Related papers: Identifiability of parametric random matrix models
When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide range of unseen scenarios, as well as for understanding the underlying mechanisms.…
We find the asymptotic spectral distribution of random Kummer matrix. Then we formulate and prove a~free analogue of HV independence property, which is known for classical Kummer and Gamma random variables and for Kummer and Wishart…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
In this article, a novel identification test is proposed, which can be applied to parameteric models such as Mixture of Normal (MN) distributions, Markow Switching(MS), or Structural Autoregressive (SVAR) models. In the approach, it is…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…
The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been…
A model of rank polysemantic distribution with a minimal number of fitting parameters is offered. In an ideal case a parameter-free description of the dependence on the basis of one or several immediate features of the distribution is…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is…