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[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM)…

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving…

Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance…

The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it…

We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…

There has been considerable recent interest in algorithms for finding communities in networks - groups of vertex within which connections are dense (frequent), but between which connections are sparser (rare). Most of the current literature…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

It is important to predict any adversarial attacks and their types to enable effective defense systems. Often it is hard to label such activities as malicious ones without adequate analytical reasoning. We propose the use of Hidden Markov…

The latent position network model (LPM) is a popular approach for the statistical analysis of network data. A central aspect of this model is that it assigns nodes to random positions in a latent space, such that the probability of an…

There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…

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…

A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown…

Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or…

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 structure of interstellar medium can be characterised at large scales in terms of its global statistics (e.g. power spectra) and at small scales by the properties of individual cores. Interest has been increasing in structures at…

Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion,…

Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with…

Discovery and recognition of Group Activities (GA) based on imagery data processing have significant applications in persistent surveillance systems, which play an important role in some Internet services. The process is involved with…

Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of…

We propose a copula-based extension of the hidden Markov model (HMM) which applies when the observations recorded at each time in the sample are multivariate. The joint model produced by the copula extension allows decoding of the hidden…