Related papers: Minimal Realization Problems for Hidden Markov Mod…

Lane determination and lane sequence determination are important components for many Connected and Automated Vehicle (CAV) applications. Lane determination has been solved using Hidden Markov Model (HMM) among other methods. The existing…

The aim of this paper is to address two related estimation problems arising in the setup of hidden state linear time invariant (LTI) state space systems when the dimension of the hidden state is unknown. Namely, the estimation of any finite…

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…

We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…

The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its…

In this paper we consider a transformer with an $n$-gram structure, such as the one underlying ChatGPT. The transformer provides next word probabilities, which can be used to generate word sequences. We consider methods for computing word…

Recently, hidden Markov models (HMMs) have achieved promising results for offline handwritten Chinese text recognition. However, due to the large vocabulary of Chinese characters with each modeled by a uniform and fixed number of hidden…

This paper proposes a computationally efficient method of solving evaluation problem of Hidden Markov Model (HMM) with a given set of discrete observation symbols, number of states and probability distribution matrices. The observation…

As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited…

Hidden Markov models (HMMs) offer a robust and efficient framework for analyzing time series data, modelling both the underlying latent state progression over time and the observation process, conditional on the latent state. However, a…

Recent years have seen substantial advances in the development of biofunctional materials using synthetic polymers. The growing problem of elusive sequence-functionality relations for most biomaterials has driven researchers to seek more…

Kullback Leibler (KL) control problems allow for efficient computation of optimal control by solving a principal eigenvector problem. However, direct applicability of such framework to continuous state-action systems is limited. In this…

Human motion plays an important role in many fields. Large databases exist that store and make available recordings of human motions. However, annotating each motion with multiple labels is a cumbersome and error-prone process. This…

An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational…

We consider a class of filtering problems for large populations where each individual is modeled by the same hidden Markov model (HMM). In this paper, we focus on aggregate inference problems in HMMs with discrete state space and continuous…

State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of…

In the classical setting, the training of a Hidden Markov Model (HMM) typically relies on a single, sufficiently long observation sequence that can be regarded as representative of the underlying stochastic process. In this context, the…

In this note we provide detailed derivations of two versions of small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We include derivations…

Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…

We study the challenge of predicting the time at which a competitor product, such as a novel high-capacity EV battery or a new car model, will be available to customers; as new information is obtained, this time-to-market estimate is…