Related papers: A Data-Driven McMillan Degree Lower Bound
We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown and…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
The inference of a large symmetric signal-matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks…
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite…
This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that…
Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For…
We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
In this paper, we address the classical problem of maximum-likelihood (ML) detection of data in the presence of random phase noise. We consider a system, where the random phase noise affecting the received signal is first compensated by a…
Distance-based supervised method, the minimal learning machine, constructs a predictive model from data by learning a mapping between input and output distance matrices. In this paper, we propose new methods and evaluate how their core…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
We study discrete dynamics governed by a difference inclusion whose increment is the sum of a selection from a set-valued map and a noise term. For any bounded realization, convergence follows once the inter-iterate diameter is controlled…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
In this paper we study the problem of learning minimum-energy controls for linear systems from heterogeneous data. Specifically, we consider datasets comprising input, initial and final state measurements collected using experiments with…
In this paper, we present a data-driven approach to identify second-order systems, having internal Rayleigh damping. This means that the damping matrix is given as a linear combination of the mass and stiffness matrices. These systems…
Self-learning is a classical approach for learning with both labeled and unlabeled observations which consists in giving pseudo-labels to unlabeled training instances with a confidence score over a predetermined threshold. At the same time,…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…