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We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction…

In machine learning, a nonparametric forecasting algorithm for time series data has been proposed, called the kernel spectral hidden Markov model (KSHMM). In this paper, we propose a technique for short-term wind-speed prediction based on…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

The study of animal behavioural states inferred through hidden Markov models and similar state switching models has seen a significant increase in popularity in recent years. The ability to account for varying levels of behavioural scale…

A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…

The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we…

Hidden Markov models (HMMs) have been extensively used in the univariate and multivariate literature. However, there has been an increased interest in the analysis of matrix-variate data over the recent years. In this manuscript we…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

Dynamic modeling of longitudinal networks has been an increasingly important topic in applied research. While longitudinal network data commonly exhibit dramatic changes in its structures, existing methods have largely focused on modeling…

Electronic health records contain valuable information for monitoring patients' health trajectories over time. Disease progression models have been developed to understand the underlying patterns and dynamics of diseases using these data as…

We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…

This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling…

In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…

We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…

This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The…

Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium…

Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal…

A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…

We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…