Related papers: On Robustness of Principal Component Regression
We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates $p$ can be up to a constant fraction of sample size $n$. In this regime, an important topic is to propose…
This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves…
Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be…
Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…
Ensuring safety of nonlinear systems under model uncertainty and external disturbances is crucial, especially for real-world control tasks. Predictive methods such as robust model predictive control (RMPC) require solving nonconvex…
This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…
Energy-based learning algorithms, such as predictive coding (PC), have garnered significant attention in the machine learning community due to their theoretical properties, such as local operations and biologically plausible mechanisms for…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with…
An approach is presented for robustness analysis and quantum (unitary) control synthesis based on the classic method of averaging. The result is a multicriterion optimization competing the nominal (uncertainty-free) fidelity with a well…