Related papers: Statistical inference for Axiom A attractors
Extracting useful information from data is a fundamental challenge across disciplines as diverse as climate, neuroscience, genetics, and ecology. In the era of ``big data'', data is ubiquitous, but appropriated methods are needed for…
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The wave properties of complex scattering systems that are large compared to the wavelength, and show chaos in the classical limit, are extremely sensitive to system details. A solution to the wave equation for a specific configuration can…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
In-depth studies of sociotechnical systems are largely limited to single instances. Network surveys are expensive, and platforms vary in important ways, from interface design, to social norms, to historical contingencies. With single…
We investigate how individuals form expectations about population behavior using statistical inference based on observations of their social relations. Misperceptions about others' connectedness and behavior arise from sampling bias…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
Uncertainty plays a key role in future prediction. The future is uncertain. That means there might be many possible futures. A future prediction method should cover the whole possibilities to be robust. In autonomous driving, covering…
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…
Active inference has emerged as an alternative approach to control problems given its intuitive (probabilistic) formalism. However, despite its theoretical utility, computational implementations have largely been restricted to…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…