6 papers
Beyond independent component analysis: identifiability and algorithms
Alvaro Ribot, Anna Seigal, Piotr Zwiernik
Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are d…
Orthogonal eigenvectors and singular vectors of tensors
Alvaro Ribot, Anna Seigal, Piotr Zwiernik
The spectral theorem says that a real symmetric matrix has an orthogonal basis of eigenvectors and that, for a matrix with distinct eigenvalues, the basis is unique (up to signs).…
Linear causal disentanglement via higher-order cumulants
Paula Leyes Carreno, Chiara Meroni, Anna Seigal
Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies betw…
Complete collineations for maximum likelihood estimation
Gergely Bérczi, Eloise Hamilton, Philipp Reichenbach +1
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation pro…
Rectifiable paths with polynomial log-signature are straight lines
Peter K. Friz, Terry Lyons, Anna Seigal
The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients are definite iterated integrals of the path. The signature characterises the path up…
Supermodular Rank: Set Function Decomposition and Optimization
Rishi Sonthalia, Anna Seigal, Guido Montufar
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summa…