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Multiplicative Forests for ContinuousTime Processes
"... Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuoustime Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per varia ..."
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Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuoustime Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per variable. We develop a partitionbased representation using regression trees and forests whose parameter spaces grow linearly in the number of node splits. Using a multiplicative assumption we show how to update the forest likelihood in closed form, producing efficient model updates. Our results show multiplicative forests can be learned from few temporal trajectories with large gains in performance and scalability. 1
Modeling Correlated Arrival Events with Latent SemiMarkov Processes
"... The analysis of correlated point process data has wide applications, ranging from biomedical research to network analysis. In this work, we model such data as generated by a latent collection of continuoustime binary semiMarkov processes, corresponding to external events appearing and disappear ..."
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Cited by 3 (2 self)
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The analysis of correlated point process data has wide applications, ranging from biomedical research to network analysis. In this work, we model such data as generated by a latent collection of continuoustime binary semiMarkov processes, corresponding to external events appearing and disappearing. A continuoustime modeling framework is more appropriate for multichannel point process data than a binning approach requiring time discretization, and we show connections between our model and recent ideas from the discretetime literature. We describe an efficient MCMC algorithm for posterior inference, and apply our ideas to both synthetic data and a realworld biometrics application. 1.
A survey of nonexchangeable priors for Bayesian nonparametric models
, 2014
"... Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do ..."
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Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.
Efficient ContinuousTime Markov Chain Estimation
"... Many problems of practical interest rely on Continuoustime Markov chains (CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible with existing methods. For problems with countably infinite sta ..."
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Many problems of practical interest rely on Continuoustime Markov chains (CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible with existing methods. For problems with countably infinite states, where classical methods such as matrix exponentiation are not applicable, the main alternative has been particle Markov chain Monte Carlo methods imputing both the holding times and sequences of visited states. We propose a particlebased Monte Carlo approach where the holding times are marginalized analytically. We demonstrate that in a range of realistic inferential setups, our scheme dramatically reduces the variance of the Monte Carlo approximation and yields more accurate parameter posterior approximations given a fixed computational budget. These experiments are performed on both synthetic and real datasets, drawing from two important examples of CTMCs having combinatorial state spaces: stringvalued mutation models in phylogenetics and nucleic acid folding pathways. 1.
A unifying representation for a class of dependent random measures
, 1211
"... We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measure ..."
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We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariatedependent latent feature model and topic model that obtain superior predictive performance. 1
Markovmodulated Marked Poisson Processes for Checkin Data
"... Abstract We develop continuoustime probabilistic models to study trajectory data consisting of times and locations of user 'checkins'. We model the data as realizations of a marked point process, with intensity and markdistribution modulated by a latent Markov jump process (MJP). We al ..."
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Abstract We develop continuoustime probabilistic models to study trajectory data consisting of times and locations of user 'checkins'. We model the data as realizations of a marked point process, with intensity and markdistribution modulated by a latent Markov jump process (MJP). We also include userheterogeneity in our model by assigning each user a vector of 'preferred locations'. Our model extends latent Dirichlet allocation by dropping the bagofwords assumption and operating in continuous time. We show how an appropriate choice of priors allows efficient posterior inference. Our experiments demonstrate the usefulness of our approach by comparing with various baselines on a variety of tasks.
Supplementary Document
"... This Supplement contains the proofs and pseudocodes of the methods referenced in the Methodology section of the paper, as well as supplemental figures and tables for the Numerical examples section of the paper. The proofs involve the basic properties of our CTMC approach, and provide rigorous justi ..."
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This Supplement contains the proofs and pseudocodes of the methods referenced in the Methodology section of the paper, as well as supplemental figures and tables for the Numerical examples section of the paper. The proofs involve the basic properties of our CTMC approach, and provide rigorous justification for the algorithms presented in the paper. The pseudocodes illustrate the overviews of the steps of different methods used in the manuscript. The supplemental figures and tables also provide more extensive justification for the practical applicability of our method to both the phylogenetic and RNA settings. 1