Related papers: Inference for Low-Rank Models
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…
A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…
This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modeling such heterogeneity. We…
We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish…
Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn…
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are…
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…
Diffusion models have become the de facto standard for modern visual generation, including well-established frameworks such as latent diffusion and flow matching. Recently, modeling high-order dynamics has emerged as a promising frontier in…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…