Related papers: Kotlarski's lemma for dyadic models
Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. These subcommunities are informative for understanding the…
When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
Within network analysis, the analytical maximum entropy framework has been very successful for different tasks as network reconstruction and filtering. In a recent paper, the same framework was used for link-prediction for monopartite…
We develop local stable group theory directly from topological dynamics, and extend the main results in this subject to the setting of stability "in a model". Specifically, given a group $G$, we analyze the structure of sets $A\subseteq G$…
Recent CDF measurements of the inclusive cross section for a double parton scattering attach a great importance to any theoretical calculations of two-particle distribution functions. Using a parton interpretation of the leading logarithm…
We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
As more and more network-structured data sets are available, the statistical analysis of valued graphs has become common place. Looking for a latent structure is one of the many strategies used to better understand the behavior of a…
We present a probabilistic model for learning from dynamic relational data, wherein the observed interactions among networked nodes are modeled via the Bernoulli Poisson link function, and the underlying network structure are characterized…
An important step in unveiling the relation between network structure and dynamics defined on networks is to detect communities, and numerous methods have been developed separately to identify community structure in different classes of…
We establish a dynamical version of Kuratowski-Mycielski Theorem on the existence of "large" invariant dependent sets. We apply this result to the study of invariant chaotic sets in topological dynamical systems, simplify many known results…
We introduce a categorical framework for diffusion on network-structured data valued in weighted lattices, extending the Laplacian paradigm beyond the category of Hilbert spaces. Central to our approach is the Lawvere Laplacian, an…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of…
We present a mechanism for detecting adversarial examples based on data representations taken from the hidden layers of the target network. For this purpose, we train individual autoencoders at intermediate layers of the target network.…
By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an…
Kotlarski's identity has been widely used in applied economic research. However, how to conduct inference based on this popular identification approach has been an open question for two decades. This paper addresses this open problem by…
We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…