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The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning…
The detection of change-points in heterogeneous sequences is a statistical challenge with many applications in fields such as finance, signal analysis and biology. A wide variety of literature exists for finding an ideal set of…
With the symbolic framework of Probability Bracket Notation (PBN), the Markov Sequence Projector (MSP) is introduced to expand the evolution formula of Homogeneous Markov Chains (HMCs). The well-known weather example, a Visible Markov Model…
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models…
The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
This work proposes a multi-agent filtering algorithm over graphs for finite-state hidden Markov models (HMMs), which can be used for sequential state estimation or for tracking opinion formation over dynamic social networks. We show that…
Non-homogeneous hidden Markov models (NHHMM) are a subclass of dependent mixture models used for semi-supervised learning, where both transition probabilities between the latent states and mean parameter of the probability distribution of…
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…
This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on…
Modern vehicles are equipped with increasingly complex sensors. These sensors generate large volumes of data that provide opportunities for modeling and analysis. Here, we are interested in exploiting this data to learn aspects of behaviors…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
Practitioners use Hidden Markov Models (HMMs) in different problems for about sixty years. Besides, Conditional Random Fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We…
In this study, we address the interpretability issue in complex, black-box Machine Learning models applied to sequence data. We introduce the Model-Based tree Hidden Semi-Markov Model (MOB-HSMM), an inherently interpretable model aimed at…
The analysis of physiological processes over time are often given by spectrometric or gene expression profiles over time with only few time points but a large number of measured variables. The analysis of such temporal sequences is…
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) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…
Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful,…
Hidden Markov models (HMM) are commonly used in generation tasks and have demonstrated strong capabilities in neuro-symbolic applications for the Markov property. These applications leverage the strengths of neural networks and symbolic…
In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking…