Session 42: Machine learning, classification and designs

Session title: Machine learning, classification and designs
Organizer: Annie Qu (UIUC)
Chair: Annie Qu (UIUC)
Time: June 6th, 1:15pm – 2:45pm
Location: VEC 1202 /1203

Speech 1: Efficient Gaussian Process Modeling using Experimental Design-based Subagging
Speaker: Ying Hung (Rutgers)
Abstract: We address two important issues in Gaussian process (GP) modeling. One is how to reduce the computational complexity in GP modeling and the other is how to simultaneous perform variable selection and estimation for the mean function of GP models. Estimation is computationally intensive for GP models because it heavily involves manipulations of an n-by-n correlation matrix, where n is the sample size. Conventional penalized likelihood approaches are widely used for variable selection. However the computational cost of the penalized likelihood estimation (PMLE) or the corresponding one-step sparse estimation (OSE) can be prohibitively high as the sample size becomes large, especially for GP models. To address both issues, we propose an efficient subsample aggregating (subagging) approach with an experimental design-based subsampling scheme. The proposed method is computationally cheaper, yet it can be shown that the resulting subagging estimators achieve the same efficiency as the original PMLE and OSE asymptotically. The finite-sample performance is examined through simulation studies. Application of the proposed methodology to a data center thermal study reveals some interesting information, including identifying an efficient cooling mechanism.

Speech 2: Structural Learning and Integrative Decomposition of Multi-View Data
Speaker: Irina Gaynanova (Texas A&M)
Abstract: The increased availability of the multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduction, association analysis between the views, and further learning tasks such as consensus clustering. Despite these advances, there remain significant challenges in modeling partially-shared components, and identifying the number of components of each type (shared/partially-shared/individual). In this work, we formulate a novel linked component model that directly incorporates partially-shared structures. We call this model SLIDE for Structural Learning and Integrative DEcomposition of multi-view data. We prove the existence of SLIDE decomposition and explicitly characterize the identifiability conditions. The proposed model fitting and selection techniques allow for joint identification of the number of components of each type, in contrast to existing sequential approaches. In our empirical studies, SLIDE demonstrates excellent performance in both signal estimation and component selection. We further illustrate the methodology on the breast cancer data from The Cancer Genome Atlas repository. This is joint work with Gen Li.

Speech 3: Shrinking characteristics of precision matrix estimators
Speaker: Adam Rothman (U. of Minnesota)
Abstract: We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative log-likelihood plus an L1 penalty on a linear function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and we propose an alternating direction method of multipliers algorithm for their computation. Our simulation studies show that our estimators can perform better than competitors when they are used to fit predictive models. In particular, we illustrate cases where our precision matrix estimators perform worse at estimating the population precision matrix while performing better at prediction.  This is joint work with Aaron Molstad.