Timezone: »
Poster
Sparse Estimation Using General Likelihoods and Non-Factorial Priors
David P Wipf · Sri Nagarajan
Finding maximally sparse representations from overcomplete feature dictionaries frequently involves minimizing a cost function composed of a likelihood (or data fit) term and a prior (or penalty function) that favors sparsity. While typically the prior is factorial, here we examine non-factorial alternatives that have a number of desirable properties relevant to sparse estimation and are easily implemented using an efficient, globally-convergent reweighted $\ell_1$ minimization procedure. The first method under consideration arises from the sparse Bayesian learning (SBL) framework. Although based on a highly non-convex underlying cost function, in the context of canonical sparse estimation problems, we prove uniform superiority of this method over the Lasso in that, (i) it can never do worse, and (ii) for any dictionary and sparsity profile, there will always exist cases where it does better. These results challenge the prevailing reliance on strictly convex penalty functions for finding sparse solutions. We then derive a new non-factorial variant with similar properties that exhibits further performance improvements in empirical tests. For both of these methods, as well as traditional factorial analogs, we demonstrate the effectiveness of reweighted $\ell_1$-norm algorithms in handling more general sparse estimation problems involving classification, group feature selection, and non-negativity constraints. As a byproduct of this development, a rigorous reformulation of sparse Bayesian classification (e.g., the relevance vector machine) is derived that, unlike the original, involves no approximation steps and descends a well-defined objective function.
Author Information
David P Wipf (AWS)
Sri Nagarajan (UCSF)
More from the Same Authors
-
2021 : A Closer Look at Distribution Shifts and Out-of-Distribution Generalization on Graphs »
Mucong Ding · Kezhi Kong · Jiuhai Chen · John Kirchenbauer · Micah Goldblum · David P Wipf · Furong Huang · Tom Goldstein -
2022 Poster: Learning Enhanced Representation for Tabular Data via Neighborhood Propagation »
Kounianhua Du · Weinan Zhang · Ruiwen Zhou · Yangkun Wang · Xilong Zhao · Jiarui Jin · Quan Gan · Zheng Zhang · David P Wipf -
2022 Spotlight: Lightning Talks 5B-3 »
Yanze Wu · Jie Xiao · Nianzu Yang · Jieyi Bi · Jian Yao · Yiting Chen · Qizhou Wang · Yangru Huang · Yongqiang Chen · Peixi Peng · Yuxin Hong · Xintao Wang · Feng Liu · Yining Ma · Qibing Ren · Xueyang Fu · Yonggang Zhang · Kaipeng Zeng · Jiahai Wang · GEN LI · Yonggang Zhang · Qitian Wu · Yifan Zhao · Chiyu Wang · Junchi Yan · Feng Wu · Yatao Bian · Xiaosong Jia · Ying Shan · Zhiguang Cao · Zheng-Jun Zha · Guangyao Chen · Tianjun Xiao · Han Yang · Jing Zhang · Jinbiao Chen · MA Kaili · Yonghong Tian · Junchi Yan · Chen Gong · Tong He · Binghui Xie · Yuan Sun · Francesco Locatello · Tongliang Liu · Yeow Meng Chee · David P Wipf · Tongliang Liu · Bo Han · Bo Han · Yanwei Fu · James Cheng · Zheng Zhang -
2022 Spotlight: Self-supervised Amodal Video Object Segmentation »
Jian Yao · Yuxin Hong · Chiyu Wang · Tianjun Xiao · Tong He · Francesco Locatello · David P Wipf · Yanwei Fu · Zheng Zhang -
2022 Spotlight: NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification »
Qitian Wu · Wentao Zhao · Zenan Li · David P Wipf · Junchi Yan -
2022 Spotlight: Lightning Talks 1B-1 »
Qitian Wu · Runlin Lei · Rongqin Chen · Luca Pinchetti · Yangze Zhou · Abhinav Kumar · Hans Hao-Hsun Hsu · Wentao Zhao · Chenhao Tan · Zhen Wang · Shenghui Zhang · Yuesong Shen · Tommaso Salvatori · Gitta Kutyniok · Zenan Li · Amit Sharma · Leong Hou U · Yordan Yordanov · Christian Tomani · Bruno Ribeiro · Yaliang Li · David P Wipf · Daniel Cremers · Bolin Ding · Beren Millidge · Ye Li · Yuhang Song · Junchi Yan · Zhewei Wei · Thomas Lukasiewicz -
2022 Poster: NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification »
Qitian Wu · Wentao Zhao · Zenan Li · David P Wipf · Junchi Yan -
2022 Poster: Transformers from an Optimization Perspective »
Yongyi Yang · zengfeng Huang · David P Wipf -
2022 Poster: Descent Steps of a Relation-Aware Energy Produce Heterogeneous Graph Neural Networks »
Hongjoon Ahn · Yongyi Yang · Quan Gan · Taesup Moon · David P Wipf -
2022 Poster: Self-supervised Amodal Video Object Segmentation »
Jian Yao · Yuxin Hong · Chiyu Wang · Tianjun Xiao · Tong He · Francesco Locatello · David P Wipf · Yanwei Fu · Zheng Zhang -
2022 Poster: Learning Manifold Dimensions with Conditional Variational Autoencoders »
Yijia Zheng · Tong He · Yixuan Qiu · David P Wipf -
2021 : A Closer Look at Distribution Shifts and Out-of-Distribution Generalization on Graphs »
Mucong Ding · Kezhi Kong · Jiuhai Chen · John Kirchenbauer · Micah Goldblum · David P Wipf · Furong Huang · Tom Goldstein -
2020 Poster: Further Analysis of Outlier Detection with Deep Generative Models »
Ziyu Wang · Bin Dai · David P Wipf · Jun Zhu -
2012 Poster: Dual-Space Analysis of the Sparse Linear Model »
David P Wipf -
2011 Poster: Sparse Estimation with Structured Dictionaries »
David P Wipf -
2011 Spotlight: Sparse Estimation with Structured Dictionaries »
David P Wipf -
2008 Poster: Estimating the Location and Orientation of Complex, Correlated Neural Activity using MEG »
David P Wipf · Julia Owen · Hagai Attias · Kensuke Sekihara · Sri Nagarajan -
2008 Spotlight: Estimating the Location and Orientation of Complex, Correlated Neural Activity using MEG »
David P Wipf · Julia Owen · Hagai Attias · Kensuke Sekihara · Sri Nagarajan -
2007 Poster: A New View of Automatic Relevance Determination »
David P Wipf · Srikantan Nagarajan -
2006 Poster: Analysis of Empirical Bayesian Methods for Neuroelectromagnetic Source Localization »
David P Wipf · Rey R Ramirez · Jason A Palmer · Scott Makeig · Bhaskar Rao -
2006 Spotlight: Analysis of Empirical Bayesian Methods for Neuroelectromagnetic Source Localization »
David P Wipf · Rey R Ramirez · Jason A Palmer · Scott Makeig · Bhaskar Rao