65 problems

Conjecture on the necessity of global (PI). The gap between chamber-wise and global (PI) is structurally necessary in the non-injective setting; investigating this gap should lead…

Third-moment finite-candidate conjecture. Moments up to degree three should generically restrict the solution set to finitely many candidates.

Let $\mathcal{G}$ be any family of non-complete graphs, and let $M_G$ denote the homoscedastic linear structural equation model associated with $G\in\mathcal{G}$. Generic identifia…

Let $\mathcal{M}$ be an identifiable linear compartmental model whose Jacobian matrix is not square, so its singular locus is defined by the maximal minors of the Jacobian. An edge…

Let $\widetilde{\mathcal{M}}$ be a strongly connected linear compartmental model with at least one input and exactly one leak. A model is generically locally identifiable if its pa…

For a fixed ReLU-network architecture, let $\mathcal{P}$ denote the parameter space obtained from the space of weights by taking into account the trivial scaling and permutation sy…

Width-one identifiability conjecture. 1. There exist architectures $\mathcal{A}=(n_0,\ldots,n_{L+1})$ with $n_\ell=1$ for some $\ell\leq L$ for which no identifiable parameters exi…

Let $Z_i$ ($i\in[d_z]$) be latent variables and let $A$ be a set of observed variables whose support sets $I_j$ satisfy the sufficient diversity condition: for each latent variable…

Consider a finite set of spatial locations and a model whose covariance structure is given by a parsimonious Matérn covariance structure. Finite-location identifiability conjecture…

MHA weak identifiability conjecture. For every parameter $\theta\in\Theta$ of an MHA model, the parameter $\theta$ is weakly identifiable with respect to the symmetry group

Weak identifiability conjecture. With mild assumptions on the activation function $\sigma$, for every parameter $\theta \in \Theta$ of an MLP, there exists a parameter…

Let $X_1 \sim \operatorname{Laplace}(0,1/\sqrt{2})$ and $X_2 \sim \operatorname{t}_5(0,\sqrt{3/5})$, as in the third example, and let $\mathcalB_0$ denote the solution set consider…

Orthogonal identifiability conjecture. Under suitable regularity conditions, the conclusion of Proposition remains valid up to an orthogonal transformation for any two Borel probab…

Let $G=(V \cup \mathcal{H},D)$ be a factor analysis graph. M-identifiability and extended M-identifiability are the two identifiability properties defined by the matching criterion…

Let $n \geq 3$, and let $\mathcal{M} = (G, \textit{In}, \textit{Out}, \textit{Leak})$ be an $n$-compartment directed-cycle model with $\textit{In}=\{1\}$ and $\textit{Out}=\{p\}$,…

Two-orthogonal uniqueness and stabilization conjecture. A generic two-orthogonal tensor in $\mathbb{R}^{n_1}\otimes\cdots\otimes\mathbb{R}^{n_d}$ has a unique two-orthogonal decomp…

Let $k$ be the number of components in a mixture, and let $d$ denote the number of moments used. Rational identifiability means that, for generic sample moments for which the momen…

Consider $k$-mixtures of the Gaussian, gamma, and inverse Gaussian distributions, and let $d$ denote the number of moments used. Rational identifiability means that, for generic sa…

Let normalized deep self-attention networks be parametrized via $(\mathbf{M},L)$, where these parameters encode the network as defined in the paper. The normalization removes layer…

Knowns-and-unknowns sufficiency conjecture. Condition should be sufficient for identifiability in multi-channel factor analysis.

Shapiro's conjecture. The identifiability threshold that is generically sufficient for local identifiability should also be generically sufficient for global identifiability.

General-dimensional characterization conjecture. The following conditions are equivalent:

Let $sigma_{delta}^2(\cdot,\widehat{\alpha})$ be the variance function of the model, with $sigma_{Y,\delta}^2(\cdot,\widehat{\alpha})$ denoting the contribution associated with…

Degree conjecture. For all other models, the degree is greater than $1$.

Let $\mathcal{S}$ be the Segre variety of rank-$1$ tensors in $\mathbb{K}^{n_1\times\dots\times n_d}$, and let $\sigma_r(\mathcal{S})$ be the Zariski closure of the set of tensors…