Davies-Batista, Dewi (2025) Hybrid Continuous Mixtures of Probabilistic Circuits. Master's Thesis / Essay, Applied Mathematics.
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Abstract
We offer a tutorial-like overview of probabilistic circuits (PCs), a class of generative probabilistic models which offer tractable means of answering evidence and marginal queries exactly. A motivation of their application to tractable probabilistic inference with complete or missing data is then presented. An overview of continuous mixtures of PCs (CMPCs) is then given and a review of their application to density estimation and sampling is offered. We follow by introducing hybrid CMPCs which are CMPCs trained in a manner which encourages both generative and discriminative learning. The extent to which either learning paradigm is encouraged during training is dictated by a mixing hyperparameter λ ∈ [0, 1]. Typically, deep learning models are trained under a single paradigm as few model classes facilitate a hybrid learning objective. To investigate the trade-off of generative and discriminative power as the mixing hyperparmeter varies, we train hybrid CMPCs for λ ∈ {0, 0.2, 0.4, 0.6, 0.8, 1} on Binary MNIST. We evaluate two complementary criteria of each hybrid CMPC: its classification accuracy on incomplete samples of Binary MNIST and the visual quality of samples drawn from the model. Our experiments demonstrate that hybrid CMPCs trained with intermediate values of λ ∈ [0.4, 0.6] yield an effective balance, obtaining high classification accuracies while maintaining reasonable sample quality.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Grzegorczyk, M.A. and Jaeger, H. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 06 Aug 2025 06:39 |
| Last Modified: | 06 Aug 2025 06:39 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36691 |
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