Related papers: The entropy rate of Linear Additive Markov Process…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
We consider a pair of correlated processes {Z_n} and {S_n} (two sided), where the former is observable and the later is hidden. The uncertainty in the estimation of Z_n upon its finite past history is H(Z_n|Z_0^{n-1}), and for estimation of…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Modern language models rely on the transformer architecture and attention mechanism to perform language understanding and text generation. In this work, we study learning a 1-layer self-attention model from a set of prompts and associated…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward…
In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…
We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of…
We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes. We establish the fact that quick energy exchange inevitably induces large…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational…
We prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is jointly analytic as a function of…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…