Related papers: Robust Regularized Low-Rank Matrix Models for Regr…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro factorization, but these approaches can suffer from slow convergence, especially when dealing with solutions characterized by a large condition number,…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…
We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
In this work we collect and compare to each other many different numerical methods for regularized regression problem and for the problem of projection on a hyperplane. Such problems arise, for example, as a subproblem of demand matrix…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
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…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…