Related papers: On Computing the Total Variation Distance of Hidde…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determining the interleaving distance in several settings. We show…
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic…
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm for hidden Markov models, in a…
Total variation distance (TV distance) is an important measure for the difference between two distributions. Recently, there has been progress in approximating the TV distance between product distributions: a deterministic algorithm for a…
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…
We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are $1$-interleaved is NP-complete, already for bigraded, interval…
The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…
In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$…
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…
Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.
Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function,…
A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…
Our model is a constrained homogeneous random walk in a nonnegative orthant Z_+^d. The convergence to stationarity for such a random walk can often be checked by constructing a Lyapunov function. The same Lyapunov function can also be used…