Related papers: Two-sided Matrix Regression
We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…
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…
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…
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We study adaptive two-sided assortment optimization for revenue maximization in choice-based matching platforms. The platform has two sides of agents, an initiating side, and a responding side. The decision-maker sequentially selects agents…
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…
This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the…
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…
Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…
We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius…
In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank.…