• Corpus ID: 246276100

Zero-Truncated Poisson Regression for Zero-Inflated Multiway Count Data

  title={Zero-Truncated Poisson Regression for Zero-Inflated Multiway Count Data},
  author={O. Gonz'alez L'opez and Daniel M. Dunlavy and Richard B. Lehoucq},
. We propose a novel statistical inference paradigm for zero-inflated multiway count data that dispenses with the need to distinguish between true and false zero counts. Our approach ignores all zero entries and applies zero-truncated Poisson regression on the positive counts. Inference is accomplished via tensor completion that imposes low-rank structure on the Poisson parameter space. Our main result shows that an N -way rank- R parametric tensor M ∈ (0 , ∞ ) I ×···× I generating Poisson… 

Figures and Tables from this paper

Frugal hyperspectral imaging via low rank tensor reconstruction
A remote hyperspectral (HS) imaging work flow that relays spectral and spatial information of a scene via a minimal amount of encoded samples along with a robust data reconstruction scheme that outperforms state of the art methods, achieving noise attenuation while reducing the amount of collected data by a factor of 1/14.


Variational Inference for sparse network reconstruction from count data
This work adopts a latent model where it directly model counts by means of Poisson distributions that are conditional to latent (hidden) Gaussian correlated variables, and shows that this approach is highly competitive with the existing methods on simulation inspired from microbiological data.
A review on models for count data with extra zeros
Typically, the zero inflated models are usually used in modelling count data with excess zeros. The existence of the extra zeros could be structural zeros or random which occur by chance. These types
The Analysis of Count Data: Over-dispersion and Autocorrelation
I begin this paper by describing several methods that can be used to analyze count data. Starting with relatively familiar maximum likelihood methods-Poisson and negative binomial regression-I then
The Analysis of Count Data: A Gentle Introduction to Poisson Regression and Its Alternatives
Two variants of Poisson regression, overdispersedPoisson regression and negative binomial regression, are introduced that may provide more optimal results when a key assumption of standard Poisson regressors is violated.
On Tensors, Sparsity, and Nonnegative Factorizations
This paper proposes that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution, and presents a new algorithm for Poisson tensor factorization called CANDECOMP--PARAFAC alternating Poisson regression (CP-APR), based on a majorization-minimization approach.
Stochastic Gradients for Large-Scale Tensor Decomposition
This work proposes using stochastic gradients for efficient generalized canonical polyadic tensor decomposition of large-scale tensors of sparse and dense tensors using two types of stratified sampling that give precedence to sampling nonzeros.
Generalized Canonical Polyadic Tensor Decomposition
This work develops a generalized canonical polyadic (GCP) low-rank tensor decomposition that allows other loss functions besides squared error, and presents a variety statistically-motivated loss functions for various scenarios.
Network analysis for count data with excess zeros
A penalized version of zero inflated spatial Poisson regression is presented and an efficient EM algorithm built on coordinate descent is derived that may help in identifying biological pathways linked to sex hormone regulation and thus understanding underlying mechanisms of the gender differences.
What does a zero mean? Understanding false, random and structural zeros in ecology
Zeros (i.e. events that do not happen) are the source of two common phenomena in count data: overdispersion and zero‐inflation. Zeros have multiple origins in a dataset: false zeros occur due to
Poisson Matrix Recovery and Completion
  • Yang Cao, Yao Xie
  • Computer Science
    IEEE Transactions on Signal Processing
  • 2016
The results highlight a few important distinctions of the Poisson case compared to the prior work including having to impose a minimum signal-to-noise requirement on each observed entry and a gap in the upper and lower bounds.