Mixture Markov Research Articles

Hidden Markov Mixtures for Change Detection in Unevenly Spaced Time Series

This work tackles sequential data change-point detection, a research area with various applications in different fields. It focuses on analyzing sequential data such that the distance between locations of consecutive observations is not fixed. The models developed here for change detection extend a Hidden Markov Mixture approach originally designed to handle irregular spacing to improve the identification of atypical values. These models consider the probability of Markov dependence explained by the distance between locations. Bayesian inference is carried out via Gibbs Sampling. Informative priors for the dependency structure are crucial to identify clusters. The models adapt these priors to enable change identification in a general setting. Two mixture models are formulated: one for mean changes and another for mean or variance changes. Post-processing strategies are suggested to categorize observations among the components to facilitate change identification by the mixtures. These strategies are based on maximum posterior probability and consider the uncertainty associated with classifications. Models and clustering performances are evaluated in simulation studies including a Monte Carlo scheme. The analysis also explores three real illustrations. Finally, the proposed approaches are compared to existing clustering and change detection methods available in the literature.

Clustering Sequence Data with Mixture Markov Chains with Covariates Using Multiple Simplex Constrained Optimization Routine (MSiCOR)

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However, the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization (EM) algorithm remains one of the most popular ways to estimate the MMM parameters, however, convergence of EM algorithm is not always guaranteed. Given the computational challenges in maximizing the mixture likelihood on the constrained parameter space, we develop a pattern search-based global optimization technique which can optimize any objective function on a collection of simplexes, which is eventually used to maximize MMM likelihood. This is shown to outperform other related global optimization techniques. In simulation experiments, the proposed method is shown to outperform the expectation-maximization (EM) algorithm in the context of MMM estimation performance. The proposed method is applied to cluster Multiple sclerosis (MS) patients based on their treatment sequences of disease-modifying therapies (DMTs). We also propose a novel method to cluster people with MS based on DMT prescriptions and associated clinical features (covariates) using MMM with covariates. Based on the analysis, we divided MS patients into three clusters. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters. Supplementary materials for this article are available online.

Jobs-housing balance and travel patterns among different occupations as revealed by Hidden Markov mixture models: the case of Hong Kong

Jobs-housing balance and travel patterns among different occupations as revealed by Hidden Markov mixture models: the case of Hong Kong

Hidden Markov Mixture of Gaussian Process Functional Regression: Utilizing Multi-Scale Structure for Time Series Forecasting

The mixture of Gaussian process functional regressions (GPFRs) assumes that there is a batch of time series or sample curves that are generated by independent random processes with different temporal structures. However, in real situations, these structures are actually transferred in a random manner from a long time scale. Therefore, the assumption of independent curves is not true in practice. In order to get rid of this limitation, we propose the hidden-Markov-based GPFR mixture model (HM-GPFR) by describing these curves with both fine- and coarse-level temporal structures. Specifically, the temporal structure is described by the Gaussian process model at the fine level and the hidden Markov process at the coarse level. The whole model can be regarded as a random process with state switching dynamics. To further enhance the robustness of the model, we also give a priori parameters to the model and develop a Bayesian-hidden-Markov-based GPFR mixture model (BHM-GPFR). The experimental results demonstrated that the proposed methods have both high prediction accuracy and good interpretability.

Predicting the stability of early employment with its timing and childhood social and health-related predictors: a mixture Markov model approach.

To extend work careers, it is important to focus on all working-aged people including young adults. The aim of this study was to identify typical patterns of work participation among young adults after their first entry into the labour market and to examine whether the timing of entry together with parental and own socio-economic position and health predict early work participation. More in-depth understanding of early careers and their early determinants is important to plan targeted interventions and to promote more stable work participation among young adults. We used the Finnish Birth Cohort 1987 including data from several registers from all 59,476 children born in 1987 as well as their parents, followed until 2015. We estimated a mixture Markov model that allowed for joint identification of latent classes of labour-market attachment, estimation of labour-market transitions within classes, and prediction of class membership using childhood social and health-related determinants. We observed that the first entry into the labour market as measured by six months in continuous employment was not a permanent entry for many, not only due to negative reasons such as unemployment and ill health but also due to more voluntary reasons such as studies. Individuals entering the labour market at a later age were more likely to be in continuous employment thereafter. More advantaged background predicted exits due to studies or - when following a late entry - stable employment, while disadvantaged background factors predicted more unstable work and long-term exits from the labour market.

