Related papers: Markov-Modulated Linear Regression
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different…
For a class of stationary Markov-dependent sequences $(A_n,B_n)\in\mathbb{R}^2,$ we consider the random linear recursion $S_n=A_n+B_nS_{n-1},$ $n\in\mathbb{Z},$ and show that the distribution tail of its stationary solution has a power law…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. The behavior data in these systems are generated…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…
We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is $k$, the resulting model is a continuous-time Markov chain on $k$ states and, as a consequence of the product…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
AI training datasets will inevitably contain AI-generated examples, leading to ``feedback'' in which the output of one model impacts the training of another. It is known that such iterative feedback can lead to model collapse, yet the…
A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
In this paper, we study Markov-dependent reflected autoregressive processes, and other related models the analysis of which results in a vector-valued fixed-point functional equation of a certain type. In queueing terms, such processes…
In this work we present a modified neural network model which is capable to simulate Markov Chains. We show how to express and train such a network, how to ensure given statistical properties reflected in the training data and we…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…