Related papers: Analytic Properties of Trackable Weak Models
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out…
Multilayer networks generalize single-layered connectivity data in several directions. These generalizations include, among others, settings where multiple types of edges are observed among the same set of nodes (edge-colored networks) or…
We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense (average degree…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…
In this paper, we prove that finite state space non parametric hidden Markov models are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly…
Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained…
Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…