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The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

Methodology · Statistics 2009-02-20 Aurore Delaigle , Peter Hall , Tatiyana V. Apanasovich

To obtain a large amount of training labels inexpensively, researchers have recently adopted the weak supervision (WS) paradigm, which leverages labeling rules to synthesize training labels rather than using individual annotations to…

Computation and Language · Computer Science 2022-10-10 Linxin Song , Jieyu Zhang , Tianxiang Yang , Masayuki Goto

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…

Information Theory · Computer Science 2021-06-29 HanQin Cai , Jian-Feng Cai , Ke Wei

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…

Information Theory · Computer Science 2020-06-25 Namrata Vaswani , Thierry Bouwmans , Sajid Javed , Praneeth Narayanamurthy

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Statistics Theory · Mathematics 2013-05-27 Zongming Ma

Convolutional Neural Networks (CNNs) are hard to deploy on edge devices due to its high computation and storage complexities. As a common practice for model compression, network pruning consists of two major categories: unstructured and…

Computer Vision and Pattern Recognition · Computer Science 2023-11-30 Yuchuan Tian , Hanting Chen , Tianyu Guo , Chao Xu , Yunhe Wang

Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs…

Machine Learning · Statistics 2020-11-05 Jiakou Liu , Xiong Xiong , Pei-Wei Ren , Da Zhao , Chun-Na Li , Yuan-Hai Shao

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization…

Machine Learning · Computer Science 2016-12-09 Yuanzhi Li , Yingyu Liang , Andrej Risteski

This paper provides a comprehensive estimation framework via nuclear norm plus $l_1$ norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive…

Statistics Theory · Mathematics 2021-04-07 Matteo Farnè , Angela Montanari

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…

Computational Complexity · Computer Science 2019-02-21 Matthew Brennan , Guy Bresler

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Machine Learning · Statistics 2023-02-23 Harry Dong , Tian Tong , Cong Ma , Yuejie Chi

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

Machine Learning · Computer Science 2019-04-19 Jicong Fan , Tommy W. S. Chow

Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we…

Statistics Theory · Mathematics 2008-07-31 Jianhua Z. Huang , Haipeng Shen , Andreas Buja

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

Methodology · Statistics 2019-12-16 Matteo Farnè , Angela Montanari

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

Machine Learning · Statistics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA…

Information Theory · Computer Science 2017-05-30 Huynh Van Luong , Nikos Deligiannis , Jurgen Seiler , Soren Forchhammer , Andre Kaup

Latent Class Analysis (LCA) is widely used to identify unobserved subgroups in social and behavioural sciences. A long-standing challenge for LCA is the interpretability of the latent classes, due to the high complexity of the estimated…

Methodology · Statistics 2026-05-20 Yuxuan Xu , Lea Kaufmann , Yunxiao Chen , Maria Kateri , Irini Moustaki

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…

Machine Learning · Computer Science 2016-03-29 Feiping Nie , Heng Huang