@article{heng_zhou_chi_2023, title={Bayesian Trend Filtering via Proximal Markov Chain Monte Carlo}, volume={2}, ISSN={["1537-2715"]}, url={https://doi.org/10.1080/10618600.2023.2170089}, DOI={10.1080/10618600.2023.2170089}, abstractNote={Abstract Proximal Markov chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations of proximal MCMC, however, require hyperparameters and regularization parameters to be prespecified. In this article, we extend the paradigm of proximal MCMC through introducing a novel new class of nondifferentiable priors called epigraph priors. As a proof of concept, we place trend filtering, which was originally a nonparametric regression problem, in a parametric setting to provide a posterior median fit along with credible intervals as measures of uncertainty. The key idea is to replace the nonsmooth term in the posterior density with its Moreau-Yosida envelope, which enables the application of the gradient-based MCMC sampler Hamiltonian Monte Carlo. The proposed method identifies the appropriate amount of smoothing in a data-driven way, thereby automating regularization parameter selection. Compared with conventional proximal MCMC methods, our method is mostly tuning free, achieving simultaneous calibration of the mean, scale and regularization parameters in a fully Bayesian framework. Supplementary materials for this article are available online.}, journal={JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS}, author={Heng, Qiang and Zhou, Hua and Chi, Eric C.}, year={2023}, month={Feb} }
 @article{heng_chi_liu_2023, title={Robust Low-Rank Tensor Decomposition with the L-2 Criterion}, ISSN={["1537-2723"]}, url={https://doi.org/10.1080/00401706.2023.2200541}, DOI={10.1080/00401706.2023.2200541}, abstractNote={Abstract The growing prevalence of tensor data, or multiway arrays, in science and engineering applications motivates the need for tensor decompositions that are robust against outliers. In this article, we present a robust Tucker decomposition estimator based on the L2 criterion, called the Tucker- . Our numerical experiments demonstrate that Tucker- has empirically stronger recovery performance in more challenging high-rank scenarios compared with existing alternatives. The appropriate Tucker-rank can be selected in a data-driven manner with cross-validation or hold-out validation. The practical effectiveness of Tucker- is validated on real data applications in fMRI tensor denoising, PARAFAC analysis of fluorescence data, and feature extraction for classification of corrupted images.}, journal={TECHNOMETRICS}, author={Heng, Qiang and Chi, Eric C. and Liu, Yufeng}, year={2023}, month={May} }