Related papers: Necessary and sufficient conditions for identifiab…
Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the…
Probability of necessity and sufficiency (PNS) measures the likelihood of a feature set being both necessary and sufficient for predicting an outcome. It has proven effective in guiding representation learning for unimodal data, enhancing…
A number of ill-posed inverse problems in signal processing, like blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems (BIPs), i.e. the…
When fitting a multi-parameter model to a data set, computer algorithms may suggest that a range of parameters provide equally reasonable fits, making the parameter estimation difficult. Here, we prove this fact for an SIR model. We say a…
There has been growing interest in recent years in Q-matrix based cognitive diagnosis models. Parameter estimation and respondent classification under these models may suffer due to identifiability issues. Non-identifiability can be…
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…
Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous…
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
It is demonstrated that a necessary and sufficient condition that the Fisher information matrix of an ARMA model be nonsingular is that the model not be redundant, that is, the autoregressive and moving-average polynomials do not share…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…
Because of the base pairing rules in DNA, some mutations experienced by a portion of DNA during its evolution result in the same substitution, as we can only observe differences in coupled nucleotides. Then, in the absence of a bias between…
The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…
Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
Compound matrices have found applications in many fields of science including systems and control theory. In particular, a sufficient condition for $k$-contraction is that a logarithmic norm (also called matrix measure) of the $k$-additive…
Recent outbreaks of monkeypox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The…
We give a sufficient condition of nonlocality in order to reproduce singlet spin correlations. For a given pair of hidden variables and measurement directions this condition determines only the product of the outcomes and reproduces…
Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions…
I develop a revealed preference framework to test whether an aggregate allocation of indivisible objects satisfies Pareto efficiency and individual rationality (PI) without observing individual preferences. Exploiting the type-based…