We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary continuous marginal densities. We formulate our model as a non-parametric Bayesian mixture, while providing efficient MCMC inference. Experiments on synthetic and real data demonstrate that the increased flexibility of the copula mixture significantly improves the clustering and the interpretability of the results.
The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these types of dependencies, we propose a novel vine copula mixture model for continuous data. We discuss the model selection and parameter estimation problems and further formulate a new model-based clustering algorithm. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. Our simulation experiments illustrate…
Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random variable. Insurance companies in particular must investigate such dependencies between different lines of business and the effects that an extreme loss event, such as an earthquake or hurricane, has across multiple lines of business simultaneously. Copulas provide a popular model-based approach to analysing the dependency between risks, and the coefficient of tail d…
A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study
Department of Mathematics, University of Louisiana at Lafayette（数学系，路易斯安那州立大学拉斐特分校）；Department of Physical Sciences & Mathematics, West Liberty University（物理科学与数学系，韦斯特利比大学）；Department of Mathematics and Statistics, Minnesota State University（数学与统计学系，明尼苏达州立大学）；Department of Statistics, formerly of Presidency College, Kolkata, India（统计学系，原加尔各答 Presidency College）；Department of Kinesiology, University of Louisiana at Lafayette（运动科学系，路易斯安那州立大学拉斐特分校）；Department of Mathematics and Statistics, Texas Tech University（数学与统计学系，德克萨斯技术大学）；The Office of Vice President for Research, Innovation, and Economic Development, University of Louisiana at Lafayette（研究、创新与经济发展副总监办公室，路易斯安那州立大学拉斐特分校）
We consider learning continuous probabilistic graphical models in the face of missing data. For non-Gaussian models, learning the parameters and structure of such models depends on our ability to perform efficient inference, and can be prohibitive even for relatively modest domains. Recently, we introduced the Copula Bayesian Network (CBN) density model - a flexible framework that captures complex high-dimensional dependency structures while offering direct control over the univariate marginals, leading to improved generalization. In this work we show that the CBN model also offers significant…
Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas. First, our pair copula family selection procedure extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families. Second, our method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference. The merits of our approach…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-f…
A characteristic feature of time-to-event data analysis is possible censoring of the event time. Most of the statistical learning methods for handling censored data are limited by the assumption of independent censoring, even if this can lead to biased predictions when the assumption does not hold. This paper introduces Clayton-boost, a boosting approach built upon the accelerated failure time model, which uses a Clayton copula to handle the dependency between the event and censoring distributions. By taking advantage of a copula, the independent censoring assumption is not needed any more. Du…
Use copula to model dependency of variable extends multivariate gaussian assumption. In this paper we first empirically studied copula regression model with continous response. Both simulation study and real data study are given. Secondly we give a novel copula regression model with binary outcome, and we propose a score gradient estimation algorithms to fit the model. Both simulation study and real data study are given for our model and fitting algorithm.
In recent biomedical scientific problems, it is a fundamental issue to integratively cluster a set of objects from multiple sources of datasets. Such problems are mostly encountered in genomics, where data is collected from various sources, and typically represent distinct yet complementary information. Integrating these data sources for multi-source clustering is challenging due to their complex dependence structure including directional dependency. Particularly in genomics studies, it is known that there is certain directional dependence between DNA expression, DNA methylation, and RNA expre…
We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. This approach combines established methods to model (spatial) dependencies. On the one hand the geostatistical concept utilizing spatial differences between the variable locations to model the extend of spatial dependencies is applied. On the other hand the flexible class of C-vine copulas is utilized to model the spatial dependency structure locally. These local C-vine copulas are parametrized jointly, exploiting an existing relationship betwee…
This paper describes a novel sensitivity analysis method, able to handle dependency relationships between model parameters. The starting point is the popular Morris (1991) algorithm, which was initially devised under the assumption of parameter independence. This important limitation is tackled by allowing the user to incorporate dependency information through a copula. The set of model runs obtained using latin hypercube sampling, are then used for deriving appropriate sensitivity measures. Delft3D-WAQ (Deltares, 2010) is a sediment transport model with strong correlations between input param…
We propose a new class of multivariate survival models based on archimedean copulas with margins modeled by the Yang and Prentice (YP) model. The Ali-Mikhail-Haq (AMH), Clayton, Frank, Gumbel-Hougaard (GH), and Joe copulas are employed to accommodate the dependency among marginal distributions. Baseline distributions are modeled semiparametrically by the piecewise exponential (PE) distribution and the Bernstein polynomials. The new class of models possesses some attractive features: i) the ability to take into account survival data with crossing survival curves; ii) the inclusion of the well-k…