Modeling and predicting students’ engagement behaviors using mixture Markov models

Modeling and predicting students’ engagement behaviors using mixture Markov models

Towards a Better Characterization of Career Paths: Sequential Job Embedding and Mixture Markov Models

Towards a Better Characterization of Career Paths: Sequential Job Embedding and Mixture Markov Models

Stationarity and ergodicity of Markov switching positive conditional mean models

A general Markov‐Switching autoregressive conditional mean model, valued in the set of non‐negative numbers, is considered. The conditional distribution of this model is a finite mixture of non‐negative distributions whose conditional mean follows a GARCH‐like dynamics with parameters depending on the state of a Markov chain. Three different variants of the model are examined depending on how the lagged‐values of the mixing variable are integrated into the conditional mean equation. The model includes, in particular, Markov mixture versions of various well‐known non‐negative time series models such as the autoregressive conditional duration model, the integer‐valued GARCH (INGARCH) model, and the Beta observation driven model. For the three variants of the model, conditions are given for the existence of a stationary and ergodic solution. The proposed conditions match those already known for Markov‐switching GARCH models. We also give conditions for finite marginal moments. Applications to various mixture and Markov mixture count, duration and proportion models are provided.

Cell Heterogeneity Analysis in Single-Cell RNA-seq Data Using Mixture Exponential Graph and Markov Random Field Model.

Advanced single-cell profiling technologies promote exploration of cell heterogeneity, and clustering of single-cell RNA (scRNA-seq) data enables discovery of coexpression genes and network relationships between genes. In particular, single-cell profiling of circulating tumor cells (CTCs) can provide unique insights into tumor heterogeneity (including in triple-negative breast cancer (TNBC)), while scRNA-seq leads to better understanding of subclonal architecture and biological function. Despite numerous reports suggesting a direct correlation between circulating tumor cells (CTCs) and poor clinical outcomes, few studies have provided a thorough heterogeneity characterization of CTCs. In addition, TNBC is a disease with not only intertumor but also intratumor heterogeneity and represents various biological distinct subgroups that may have relationships with immune functions that are not clearly established yet. In this article, we introduce a new scheme for detecting genotypic characterization of single-cell heterogeneities and apply it to CTC and TNBC single-cell RNA-seq data. First, we use an existing mixture exponential family graph model to partition the cell-cell network; then, with the Markov random field model, we obtain more flexible network rewiring. Finally, we find the cell heterogeneity and network relationships according to different high coexpression gene modules in different cell subsets. Our results demonstrate that this scheme provides a reasonable and effective way to model different cell clusters and different biological enrichment gene clusters. Thus, using different internal coexpression genes of different cell clusters, we can infer the differences in tumor composition and diversity.

Markovian Adaptive Filtering Algorithm for Block-Sparse System Identification

In this brief, a novel adaptive filtering algorithm for block-sparse system identification called, Block-Sparse Adaptive Bayesian Algorithm (BS-ABA) is proposed. We use a Gaussian Markov (GM) model to generate the unknown block-sparse system. In the proposed algorithm, a maximum a posteriori (MAP) estimation procedure is used to estimate the adaptive filter coefficients which characterized by a Gaussian Mixture Markov (GMM) model. Moreover, the convergence in the mean of the proposed algorithm is provided in this brief. Simulation results show that the computational complexity of the proposed algorithm is less than some recent algorithms, while the performance is comparable to them.

How does enterprise IoT traffic evolve? Real-world evidence from a Finnish operator

The adoption of Internet of Things (IoT) technologies in businesses is increasing and thus enterprise IoT (EIoT) is seemingly shifting from hype to reality. However, the actual use of EIoT over significant timescales has not been empirically analyzed. In other words, the reality remains unexplored. Furthermore, despite the variety of EIoT verticals, the use of IoT across vertical industries has not been compared. This paper uses a two-year EIoT dataset from a major Finnish mobile network operator to investigate device use across industries, cellular traffic patterns, and mobility patterns. We present a variety of novel findings: EIoT traffic volume per device has increased three-fold over the last two years, the share of LTE-enabled devices has remained low at around 2% and that 30% of EIoT devices are still 2G only, and there are order of magnitude differences between different industries’ EIoT traffic and mobility. We also show that daily traffic can be clustered into only three patterns, differing mainly in the presence and timing of a peak hour. Beyond these descriptive results, modeling and forecasting is conducted for both traffic and mobility. We forecast the total daily EIoT traffic through a temporal regression model and achieve an error of about 15% over medium-term (30 to 180 day) horizons. We also model device mobility through a Markov mixture model and quantify the upper bound of predictability for device mobility.

