Related papers: Identifiability of parametric random matrix models
We continue studies of the uncertainty quantification problem in emission tomographies such as PET or SPECT when additional multimodal data (e.g., anatomical MRI images) are available. To solve the aforementioned problem we adapt the…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
In this paper, we first consider the parameter estimation of a multivariate random process distribution using multivariate Gaussian mixture law. The labels of the mixture are allowed to have a general probability law which gives the…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
The paper continues previous works which study the behavior of second correlation function of characteristic polynomials of the special case of $n\times n$ one-dimensional Gaussian Hermitian random band matrices, when the covariance of the…
We consider the random matrix obtained by picking vectors randomly from a large collection of mutually unbiased bases of $\mathbb{C}^n$, and prove that the spectral distribution converges to the Marchenko-Pastur law. This shows that vectors…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
This paper presents a method for investigating, through an automatic procedure, the (lack of) identifiability of parametrized dynamical models. This method takes into account constraints on parameters and returns parameters whose…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's…
We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
Image classifiers often use spurious patterns, such as "relying on the presence of a person to detect a tennis racket, which do not generalize. In this work, we present an end-to-end pipeline for identifying and mitigating spurious patterns…