Integrated Completed Likelihood Research Articles

Are information criteria good enough to choose the right the number of regimes in hidden Markov models?

Selecting the number of regimes in Hidden Markov models is an important problem. Many criteria are used to do so, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated completed likelihood (ICL), deviance information criterion (DIC), and Watanabe-Akaike information criterion (WAIC), to name a few. In this article, we introduced goodness-of-fit tests for general Hidden Markov models with covariates, where the distribution of the observations is arbitrary, i.e. continuous, discrete, or a mixture of both. A selection procedure is proposed based on this goodness-of-fit test. The main aim of this article is to compare the classical information criterion with the new criterion when the outcome is either continuous, discrete or zero-inflated. Numerical experiments assess the finite sample performance of the goodness-of-fit tests, and comparisons between the different criteria are made.

Abstract 11546: Functional Co-Clustering of Physical Activity Patterns Among Sexual and Gender Minority Adults

Introduction: Physical activity (PA) is a important modifiable risk factor for cardiovascular disease (CVD) and CVD mortality. There is growing evidence that sexual and gender minority (SGM; lesbian/gay, bisexual, transgender) adults are at higher risk of insufficient PA and CVD. Accelerometers allow for collection of granular PA data that can identify individual- and temporal heterogeneity in daily patterns. To date, no studies have investigated accelerometry-based PA patterns among SGM adults. Goal: To characterize daily PA trajectories among SGM adults and identify distinct phenotypes using a time series-based clustering technique. Methods: We recruited an online sample of healthy SGM adults in the United States who completed continuous wrist-worn accelerometry for 30 days to collect step counts. For clustering, we used a functional latent block models (FLBMs), where each 24-hour period was a Fourier-smoothed data curve. FLBMs allow hierarchical time-series data clustering by simultaneously clustering person- and day-level data. The optimal number of clusters was selected using the integrated completed likelihood (ICL) criterion. Results: Forty-two SGM adults with a mean age of 27.0 years (+/- 7.7) provided 1207 person-level days of accelerometry (range=6-31 days/person). A final model with 4 blocks (2 x 2 clusters) provided the best fit (ICL= -70086.4). Two person-level clusters were identified, which were characterized by differences in the amount and distribution of steps throughout the day were identified. Cluster 1 (n=26) had higher overall steps counts with significant morning and evening increases in step counts. Cluster 2 (n=16) had fewer steps that were within a narrower time period. We further identified 2 day-level clusters. Cluster 2 (n=14) had a wider temporal distribution of step counts and a higher variance on weekend days vs. weekdays relative to Cluster 1 (n=17). Conclusions: This is the first study to elucidate daily PA trajectories in SGM people. Using FLBM, we accounted for individual heterogeneity and relations among days. Findings can help identify individuals at increased risk of physical inactivity and subsequent negative health outcomes, providing important knowledge to inform behavioral interventions.

Unsupervised classification of CIGALE galaxy spectra

Aims. Our study aims at providing deeper insight into the power and limitation of an unsupervised classification algorithm (called Fisher-EM) on spectra of galaxies. This algorithm uses a Gaussian mixture in a discriminative latent subspace. To this end, we investigate the capacity of this algorithm to segregate the physical parameters used to generate mock spectra and the influence of the noise on the classification. Methods. With the code CIGALE and different values for nine input parameters characterising the stellar population, we simulated a sample of 11 475 optical spectra of galaxies containing 496 monochromatic fluxes. The statistical model and the optimum number of clusters are given in Fisher-EM by the integrated completed likelihood (ICL) criterion. We repeated the analyses several times to assess the robustness of the results. Results. Two distinct classifications can be distinguished in the case of the noiseless spectra. The classification with more than 13 clusters disappears when noise is added, while the classification with 12 clusters is very robust against noise down to a signal-to-noise ratio (S/N) of 3. At S/N = 1, the optimum is 5 clusters, but the classification is still compatible with the previous classification. The distribution of the parameters used for the simulation shows an excellent discrimination between classes. A higher dispersion both in the spectra within each class and in the parameter distribution leads us to conclude that despite a much higher ICL, the classification with more than 13 clusters in the noiseless case is not physically relevant. Conclusions. This study yields two conclusions that are valid at least for the Fisher-EM algorithm. Firstly, the unsupervised classification of spectra of galaxies is both reliable and robust to noise. Secondly, such analyses are able to extract the useful physical information contained in the spectra and to build highly meaningful classifications. In an epoch of data-driven astrophysics, it is important to trust unsupervised machine-learning approaches that do not require training samples that are unavoidably biased.

