Related papers: On signal detection and confidence sets for low ra…
Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the…
A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank…
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
We study modeling and identification of processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…
We consider relative error low rank approximation of $tensors$ with respect to the Frobenius norm: given an order-$q$ tensor $A \in \mathbb{R}^{\prod_{i=1}^q n_i}$, output a rank-$k$ tensor $B$ for which $\|A-B\|_F^2 \leq (1+\epsilon)$OPT,…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…
In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In…
While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and…
Let $A:[0,1]\rightarrow\mathbb{H}_m$ (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in H\"{o}lder class $\Sigma(\beta,L)$. The goal of this paper is to study statistical estimation of $A$ based…