TY - GEN
T1 - Priors for diversity in generative latent variable models
AU - Zou, James Y.
AU - Adams, Ryan P.
PY - 2012
Y1 - 2012
N2 - Probabilistic latent variable models are one of the cornerstones of machine learning. They offer a convenient and coherent way to specify prior distributions over unobserved structure in data, so that these unknown properties can be inferred via posterior inference. Such models are useful for exploratory analysis and visualization, for building density models of data, and for providing features that can be used for later discriminative tasks. A significant limitation of these models, however, is that draws from the prior are often highly redundant due to i.i.d. assumptions on internal parameters. For example, there is no preference in the prior of a mixture model to make components non-overlapping, or in topic model to ensure that co-occurring words only appear in a small number of topics. In this work, we revisit these independence assumptions for probabilistic latent variable models, replacing the underlying i.i.d. prior with a determinantal point process (DPP). The DPP allows us to specify a preference for diversity in our latent variables using a positive definite kernel function. Using a kernel between probability distributions, we are able to define a DPP on probability measures. We show how to perform MAP inference with DPP priors in latent Dirichlet allocation and in mixture models, leading to better intuition for the latent variable representation and quantitatively improved unsupervised feature extraction, without compromising the generative aspects of the model.
AB - Probabilistic latent variable models are one of the cornerstones of machine learning. They offer a convenient and coherent way to specify prior distributions over unobserved structure in data, so that these unknown properties can be inferred via posterior inference. Such models are useful for exploratory analysis and visualization, for building density models of data, and for providing features that can be used for later discriminative tasks. A significant limitation of these models, however, is that draws from the prior are often highly redundant due to i.i.d. assumptions on internal parameters. For example, there is no preference in the prior of a mixture model to make components non-overlapping, or in topic model to ensure that co-occurring words only appear in a small number of topics. In this work, we revisit these independence assumptions for probabilistic latent variable models, replacing the underlying i.i.d. prior with a determinantal point process (DPP). The DPP allows us to specify a preference for diversity in our latent variables using a positive definite kernel function. Using a kernel between probability distributions, we are able to define a DPP on probability measures. We show how to perform MAP inference with DPP priors in latent Dirichlet allocation and in mixture models, leading to better intuition for the latent variable representation and quantitatively improved unsupervised feature extraction, without compromising the generative aspects of the model.
UR - http://www.scopus.com/inward/record.url?scp=84877737917&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84877737917&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84877737917
SN - 9781627480031
T3 - Advances in Neural Information Processing Systems
SP - 2996
EP - 3004
BT - Advances in Neural Information Processing Systems 25
T2 - 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Y2 - 3 December 2012 through 6 December 2012
ER -