Clinical phenotyping in sarcoidosis using cluster analysis

BackgroundMost phenotyping paradigms in sarcoidosis are based on expert opinion; however, no paradigm has been widely adopted because of the subjectivity in classification. We hypothesized that cluster analysis could be performed on common clinical variables to define more objective sarcoidosis phenotypes.MethodsWe performed a retrospective cohort study of 554 sarcoidosis cases to identify distinct phenotypes of sarcoidosis based on 29 clinical features. Model-based clustering was performed using the VarSelLCM R package and the Integrated Completed Likelihood (ICL) criteria were used to estimate number of clusters. To identify features associated with cluster membership, features were ranked based on variable importance scores from the VarSelLCM model, and additional univariate tests (Fisher’s exact test and one-way ANOVA) were performed using q-values correcting for multiple testing. The Wasfi severity score was also compared between clusters.ResultsCluster analysis resulted in 6 sarcoidosis phenotypes. Salient characteristics for each cluster are as follows: Phenotype (1) supranormal lung function and majority Scadding stage 2/3; phenotype (2) supranormal lung function and majority Scadding stage 0/1; phenotype (3) normal lung function and split Scadding stages between 0/1 and 2/3; phenotype (4) obstructive lung function and majority Scadding stage 2/3; phenotype (5) restrictive lung function and majority Scadding stage 2/3; phenotype (6) mixed obstructive and restrictive lung function and mostly Scadding stage 4. Although there were differences in the percentages, all Scadding stages were encompassed by all of the phenotypes, except for phenotype 1, in which none were Scadding stage 4. Clusters 4, 5, 6 were significantly more likely to have ever been on immunosuppressive treatment and had higher Wasfi disease severity scores.ConclusionsCluster analysis produced 6 sarcoidosis phenotypes that demonstrated less severe and severe phenotypes. Phenotypes 1, 2, 3 have less lung function abnormalities, a lower percentage on immunosuppressive treatment and lower Wasfi severity scores. Phenotypes 4, 5, 6 were characterized by lung function abnormalities, more parenchymal abnormalities, an increased percentage on immunosuppressive treatment and higher Wasfi severity scores. These data support using cluster analysis as an objective and clinically useful way to phenotype sarcoidosis subjects and to empower clinicians to identify those with more severe disease versus those who have less severe disease, independent of Scadding stage.

High Incidence of TP53 and Epigenetic Modifying Oncogenes Mutations in a Large Cohort of Patients Enrolled in Phase 1 Clinical Trials for Relapsed or Refractory Diffuse Large B-Cell Lymphoma

High Incidence of TP53 and Epigenetic Modifying Oncogenes Mutations in a Large Cohort of Patients Enrolled in Phase 1 Clinical Trials for Relapsed or Refractory Diffuse Large B-Cell Lymphoma

Clustering Approach toward Large Truck Crash Analysis

Heterogeneity of crash data masks the underlying crash patterns and perplexes crash analysis. This paper aims to explore an advanced high-dimensional clustering approach to investigate heterogeneity in large datasets. Detailed records of crashes involving large trucks occurring in the state of Florida between 2007 and 2016 were examined to identify truck crash patterns and significant conditions contributing to the patterns. The block clustering method was applied to more than 220,000 crash records with nearly 200 attributes. The analysis showed promising results in segmenting a large heterogeneous dataset into meaningful subgroups (with 95.72% average degree of homogeneity for selected blocks). The goodness of fit for clustering methods is evaluated and both integrated completed likelihood (ICL) and pseudo-likelihood values improved significantly (20.8% and 21.1% respectively). Attribute clustering showed distinct characteristics for each cluster. Crash clustering revealed significant differences among the clusters and suggested that this crash dataset could be portioned as same-direction, opposing-direction, and single-vehicle crashes. Individual blocks defined by both row and column clustering were further investigated to better understand the contribution set of conditions that lead to large truck crashes. Major features for each of the three major types of crashes were analyzed, which may provide additional insights to develop potential countermeasures and strategies that target specific segments. The clustering approach could be used as a preanalysis method to identify homogeneous subgroups for further analysis, which will help enhance the effectiveness of safety programs.

Choosing the number of clusters in a finite mixture model using an exact integrated completed likelihood criterion

The integrated completed likelihood (ICL) criterion has proven to be a very popular approach in model-based clustering through automatically choosing the number of clusters in a mixture model. This approach effectively maximises the complete data likelihood, thereby including the allocation of observations to clusters in the model selection criterion. However for practical implementation one needs to introduce an approximation in order to estimate the ICL. Our contribution here is to illustrate that through the use of conjugate priors one can derive an exact expression for ICL and so avoiding any approximation. Moreover, we illustrate how one can find both the number of clusters and the best allocation of observations in one algorithmic framework. The performance of our algorithm is presented on several simulated and real examples.

