Related papers: The entropy rate of Linear Additive Markov Process…
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…
In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize…
We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…
The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be…
The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model…
This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
Learned image compression methods have attracted great research interest and exhibited superior rate-distortion performance to the best classical image compression standards of the present. The entropy model plays a key role in learned…
Deploying LLMs raises two coupled challenges: (1) monitoring--estimating where a model underperforms as traffic and domains drift--and (2) improvement--prioritizing data acquisition to close the largest performance gaps. We test whether an…
Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…
We consider the problem of estimating the mean entropy production rate in a nonequilibrium process from the measurements of first-passage quantities associated with a single current. For first-passage processes with large thresholds, Refs.…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically…
Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication or locomotion. Given time series observations of intra-, inter- or multicellular processes,…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching.…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…