Beta-Negative Binomial Process and Poisson Factor Analysis
By Mingyuan Zhou, Lauren Hannah, David B. Dunson, Lawrence Carin. 2011
257 citations recorded by the source corpus.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a \multiscoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an innite Poisson factor analysis model. A nite approximation for the beta process L evy random measure is constructed for convenient implementation. Ecient MCMC computations are performed with data augmentation and marginalization techniques. Encouraging results are shown on document count matrix factorization.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Dit-Yan Yeung
- Hao Wang
- David M. Blei
- Lawrence Carin
- Zhe Gan
- Chunyuan Li
- Rajesh Ranganath
- Jianfeng Gao
In Mathematical Physics
- Dit-Yan Yeung
- Hao Wang
- David M. Blei
- Prem Gopalan
- Francisco J. R. Ruiz
- Zhe Gan
- Lawrence Carin
- Rajesh Ranganath
In Statistics and Probability
- David M. Blei
- Rajesh Ranganath
- Prem Gopalan
- Francisco J. R. Ruiz
- Dit-Yan Yeung
- Hao Wang
- Zhe Gan
- Piyush Rai
Citations in the corpus
- Natural-Parameter Networks: A Class of Probabilistic Neural Networks (2016, methodology): “For example, in gamma distributions p ( x | c, d ) = Γ( c ) − 1 d c x c − 1 exp( − dx ) , we use proxy natural parameters ( c, d ) during computation rather than the natural parameters ( c − 1 , − d ) .”
- Scalable Recommendation with Poisson Factorization (2013, methodology): “Future work includes extensions to HPF, to provide coldstart recommendations using text data [33], and to infer the number of latent components using Bayesian nonparametric assumptions [35]; and stochastic variational inference [14], to analyze data sets larger than those we studied.”
- Deep Generative Models for Relational Data with Side Information (2017, methodology): “The first data augmentation technique we use is based on the Poissonmultinomial equivalence (Zhou et al., 2012).”
- Bayesian Nonparametric Poisson Factorization for Recommendation Systems (2014, methodology): “For convenience, and similarly to previous works (Dunson & Herring, 2005; Zhou et al., 2012; Gopalan et al., 2013), we introduce for each user-item pair”
- Focus Attention: Promoting Faithfulness and Diversity in Summarization (2021, methodology): “(2020c) use Poisson factor analysis (Zhou et al., 2012), to synthesize topic vectors for the input.”
- Deep Poisson Factor Modeling (2015, methodology): “Further details on perplexity evaluation for PFA models can be found in [6, 32].”
- A Survey on Bayesian Deep Learning (2016, methodology): “Poisson Factor Analysis : PFA assumes a discrete P -by- N matrix X containing word counts of N documents with a vocabulary size of P [24, 136].”