A New Approach to Dating the Reference Cycle

–This article proposes a new approach to the analysis of the reference cycle turning points, defined on the basis of the specific turning points of a broad set of coincident economic indicators. Each individual pair of specific peaks and troughs from these indicators is viewed as a realization of a mixture of an unspecified number of separate bivariate Gaussian distributions whose different means are the reference turning points. These dates break the sample into separate reference cycle phases, whose shifts are modeled by a hidden Markov chain. The transition probability matrix is constrained so that the specification is equivalent to a multiple change-point model. Bayesian estimation of finite Markov mixture modeling techniques is suggested to estimate the model. Several Monte Carlo experiments are used to show the accuracy of the model to date reference cycles that suffer from short phases, uncertain turning points, small samples, and asymmetric cycles. In the empirical section, we show the high performance of our approach to identifying the US reference cycle, with little difference from the timing of the turning point dates established by the NBER. In a pseudo real-time analysis, we also show the good performance of this methodology in terms of accuracy and speed of detection of turning point dates.

Operational safety assessment of offshore pipeline with multiple MIC defects

Microbiologically influenced corrosion (MIC) creates multiple defects. The interaction of MIC defects and their time dependence need to be considered for robust safety assessment of the asset.This paper presents a methodology for the dynamic safety assessment of the assets under the influence of MIC. The methodology is built by integrating the Bayesian Network (BN)–Markov Mixture (MM) technique with Monte Carlo simulation. The integration of BN and MM provides an empirical model to probabilistically predict the effective defect growth rate based on the multiple defects’ interaction. A rate-dependent stochastic formulation is also developed for the remaining strength and safe operating pressure prediction using the Monte Carlo simulation. The proposed methodology dynamically predicts and captures the evolving effect of corrosion defects’ interaction and effective defect growth rate on the remaining strength and survival likelihood of an in-service corroding asset. The methodology is tested on an offshore pipeline, and the dynamic effects of corrosion influencing parameters and defects’ interaction on the pipeline survivability were predicted. Critical safety influencing factors of the pipeline under complex microbial biofilm architecture were identified. The proposed methodology provides a parametric-based condition monitoring tool for effective management of MIC and ensuring safety in offshore systems.

Mixture modelling of categorical sequences with secondary components

In this paper, the forward selected first‐order Markov mixture (FSFOMM) is proposed for modelling heterogeneous categorical sequences with secondary components capable of detecting outlying sequences within each cluster. Such sequences are assumed to have different transition probabilities in certain states. The model provides an attractive and flexible tool for diagnostics of unusual behaviours and parsimonious modelling of transition probabilities. The algorithm is tested on simulated as well as real‐life datasets with promising results.

Modeling the density of US yield curve using Bayesian semiparametric dynamic Nelson-Siegel model

This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model for estimating the density of bond yields. Specifically, we model the distribution of the yield curve factors according to an infinite Markov mixture (iMM). The model allows for time variation in the mean and covariance matrix of factors in a discrete manner, as opposed to continuous changes in these parameters such as the Time Varying Parameter (TVP) models. Estimating the number of regimes using the iMM structure endogenously leads to an adaptive process that can generate newly emerging regimes over time in response to changing economic conditions in addition to existing regimes. The potential of the proposed framework is examined using US bond yields data. The semiparametric structure of the factors can handle various forms of non-normalities including fat tails and nonlinear dependence between factors using a unified approach by generating new clusters capturing these specific characteristics. We document that modeling parameter changes in a discrete manner increases the model fit as well as forecasting performance at both short and long horizons relative to models with fixed parameters as well as the TVP model with continuous parameter changes. This is mainly due to fact that the discrete changes in parameters suit the typical low frequency monthly bond yields data characteristics better.

Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models

Finite mixture models and their extensions to Markov mixture and mixture of experts models are very popular in analysing data of various kind. A challenge for these models is choosing the number of components based on marginal likelihoods. The present paper suggests two innovative, generic bridge sampling estimators of the marginal likelihood that are based on constructing balanced importance densities from the conditional densities arising during Gibbs sampling. The full permutation bridge sampling estimator is derived from considering all possible permutations of the mixture labels for a subset of these densities. For the double random permutation bridge sampling estimator, two levels of random permutations are applied, first to permute the labels of the MCMC draws and second to randomly permute the labels of the conditional densities arising during Gibbs sampling. Various applications show very good performance of these estimators in comparison to importance and to reciprocal importance sampling estimators derived from the same importance densities.

Business cycle patterns in European regions

The aim of this paper is threefold. First, we analyze the comovements of business cycles in European regions. Second, we date these business cycles and identify clusters of regions with similar business cycle behavior, using Finite Mixture Markov models. Third, we develop a new index to measure within-country homogeneity. We find that comovement among regions is, on average, quite low, although it increased during the convergence process prior to the euro cash and after the onset of the Great Recession. We identify five different groups of European regions. We also find heterogeneity in the size of border effects.

Characterizing Monetary and Fiscal Policy Rules and Interactions when Commodity Prices Matter

We examine the extent to which commodity price fluctuations matter for monetary and fiscal policy formulation in high primary commodity export economies. Markov mixture specifications of monetary and fiscal policy rules, stylized to account for commodity price slacks are estimated using specifically designed Bayesian techniques. We find that policymakers do indeed respond to commodity price slacks, and with varying degrees, depending on the policy regime in place and the country under investigation. Policy is characterized by distinctive episodes of active and passive policy regimes, driven by the response of monetary policy to inflation and the response of fiscal policy to past government debt. Moreover, monetary authorities fail to act aggressively enough to achieve announced inflation targets or to synchronize with fiscal authorities. The results hold implications for the correct specification of policy rules and interactions in DSGE models for these economies.

Adaptive Incremental Mixture Markov Chain Monte Carlo

We propose adaptive incremental mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric proposal kernel with a global rule, AIMM locally adapts a semiparametric kernel. AIMM is based on an independent Metropolis–Hastings proposal distribution which takes the form of a finite mixture of Gaussian distributions. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large. As a result, the number of components in the mixture proposal is not fixed in advance. Theoretically, we prove that there exists a stochastic process that can be made arbitrarily close to AIMM and that converges to the correct target distribution. We also illustrate that it performs well in practice in a variety of challenging situations, including high-dimensional and multimodal target distributions. Finally, the methodology is successfully applied to two real data examples, including the Bayesian inference of a semiparametric regression model for the Boston Housing dataset. Supplementary materials for this article are available online.

Novel Divide and Combine-Based Approach to Estimating Mixture Markov Model for Large Categorical Time Series Data: Application to Study of Clusters using Multiyear Travel Survey Data

Over the last few years, as with many other fields, the transportation discipline has been swept by the big data revolution. This revolution has not only brought about tremendous opportunities for conducting interesting data-driven analysis, it has also highlighted challenges associated with using traditional analytical methods to analyze these large datasets. To this end, this paper proposes a new Divide and Combine-based approach to estimating Mixture Markov models for analyzing large categorical time series data. The validity of this approach is demonstrated using a simulation study. Further, the feasibility and applicability is highlighted by conducting a clustering analysis of large activity–travel sequences using multiyear travel survey datasets. In the case study, each individual’s daily activity–travel behavior is characterized as a categorical time series that attempts to capture multiple aspects of travel and activity engagement simultaneously while also incorporating the timing and the schedule of different episodes. The proposed Divide and Combine-based Mixture Markov models are then used to cluster the large data. Subsequently, cluster compositions are explored to understand within and between-cluster differences and their associations with generational cohort factors, socioeconomic attributes, and demographic variables. As a preliminary exploration, the results suggest that travel patterns of individuals over the last three decades can be categorized into three types of travel patterns. Results also provide evidence in support of recent claims about different generational cohorts and their activity–travel behaviors.