observed, as in terrorism networks where connections are deliberately hidden to obscure key relationships. To address these challenges, we present a principled methodological framework to integrate the multiplex graph layers and nodal attributes. The approach employs time-varying stochastic latent factor models, leveraging shared latent factors to capture graph structure and its co-evolution with node attributes. Latent factors are modeled using Gaussian processes with an infinitely wide deep neural network-based covariance function, termed neural network Gaussian processes (NN-GP). The NN-GP framework on latent factors exploits the predictive power of Bayesian deep neural network architecture while propagating uncertainty for reliability. Simulation studies highlight superior performance of the proposed approach in achieving inferential objectives. The approach, termed as dynamic joint learner, enables predictive inference (with uncertainty) of diverse unobserved dynamic relationships among prominent terrorist organizations and their organization-specific attributes, as well as clustering behavior in terms of friend-and-foe relationships, which could be informative in counter-terrorism research.

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. We here consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).

Hi! We are back again with a new episode. In our third episode, we were joined by Mr. Saurabh Chopra, currently serving as a project manager for Royal Enfield; having garnered extensive strategy consulting experience at Deloitte and Accenture in the past. In this episode, Shaurya and Saurabh dig deep into exploring the minutiae on how companies are utilizing experiential marketing & technology. Specifically, the importance of voice search, AI Chatbots and Customer Acquisition for Travel sector companies and we also discuss the merits of Rentals Vs. Key Takeaway: Successful startups and established companies operate on similar key ideas and how incorporating them early in your business model could successfully future-proof your business.

Anomaly detection aims to distinguish observations that are rare and different from the majority. While most existing algorithms assume that instances are i.i.d., in many practical scenarios, links describing instance-to-instance dependencies and interactions are available. Such systems are called attributed networks. Anomaly detection in attributed networks has various applications such as monitoring suspicious accounts in social media and financial fraud in transaction networks. However, it remains a challenging task since the definition of anomaly becomes more complicated and topological structures are heterogeneous with nodal attributes. In this paper, we propose a spectral convolution and deconvolution based framework -- SpecAE, to project the attributed network into a tailored space to detect global and community anomalies. SpecAE leverages Laplacian sharpening to amplify the distances between representations of anomalies and the ones of the majority. The learned representations along with reconstruction errors are combined with a density estimation model to perform the detection. They are trained jointly as an end-to-end framework. Experiments on real-world datasets demonstrate the effectiveness of SpecAE.