Department of Statistics Graduate Student Seminar: Yura Kim and Aritra Guha, Department of Statistics, University of Michigan
Yura Kim: "Sparse K-means with a graph-induced penalty for clustering networks"
Abstract:
Clustering is a useful tool to discover previously unknown subpopulations, of special interest in neuroimaging where it is believed that many psychiatric conditions present in multiple distinct subtypes. The subjects in such neuroimaging studies are often represented via their functional or structural connectivity matrices viewed as networks, with one network per subject. Clustering with a large number of features is challenging in itself, and the network nature of the observations presents additional difficulties. A general method for clustering and feature selection in high dimensions was proposed by Witten and Tibshirani (2010), but simple feature selection via a lasso penalty is unlikely to result in meaningful interpretations in networks. Here we propose a method for clustering weighted networks, which takes advantage of the network structure of the data by imposing a group penalty on edges. The method allows us to identify clusters among subjects, as well as choose both regions and individual edges most responsible for cluster differences. We illustrate the method on both simulated data and fMRI data on schizophrenia.
Aritra Guha
Abstract:
In Bayesian estimation of finite mixture models with unknown number of components, it is a common practice to use an infinite mixture model with Dirichlet process prior for the mixing component weights. However, with this prior, the convergence rate of the posterior distribution for finite mixtures is far from optimal. An alternative approach is to use symmetric Dirichlet weights for the mixing component weights of finite mixture models, and put a prior on the number of components. In this paper we show that this approach is more amenable to optimal convergence, and we obtain an optimal √n convergence rate for the estimation of mixing measure relative to the Wasserstein metric. Furthermore, in practice the true data generating distribution may not be included in the support of the prior, sometimes due to mis-specification of kernel or mis-specification of the parameter space. In this paper, we also study the convergence behaviors of finite mixtures under these misspecified settings relative to the Wasserstein metric.
Abstract:
Clustering is a useful tool to discover previously unknown subpopulations, of special interest in neuroimaging where it is believed that many psychiatric conditions present in multiple distinct subtypes. The subjects in such neuroimaging studies are often represented via their functional or structural connectivity matrices viewed as networks, with one network per subject. Clustering with a large number of features is challenging in itself, and the network nature of the observations presents additional difficulties. A general method for clustering and feature selection in high dimensions was proposed by Witten and Tibshirani (2010), but simple feature selection via a lasso penalty is unlikely to result in meaningful interpretations in networks. Here we propose a method for clustering weighted networks, which takes advantage of the network structure of the data by imposing a group penalty on edges. The method allows us to identify clusters among subjects, as well as choose both regions and individual edges most responsible for cluster differences. We illustrate the method on both simulated data and fMRI data on schizophrenia.
Aritra Guha
Abstract:
In Bayesian estimation of finite mixture models with unknown number of components, it is a common practice to use an infinite mixture model with Dirichlet process prior for the mixing component weights. However, with this prior, the convergence rate of the posterior distribution for finite mixtures is far from optimal. An alternative approach is to use symmetric Dirichlet weights for the mixing component weights of finite mixture models, and put a prior on the number of components. In this paper we show that this approach is more amenable to optimal convergence, and we obtain an optimal √n convergence rate for the estimation of mixing measure relative to the Wasserstein metric. Furthermore, in practice the true data generating distribution may not be included in the support of the prior, sometimes due to mis-specification of kernel or mis-specification of the parameter space. In this paper, we also study the convergence behaviors of finite mixtures under these misspecified settings relative to the Wasserstein metric.
| Building: | West Hall |
|---|---|
| Event Type: | Workshop / Seminar |
| Tags: | seminar |
| Source: | Happening @ Michigan from Department of Statistics Graduate Seminar Series, Department of Statistics |
