相关论文: The infinite Viterbi alignment and decay-convexity

Since the early days of digital communication, Hidden Markov Models (HMMs) have now been routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. An HMM $(X_i,Y_i)_{i\ge 1}$ assumes observations…

Since the early days of digital communication, hidden Markov models (HMMs) have now been also routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. In an HMM $(X_i,Y_i)_{i\ge 1}$, observations…

For hidden Markov models one of the most popular estimates of the hidden chain is the Viterbi path -- the path maximising the posterior probability. We consider a more general setting, called the pairwise Markov model, where the joint…

We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to…

In a hidden Markov model, the underlying Markov chain is usually hidden. Often, the maximum likelihood alignment (Viterbi alignment) is used as its estimate. Although having the biggest likelihood, the Viterbi alignment can behave very…

This paper deals with convergence of the maximum a posterior probability path estimator in hidden Markov models. We show that when the state space of the hidden process is continuous, the optimal path may stabilize in a way which is…

The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum posterior probability (MAP).…

This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs). In particular, we propose parallel backward-forward type of filtering and smoothing algorithm as well as parallel Viterbi-type…

For hidden Markov models one of the most popular estimates of the hidden chain is the Viterbi path -- the path maximising the posterior probability. We consider a more general setting, called the pairwise Markov model (PMM), where the joint…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…

We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient…

In GNSS-denied environments, aiding a vehicle's inertial navigation system (INS) is crucial to reducing the accumulated navigation drift caused by sensor errors (e.g. bias and noise). One potential solution is to use measurements of gravity…

The EM procedure is a principal tool for parameter estimation in the hidden Markov models. However, applications replace EM by Viterbi extraction, or training (VT). VT is computationally less intensive, more stable and has more of an…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

We consider a bivariate, possibly non-homogeneous, finite-state Markov chain $(X,U)=\{(X_t,U_t)\}_{t=1}^n$. We are interested in the marginal process $X$, which typically is not a Markov chain. The goal is to find a realization (path)…

We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method,…

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…