5 papers
Poisson-response Tensor-on-Tensor Regression and Applications
Carlos Llosa-Vite, Daniel M. Dunlavy
We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distribu…
A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information
Carlos Llosa-Vite, Daniel M. Dunlavy, Richard B. Lehoucq +2
We establish parameter inference for the Poisson canonical polyadic (PCP) model of tensor count data through a latent-variable formulation. Our approach exploits the property that…
Near-Efficient and Non-Asymptotic Multiway Inference
Oscar López, Arvind Prasadan, Carlos Llosa-Vite +2
We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) param…
The Poisson tensor completion parametric estimator
Daniel M. Dunlavy, Richard B. Lehoucq, Carolyn D. Mayer +1
We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram fo…
The Average Spectrum Norm and Near-Optimal Tensor Completion
Oscar López, Richard Lehoucq, Carlos Llosa-Vite +2
We introduce a new tensor norm, the average spectrum norm, to study sample complexity of tensor completion problems based on the canonical polyadic decomposition (CPD). Properties…