Related papers: Identification of Atlas models
Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is…
Parameter identifiability refers to the capability of accurately inferring the parameter values of a model from its observations (data). Traditional analysis methods exploit analytical properties of the closed form model, in particular…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
Ito equations are derived for simple stochastic cellular automaton with parameters and compared with results obtained from the histogram method. Good agreement for various parameters supports wide applicability of the Ito equation as a…
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…
Agent-based models of disease transmission involve stochastic rules that specify how a number of individuals would infect one another, recover or be removed from the population. Common yet stringent assumptions stipulate interchangeability…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for…
Organizations leverage anomaly and changepoint detection algorithms to detect changes in user behavior or service availability and performance. Many off-the-shelf detection algorithms, though effective, cannot readily be used in large…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
Given a collection of computational models that all estimate values of the same natural process, we compare the performance of the average of the collection to the individual member whose estimates are nearest a given set of observations.…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to…
Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…