From the 1 of 6 linked papers with an AI index.
6 papers
Bayesian Networks of Density Operators
Steffen Lauritzen, Piotr Zwiernik
The paper develops quantum versions of Bayesian networks on directed acyclic graphs, introducing intrinsic and extrinsic constructions for positive‑definite density operators and p…
The Markov Marginal Problem for Density Operators
Steffen Lauritzen, Piotr Zwiernik
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a…
Learning latent tree models with small query complexity
Luc Devroye, Gabor Lugosi, Piotr Zwiernik
We consider the problem of structure recovery in a graphical model of a tree where some variables are latent. Specifically, we focus on the Gaussian case, which can be reformulated…
The Identification Problem for Linear Rational Expectations Models
Majid M. Al-Sadoon, Piotr Zwiernik
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,…
Property testing in graphical models: testing small separation numbers
Luc Devroye, Gábor Lugosi, Piotr Zwiernik
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, wh…
Entropic covariance models
Piotr Zwiernik
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature…