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Abstract Longitudinal studies with binary or ordinal responses are widely encountered in various disciplines, where the primary focus is on the temporal evolution of the probability of each response category. Traditional approaches build from the generalized mixed effects modeling framework. Even amplified with nonparametric priors placed on the fixed or random effects, such models are restrictive due to the implied assumptions on the marginal expectation and covariance structure of the responses. We tackle the problem from a functional data analysis perspective, treating the observations for each subject as realizations from subject-specific stochastic processes at the measured times. We develop the methodology focusing initially on binary responses, for which we assume the stochastic processes have Binomial marginal distributions. Leveraging the logits representation, we model the discrete space processes through continuous space processes. We utilize a hierarchical framework to model the mean and covariance kernel of the continuous space processes nonparametrically and simultaneously through a Gaussian process prior and an Inverse-Wishart process prior, respectively. The prior structure results in flexible inference for the evolution and correlation of binary responses, while allowing for borrowing of strength across all subjects. The modeling approach can be naturally extended to ordinal responses. Here, the continuation-ratio logits factorization of the multinomial distribution is key for efficient modeling and inference, including a practical way of dealing with unbalanced longitudinal data. The methodology is illustrated with synthetic data examples and an analysis of college students’ mental health status data.
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Differentially private synthetic mixed-type data generation for unsupervised learning
We introduce the DP-auto-GAN framework for synthetic data generation, which combines the low dimensional representation of autoencoders with the flexibility of Generative Adversarial Networks (GANs). This framework can be used to take in raw sensitive data and privately train a model for generating synthetic data that will satisfy similar statistical properties as the original data. This learned model can generate an arbitrary amount of synthetic data, which can then be freely shared due to the post-processing guarantee of differential privacy. Our framework is applicable to unlabeled mixed-type data, that may include binary, categorical, and real-valued data. We implement this framework on both binary data (MIMIC-III) and mixed-type data (ADULT), and compare its performance with existing private algorithms on metrics in unsupervised settings. We also introduce a new quantitative metric able to detect diversity, or lack thereof, of synthetic data.
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- PAR ID:
- 10332197
- Editor(s):
- Tsihrintzis, George A.; Virvou, Maria; Hatzilygeroudis, Ioannis
- Date Published:
- Journal Name:
- Intelligent Decision Technologies
- Volume:
- 15
- Issue:
- 4
- ISSN:
- 1872-4981
- Page Range / eLocation ID:
- 779 to 807
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.3233/IDT-210195
