9 papers
Shifted Anticoncentration for Real Gram Hafnians and Symmetric Gaussian Hafnians
Hongru Zhao
We prove a uniform shifted anticoncentration theorem for the hafnian of a real Gaussian Gram matrix under an explicit condition on the row dimension. After normalization by its roo…
Uniform Hiding and Two Routes to Relative Accuracy in Gaussian Boson Sampling
Hongru Zhao
Gaussian boson sampling requires control of how closely finite optical matrices follow Gaussian reference laws. We prove an explicit total variation bound of order between…
Convex Reparameterization and Self-Concordant Algorithms for Multivariate Regression with Covariance Estimation
Hongru Zhao, Huiqian Feng
Building on a reparameterization for multivariate linear regression that yields a jointly convex penalized likelihood in the reparameterized regression coefficient matrix and the p…
Weak Typicality of von Neumann Entanglement Entropy in Gaussian Boson Sampling
Hongru Zhao
We study the von Neumann entanglement entropy generated by a Haar distributed passive interferometer acting on equally squeezed input modes with fixed nonzero squeezing strengt…
Exact Moments of Gaussian Gram Hafnians Reveal an Threshold for Weak Anticoncentration
Hongru Zhao
Anticoncentration is central to hardness arguments for approximate sampling. In the independent Gaussian surrogate for collision free Gaussian boson sampling, the moment ratio stud…
Sharp Berry-Esseen Bounds for the Log Determinant of a Gaussian Sample Correlation Matrix
Hongru Zhao
Let be the Pearson sample correlation matrix formed from independent Gaussian observations in dimensions, and write . Under the null correlation $R…
On the Log Determinant of Sample Correlation Matrices under Gaussianity
Hongru Zhao
We prove a central limit theorem for the log determinant of a Gaussian Pearson sample correlation matrix as the dimension diverges. Only two conditions are imposed: the population…
Convergence and Stability Analysis of Self-Consuming Generative Models with Heterogeneous Human Curation
Hongru Zhao, Jinwen Fu, Tuan Pham
Self-consuming generative models have received significant attention over the last few years. In this paper, we study a self-consuming generative model with heterogeneous preferenc…
Globally-Optimal Greedy Experiment Selection for Active Sequential Estimation
Xiaoou Li, Hongru Zhao
Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequent…