Related papers: Multidimensional measures of impulsively driven st…
This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically…
The ability to distinguish between stochastic systems based on their trajectories is crucial in thermodynamics, chemistry, and biophysics. The Kullback-Leibler (KL) divergence, $D_{\text{KL}}^{AB}(0,\tau)$, quantifies the distinguishability…
The irreversibility of a stationary time series can be quantified using the Kullback-Leibler divergence (KLD) between the probability to observe the series and the probability to observe the time-reversed series. Moreover, this KLD is a…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…
The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…
A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
Kullback--Leibler (KL) divergence is a fundamental measure of the dissimilarity between two probability distributions, but it can become unstable in high-dimensional settings due to its sensitivity to mismatches in distributional support.…
The second law of thermodynamics governs that nonequilibrium systems evolve towards states of higher entropy over time. However, it does not specify the rate of this evolution and the role of fluctuations that impact the system's dynamics.…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
We present two nonparametric approaches to Kullback-Leibler (KL) control, or linearly-solvable Markov decision problem (LMDP) based on Gaussian processes (GP) and Nystr\"{o}m approximation. Compared to recently developed parametric methods,…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motion. First, the Kullback-Leibler divergence between the path probabilities of…
The underlying physics of astronomical systems governs the relation between their measurable properties. Consequently, quantifying the statistical relationships between system-level observable properties of a population offers insights into…
We introduce a stochastic approximation method for the solution of an ergodic Kullback-Leibler control problem. A Kullback-Leibler control problem is a Markov decision process on a finite state space in which the control cost is…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…