Related papers: A Data-Driven McMillan Degree Lower Bound
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…
This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a…
This paper deals with the problem of finding a low-complexity estimate of the impulse response of a linear time-invariant discrete-time dynamic system from noise-corrupted input-output data. To this purpose, we introduce an identification…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
Low-rank matrix completion is a widely studied problem with many variants. Inductive matrix completion (IMC) incorporates row and column side information to significantly narrow the search space. Prior work falls into two regimes: methods…
Double Machine Learning is often justified by nuisance-rate conditions, yet finite-sample reliability also depends on the conditioning of the orthogonal-score Jacobian. This conditioning is typically assumed rather than tracked. When…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…
We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large…
In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric…
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…
Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such…
High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…