The purpose of this study is to leverage modern technology (such as mobile or web apps in (2014)) to enrich epidemiology data and infer the transmission of disease. Homogeneity related research on population level has been intensively studied in previous work. In contrast, we develop hierarchical Graph-Coupled Hidden Markov Models (hGCHMMs) to simultaneously track the spread of infection in a small cell phone community and capture person-specific infection parameters by leveraging a link prior that incorporates additional covariates. We also reexamine the model evolution of the hGCHMM from simple HMMs and LDA, elucidating additional flexibility and interpretability. Due to the non-conjugacy of sparsely coupled HMMs, we design a new approximate distribution, allowing our approach to be more applicable to other application areas. Additionally, we investigate two common link functions, the beta-exponential prior and sigmoid function, both of which allow the development of a principled Bayesian hierarchical framework for disease transmission. The results of our model allow us to predict the probability of infection for each person on each day, and also to infer personal physical vulnerability and the relevant association with covariates. We demonstrate our approach experimentally on both simulation data and real epidemiological records.
Hidden Markov models are widely used in simulating the state space based disease progression @cite_0 @cite_16 @cite_22 @cite_2 , since HMMs actually mimic the behavior of an SIS model with discretized timestamps and are convenient in terms of the development of inference algorithm for different variants. In our work, we also adopt this basic framework to design our model. Other work like @cite_24 @cite_11 proposed a group lasso formulation or multi-task learning framework using optimization, and is far from our domain. A recent work by @cite_38 learned a continuous time series model looking at trajectories for different patients, but ignoring interactions between chains. Our work attempts to unify social network modeling of individuals using a hierarchical structure. @cite_34 utilized a fixed social network analysis on susceptible-infectious-recovered (SIR) models to identify high-risk individuals. @cite_18 's work on close proximity interactions (CPIs) of dynamic social networks at a high school indicated immunization strategies are more credible if extra contact data is provided.
@cite_38 @cite_18 @cite_22 @cite_34 @cite_0 @cite_24 @cite_2 @cite_16 @cite_11
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Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach‘s chorales and show that factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot. We have already shown that extracting long-term dependencies from sequential data is difficult, both for determimstic dynamical systems such as recurrent networks, and probabilistic models such as hidden Markov models (HMMs) or input output hidden Markov models (IOHMMs). In practice, to avoid this problem, researchers have used domain specific a-priori knowledge to give meaning to the hidden or state variables representing past context. In this paper, we propose to use a more general type of a-priori knowledge, namely that the temporal dependencies are structured hierarchically. This implies that long-term dependencies are represented by variables with a long time scale. This principle is applied to a recurrent network which includes delays and multiple time scales. Experiments confirm the advantages of such structures. A similar approach is proposed for HMMs and IOHMMs. Dynamic Bayesian networks such as Hidden Markov Models (HMMs) are successfully used as probabilistic models for human motion. The use of hidden variables makes them expressive models, but inference is only approximate and requires procedures such as particle filters or Markov chain Monte Carlo methods. In this work we propose to instead use simple Markov models that only model observed quantities. We retain a highly expressive dynamic model by using interactions that are nonlinear and non-parametric. A presentation of our approach in terms of latent variables shows logarithmic growth for the computation of exact log-likelihoods in the number of latent states. We validate our model on human motion capture data and demonstrate state-of-the-art performance on action recognition and motion completion tasks. Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial distributions over a discrete vocabulary, and the HMM parameters are set to maximize the likelihood of the observations. This paper presents a new Markovian sequence model, closely related to HMMs, that allows observations to be represented as arbitrary overlapping features (such as word, capitalization, formatting, part-of-speech), and defines the conditional probability of state sequences given observation sequences. It does this by using the maximum entropy framework to fit a set of exponential models that represent the probability of a state given an observation and the previous state. We present positive experimental results on the segmentation of FAQ’s. In this paper we present a novel approach to disambiguate textual mentions of named entities against the Wikipedia knowledge base. The conditional dependencies between different named entities across Wikipedia are represented as a Markov network. In our approach, named entities are treated as hidden variables and textual mentions as observations. The number of states and observations is huge and naively using the Viterbi algorithm to find the hidden state sequence that emits the query observation sequence is computationally infeasible, given a state space of this size. Based on an observation that is specific to the disambiguation problem, we propose an approach that uses a tailored approximation to reduce the size of the state space, making the Viterbi algorithm feasible. Results show good improvement in disambiguation accuracy relative to the baseline approach and to some state-of-the-art approaches. Also, our approach shows how, with suitable approximations, HMMs can be used in such large-scale state space problems. Summary Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness. We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that is for the density of a fixed number of consecutive observations. Using conditions on the prior, we are then able to define a consistent Bayesian estimator of the number of hidden states. It is known that the likelihood ratio test statistic for overfitted HMMs has a nonstandard behaviour and is unbounded. Our conditions on the prior may be seen as a way to penalize parameters to avoid this phenomenon. Inference of parameters is a much more difficult task than inference of marginal densities, we still provide a precise description of the situation when the observations are i.i.d. and we allow for 2 possible hidden states. In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric model where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the standard EM algorithm can be adapted to infer the model parameters. For the initialization step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the combining criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN. We present a user study and dataset designed and collected to analyze how humans use space in face-to-face interactions. In a proof-of-concept investigation into human spatial dynamics, a Hidden Markov Model (HMM) was trained over a subset of features to recognize each of three interaction cues - initiation, acceptance, and termination - in both dyadic and triadic scenarios; these cues are useful in predicting transitions into, during, and out of multi-party social encounters. It is shown that the HMM approach performed twice as well as a weighted random classifier, supporting the feasibility of recognizing and predicting social behavior based on spatial features.