Related papers: Analytic Properties of Trackable Weak Models
A path in an edge-colored graph is \textit{rainbow} if no two edges of it are colored the same. The graph is said to be \textit{rainbow connected} if there is a rainbow path between every pair of vertices. If there is a rainbow shortest…
The number of observable degrees of freedom is typically limited in experiments. Here, we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions.…
The correspondence between weighted undirected graphs and reversible Markov chains via vertex random walks is simple and well known. Leveraging this correspondence and ideas from the theory of dynamical systems, we study the structural…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
A hidden Markov model with trends is a hidden Markov model whose emission distributions are translated by a trend that depends on the current hidden state and on the current time. Contrary to standard hidden Markov models, such processes…
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…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
In this study, a spectral graph-theoretic grouping strategy for weakly supervised classification is introduced, where a limited number of labelled samples and a larger set of unlabelled samples are used to construct a larger annotated…
The dark energy component of the universe is often interpreted either in terms of a cosmological constant or as a scalar field. A generic feature of the scalar field models is that the equation of state parameter w= P/rho for the dark…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…
In this work, we present a probabilistic model for directed graphs where nodes have attributes and labels. This model serves as a generative classifier capable of predicting the labels of unseen nodes using either maximum likelihood or…
This paper considers the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. The basic theory of herdable systems is…
Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…