Related papers: Third-Order Moment Varieties of Linear Non-Gaussia…
For a graph $G$ and a positive integer $c$, let $M_c(G)$ be the size of a subgraph of $G$ induced by a randomly sampled subset of $c$ vertices. Second-order moments of $M_c(G)$ encode part of the structure of $G$. We use this fact, coupled…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
We show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\mathbb{R}^3_\lambda$ and the components of…
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
We explain the motivation and main results of our work in reference arXiv:0906.0530 [hep-th]. Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for…
Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate…
Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be…
To help resolve issues of non-realizability and restriction to homogeneity faced by analytical theories of turbulence, we explore three-dimensional homogeneous shear turbulence of incompressible Newtonian fluids via optimal control and…
Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among…
Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible…
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…
Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the…
It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…
We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined…
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…
Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph $G$, checks…
The Wishart model of random covariance or correlation matrices continues to find ever more applications as the wealth of data on complex systems of all types grows. The heavy tails often encountered prompt generalizations of the Wishart…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…