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This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

Methodology · Statistics 2018-09-12 Jianqing Fan , Yuan Ke , Kaizheng Wang

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Machine Learning · Computer Science 2019-05-31 Liu Liu , Yanyao Shen , Tianyang Li , Constantine Caramanis

We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated…

Machine Learning · Computer Science 2022-11-01 Jiachang Liu , Chudi Zhong , Margo Seltzer , Cynthia Rudin

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit…

Methodology · Statistics 2016-02-15 Xiangyu Wang , David Dunson , Chenlei Leng

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…

Machine Learning · Statistics 2017-11-22 Eugene Ndiaye , Olivier Fercoq , Alexandre Gramfort , Vincent Leclère , Joseph Salmon

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

Machine Learning · Computer Science 2015-07-21 Tianbao Yang , Lijun Zhang , Rong Jin , Shenghuo Zhu

In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…

Statistics Theory · Mathematics 2024-05-30 Xiaofei Wu , Rongmei Liang , Zhimin Zhang , Zhenyu Cui

Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…

Machine Learning · Computer Science 2020-01-10 Bingbing Jiang , Chang Li , Maarten de Rijke , Xin Yao , Huanhuan Chen

We describe a fast method to eliminate features (variables) in l1 -penalized least-square regression (or LASSO) problems. The elimination of features leads to a potentially substantial reduction in running time, specially for large values…

Machine Learning · Computer Science 2011-05-19 Laurent El Ghaoui , Vivian Viallon , Tarek Rabbani

This paper discusses the critical decision process of extracting or selecting the features in a supervised learning context. It is often confusing to find a suitable method to reduce dimensionality. There are pros and cons to deciding…

Machine Learning · Computer Science 2022-06-22 Jean-Sébastien Dessureault , Daniel Massicotte

The compression of deep neural networks (DNNs) to reduce inference cost becomes increasingly important to meet realistic deployment requirements of various applications. There have been a significant amount of work regarding network…

Machine Learning · Computer Science 2020-11-12 Tianyi Chen , Bo Ji , Yixin Shi , Tianyu Ding , Biyi Fang , Sheng Yi , Xiao Tu

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…

Information Theory · Computer Science 2015-07-21 Anastasios Kyrillidis , Luca Baldassarre , Marwa El-Halabi , Quoc Tran-Dinh , Volkan Cevher

Hyperspectral images provide abundant spatial and spectral information that is very valuable for material detection in diverse areas of practical science. The high-dimensions of data lead to many processing challenges that can be addressed…

Computer Vision and Pattern Recognition · Computer Science 2020-05-19 Saeideh Ghanbari Azar , Saeed Meshgini , Tohid Yousefi Rezaii , Soosan Beheshti

Much work has been done recently to make neural networks more interpretable, and one obvious approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression…

Machine Learning · Statistics 2021-06-17 Ismael Lemhadri , Feng Ruan , Louis Abraham , Robert Tibshirani

Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…

Machine Learning · Computer Science 2015-03-19 Qi Mao , Ivor W. Tsang

Rendering high-fidelity images from sparse point clouds is still challenging. Existing learning-based approaches suffer from either hole artifacts, missing details, or expensive computations. In this paper, we propose a novel framework to…

Computer Vision and Pattern Recognition · Computer Science 2024-07-08 Jiaxu Wang , Ziyi Zhang , Junhao He , Renjing Xu

Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…

Machine Learning · Computer Science 2015-11-19 Ning Zhang , Prathamesh Chandrasekar

Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional…

Machine Learning · Statistics 2020-01-17 Jian Huang , Yuling Jiao , Lican Kang , Jin Liu , Yanyan Liu , Xiliang Lu

As the perception range of LiDAR expands, LiDAR-based 3D object detection contributes ever-increasingly to the long-range perception in autonomous driving. Mainstream 3D object detectors often build dense feature maps, where the cost is…

Computer Vision and Pattern Recognition · Computer Science 2023-01-09 Lue Fan , Yuxue Yang , Feng Wang , Naiyan Wang , Zhaoxiang Zhang

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

Machine Learning · Statistics 2017-05-10 Yuting Ma , Tian Zheng