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We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial…
Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural…
Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…
Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…
This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units,…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…
The signal to noise ratio (SNR) fundamentally limits the information accessible by magnetic resonance imaging (MRI). This limitation has been addressed by a host of denoising techniques, recently including so-called MPPCA: Principal…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true…
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
Principal Component Analysis (PCA) is a widely utilized technique for dimensionality reduction; however, its inherent lack of interpretability-stemming from dense linear combinations of all feature-limits its applicability in many domains.…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…