More Like this

1. T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs

   Lee, Changwoo ; Zhao Tang Luo ; and Huiyan Sang ( December 2021 , Advances in neural information processing systems)

   Graphs have been commonly used to represent complex data structures. In models dealing with graph-structured data, multivariate parameters may not only exhibit sparse patterns but have structured sparsity and smoothness in the sense that both zero and non-zero parameters tend to cluster together. We propose a new prior for high-dimensional parameters with graphical relations, referred to as the Tree-based Low-rank Horseshoe (T-LoHo) model, that generalizes the popular univariate Bayesian horseshoe shrinkage prior to the multivariate setting to detect structured sparsity and smoothness simultaneously. The T-LoHo prior can be embedded in many high-dimensional hierarchical models. To illustrate its utility, we apply it to regularize a Bayesian high-dimensional regression problem where the regression coefficients are linked by a graph, so that the resulting clusters have flexible shapes and satisfy the cluster contiguity constraint with respect to the graph. We design an efficient Markov chain Monte Carlo algorithm that delivers full Bayesian inference with uncertainty measures for model parameters such as the number of clusters. We offer theoretical investigations of the clustering effects and posterior concentration results. Finally, we illustrate the performance of the model with simulation studies and a real data application for anomaly detection on a road network. The results indicate substantial improvements over other competing methods such as the sparse fused lasso. 

   more » « less
2. A neural kernel method for capturing multiscale high-dimensional micromorphic plasticity of materials with internal structures

   https://doi.org/10.1016/j.cma.2023.116317  

   Xiong, Zeyu ; Xiao, Mian ; Vlassis, Nikolaos ; Sun, WaiChing ( November 2023 , Computer Methods in Applied Mechanics and Engineering)

   De Lorenzis, L ; Papadrakakis, M ; Zohdi T.I. (Ed.)

   This paper introduces a neural kernel method to generate machine learning plasticity models for micropolar and micromorphic materials that lack material symmetry and have internal structures. Since these complex materials often require higher-dimensional parametric space to be precisely characterized, we introduce a representation learning step where we first learn a feature vector space isomorphic to a finite-dimensional subspace of the original parametric function space from the augmented labeled data expanded from the narrow band of the yield data. This approach simplifies the data augmentation step and enables us to constitute the high-dimensional yield surface in a feature space spanned by the feature kernels. In the numerical examples, we first verified the implementations with data generated from known models, then tested the capacity of the models to discover feature spaces from meso-scale simulation data generated from representative elementary volume (RVE) of heterogeneous materials with internal structures. The neural kernel plasticity model and other alternative machine learning approaches are compared in a computational homogenization problem for layered geomaterials. The results indicate that the neural kernel feature space may lead to more robust forward predictions against sparse and high-dimensional data. 

   more » « less
3. An Iterative Penalized Least Squares Approach to Sparse Canonical Correlation Analysis

   https://doi.org/10.1111/biom.13043  

   Mai, Qing ; Zhang, Xin ( February 2019 , Biometrics)

   It is increasingly interesting to model the relationship between two sets of high-dimensional measurements with potentially high correlations. Canonical correlation analysis (CCA) is a classical tool that explores the dependency of two multivariate random variables and extracts canonical pairs of highly correlated linear combinations. Driven by applications in genomics, text mining, and imaging research, among others, many recent studies generalize CCA to high-dimensional settings. However, most of them either rely on strong assumptions on covariance matrices, or do not produce nested solutions. We propose a new sparse CCA (SCCA) method that recasts high-dimensional CCA as an iterative penalized least squares problem. Thanks to the new iterative penalized least squares formulation, our method directly estimates the sparse CCA directions with efficient algorithms. Therefore, in contrast to some existing methods, the new SCCA does not impose any sparsity assumptions on the covariance matrices. The proposed SCCA is also very flexible in the sense that it can be easily combined with properly chosen penalty functions to perform structured variable selection and incorporate prior information. Moreover, our proposal of SCCA produces nested solutions and thus provides great convenient in practice. Theoretical results show that SCCA can consistently estimate the true canonical pairs with an overwhelming probability in ultra-high dimensions. Numerical results also demonstrate the competitive performance of SCCA.

    

   more » « less
4. Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms

   Little, Anna V ; Maggioni, Mauro ; Murphy, James M ( January 2020 , Journal of machine learning research)

   We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points. 

   more » « less
5. Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms

   Little, Anna ; Maggioni, Mauro ; Murphy, James M. ( January 2020 , Journal of machine learning research)

   null (Ed.)

   We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points. 

   more » « less