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Abstract High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of identifiable multilayer (potentially deep) discrete latent structure models for discrete data, termed Bayesian Pyramids. We establish the identifiability of Bayesian Pyramids by developing novel transparent conditions on the pyramid-shaped deep latent directed graph. The proposed identifiability conditions can ensure Bayesian posterior consistency under suitable priors. As an illustration, we consider the two-latent-layer model and propose a Bayesian shrinkage estimation approach. Simulation results for this model corroborate the identifiability and estimatability of model parameters. Applications of the methodology to DNA nucleotide sequence data uncover useful discrete latent features that are highly predictive of sequence types. The proposed framework provides a recipe for interpretable unsupervised learning of discrete data and can be a useful alternative to popular machine learning methods.
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Gaussian-Dirichlet Random Fields for Inference over High Dimensional Categorical Observations
We propose a generative model for the spatiotemporal distribution of high-dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier, potentially producing observations over thousands of categories. The proposed approach combines the use of Dirichlet distributions to model sparse co-occurrence relations between the observed categories using a latent variable, and Gaussian processes to model the latent variable’s spatiotemporal distribution. Experiments in this paper show that the resulting model is able to efficiently and accurately approximate the temporal distribution of high dimensional categorical measurements such as taxonomic observations of microscopic organisms in the ocean, even in unobserved (held out) locations, far from other samples. This work’s primary motivation is to enable the deployment of informative path planning techniques over high dimensional categorical fields, which until now have been limited to scalar or low dimensional vector observations.
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- PAR ID:
- 10206411
- Date Published:
- Journal Name:
- 2020 IEEE International Conference on Robotics and Automation (ICRA)
- Page Range / eLocation ID:
- 2924 to 2931
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA40945.2020.9196713
