Statistical Analysis and Data Mining最新文献

Integrative learning of multiple datasets has the potential to mitigate the challenge of small n and large p that is often encountered in analysis of big biomedical data such as genomics data. Detection of weak yet important signals can be enhanced by jointly selecting features for all datasets. However, the set of important features may not always be the same across all datasets. Although some existing integrative learning methods allow heterogeneous sparsity structure where a subset of datasets can have zero coefficients for some selected features, they tend to yield reduced efficiency, reinstating the problem of losing weak important signals. We propose a new integrative learning approach which can not only aggregate important signals well in homogeneous sparsity structure, but also substantially alleviate the problem of losing weak important signals in heterogeneous sparsity structure. Our approach exploits a priori known graphical structure of features and encourages joint selection of features that are connected in the graph. Integrating such prior information over multiple datasets enhances the power, while also accounting for the heterogeneity across datasets. Theoretical properties of the proposed method are investigated. We also demonstrate the limitations of existing approaches and the superiority of our method using a simulation study and analysis of gene expression data from ADNI.

A challenge unique to classification model development is imbalanced data. In a binary classification problem, class imbalance occurs when one class, the minority group, contains significantly fewer samples than the other class, the majority group. In imbalanced data, the minority class is often the class of interest (e.g., patients with disease). However, when training a classifier on imbalanced data, the model will exhibit bias towards the majority class and, in extreme cases, may ignore the minority class completely. A common strategy for addressing class imbalance is data augmentation. However, traditional data augmentation methods are associated with overfitting, where the model is fit to the noise in the data. In this tutorial we introduce an advanced method for data augmentation: Generative Adversarial Networks (GANs). The advantages of GANs over traditional data augmentation methods are illustrated using the Breast Cancer Wisconsin study. To promote the adoption of GANs for data augmentation, we present an end-to-end pipeline that encompasses the complete life cycle of a machine learning project along with alternatives and good practices both in the paper and in a separate video. Our code, data, full results and video tutorial are publicly available in the paper's github repository.

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a random series based on B-splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put shrinkage priors on the regression coefficients. We apply a plug-in variational Bayesian algorithm for learning the sparse precision matrix and compare the performance to a posterior Gibbs sampling scheme in a simulation study. We finally apply the proposed methods to a microarray data set. The proposed methods have better performance as the dimension increases, and in particular, the variational Bayesian approach has the potential to speed up the estimation in the Bayesian nonparanormal graphical model without the Gaussianity assumption while retaining the information to construct the graph.

The quality of a cluster analysis of unlabeled units depends on the quality of the between units dissimilarity measures. Data dependent dissimilarity is more objective than data independent geometric measures such as Euclidean distance. As suggested by Breiman, many data driven approaches are based on decision tree ensembles, such as a random forest (RF), that produce a proximity matrix that can easily be transformed into a dissimilarity matrix. A RF can be obtained using labels that distinguish units with real data from units with synthetic data. The resulting dissimilarity matrix is input to a clustering program and units are assigned labels corresponding to cluster membership. We introduce a General Iterative Cluster (GIC) algorithm that improves the proximity matrix and clusters of the base RF. The cluster labels are used to grow a new RF yielding an updated proximity matrix which is entered into the clustering program. The process is repeated until convergence. The same procedure can be used with many base procedures such as the Extremely Randomized Tree ensemble. We evaluate the performance of the GIC algorithm using benchmark and simulated data sets. The properties measured by the Silhouette Score are substantially superior to the base clustering algorithm. The GIC package has been released in R: https://cran.r-project.org/web/packages/GIC/index.html.

Many machine learning algorithms depend on weights that quantify row and column similarities of a data matrix. The choice of weights can dramatically impact the effectiveness of the algorithm. Nonetheless, the problem of choosing weights has arguably not been given enough study. When a data matrix is completely observed, Gaussian kernel affinities can be used to quantify the local similarity between pairs of rows and pairs of columns. Computing weights in the presence of missing data, however, becomes challenging. In this paper, we propose a new method to construct row and column affinities even when data are missing by building off a co-clustering technique. This method takes advantage of solving the optimization problem for multiple pairs of cost parameters and filling in the missing values with increasingly smooth estimates. It exploits the coupled similarity structure among both the rows and columns of a data matrix. We show these affinities can be used to perform tasks such as data imputation, clustering, and matrix completion on graphs.