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Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models…
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent…
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by…
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. In the article, we…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the…
In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral…
Decomposable graphical models, also known as perfect DAG models, play a fundamental role in standard approaches to probabilistic inference via graph representations in modern machine learning and statistics. However, such models are limited…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory…
A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Lattice model with long-range interaction of power-law type that is connected with difference of non-integer order is suggested. The continuous limit maps the equations of motion of lattice particles into continuum equations with fractional…