Estimation and model selection for model-based clustering with the conditional classification likelihood

The Integrated Completed Likelihood (ICL) criterion was introduced by Biernacki, Celeux and Govaert (2000) in the model-based clustering framework to select a relevant number of classes and has been used by statisticians in various application areas. A theoretical study of ICL is proposed. A contrast related to the clustering objective is introduced: the conditional classification likelihood. An estimator and model selection criteria are deduced. The properties of these new procedures are studied and ICL is proved to be an approximation of one of these criteria. We contrast these results with the current leading point of view about ICL, that it would not be consistent. Moreover these results give insights into the class notion underlying ICL and feed a reflection on the class notion in clustering. General results on penalized minimum contrast criteria and upper-bounds of the bracketing entropy in parametric situations are derived, which can be useful per se. Practical solutions for the computation of the introduced procedures are proposed, notably an adapted EM algorithm and a new initialization method for EM-like algorithms which helps to improve the estimation in Gaussian mixture models.

Flexible mixture modelling with the polynomial Gaussian cluster-weighted model

In the context of mixture models with random covariates, this article presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. First, it allows for possible nonlinear dependencies in the mixture components by considering a polynomial regression. Second, it is not restricted to be used for model-based clustering only being contextualized in the most general model-based classification framework. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). The article also investigates the conditions under which the posterior probabilities of component-membership from a polynomial Gaussian CWM coincide with those of other well-established mixture-models which are related to it. When applied to artificial and real data, the polynomial Gaussian CWM has shown to outperform the mixture of polynomial Gaussian regressions, which is its natural competitor in the class of mixture models with fixed covariates.

Fast estimation of the Integrated Completed Likelihood criterion for change-point detection problems with applications to Next-Generation Sequencing data

In this paper, we consider the Integrated Completed Likelihood (ICL) as a useful criterion for estimating the number of changes in the underlying distribution of data, specifically in problems where detecting the precise location of these changes is the main goal. The exact computation of the ICL requires O(Kn2) operations (with K the number of segments and n the number of data-points) which is prohibitive in many practical situations with large sequences of data. We describe a framework to estimate the ICL with O(K2n) complexity. Our approach is general in the sense that it can accommodate any given model distribution. We checked the run-time and validity of our approach on simulated data and demonstrate its good performance when analyzing real Next-Generation Sequencing (NGS) data using a negative binomial model. Our method is implemented in the R package postCP and available on the CRAN repository.

Extending mixtures of multivariate t-factor analyzers

Model-based clustering typically involves the development of a family of mixture models and the imposition of these models upon data. The best member of the family is then chosen using some criterion and the associated parameter estimates lead to predicted group memberships, or clusterings. This paper describes the extension of the mixtures of multivariate t-factor analyzers model to include constraints on the degrees of freedom, the factor loadings, and the error variance matrices. The result is a family of six mixture models, including parsimonious models. Parameter estimates for this family of models are derived using an alternating expectation-conditional maximization algorithm and convergence is determined based on Aitken's acceleration. Model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). This novel family of mixture models is then applied to simulated and real data where clustering performance meets or exceeds that of established model-based clustering methods. The simulation studies include a comparison of the BIC and the ICL as model selection techniques for this novel family of models. Application to simulated data with larger dimensionality is also explored.

Optimising dynamic graphical models for video content analysis

A key problem in video content analysis using dynamic graphical models is to learn a suitable model structure given observed visual data. We propose a completed likelihood AIC (CL-AIC) scoring function for solving the problem. CL-AIC differs from existing scoring functions in that it aims to optimise explicitly both the explanation and prediction capabilities of a model simultaneously. CL-AIC is derived as a general scoring function suitable for both static and dynamic graphical models with hidden variables. In particular, we formulate CL-AIC for determining the number of hidden states for a hidden Markov model (HMM) and the topology of a dynamically multi-linked HMM (DML-HMM). The effectiveness of CL-AIC on learning the optimal structure of a dynamic graphical model especially given sparse and noisy visual date is shown through comparative experiments against existing scoring functions including Bayesian information criterion (BIC), Akaike’s information criterion (AIC), integrated completed likelihood (ICL), and variational Bayesian (VB). We demonstrate that CL-AIC is superior to the other scoring functions in building dynamic graphical models for solving two challenging problems in video content analysis: (1) content based surveillance video segmentation and (2) discovering causal/temporal relationships among visual events for group activity modelling.

Assessing a mixture model for clustering with the integrated completed likelihood

We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data.