A Probabilistic Model for Discriminative and Neuro-Symbolic Semi-Supervised Learning

• URL: http://arxiv.org/abs/2006.05896v4
• Date: Mon, 31 May 2021 12:20:00 GMT
• Title: A Probabilistic Model for Discriminative and Neuro-Symbolic Semi-Supervised Learning
• Authors: Carl Allen, Ivana Bala\v{z}evi\'c, Timothy Hospedales
• Abstract summary: We present a probabilistic model for discriminative SSL, that mirrors its classical generative counterpart. We show several well-known SSL methods can be interpreted as approximating this prior, and can be improved upon. We extend the discriminative model to neuro-symbolic SSL, where label features satisfy logical rules, by showing such rules relate directly to the above prior.
• Score: 6.789370732159177
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Much progress has been made in semi-supervised learning (SSL) by combining methods that exploit different aspects of the data distribution, e.g. consistency regularisation relies on properties of $p(x)$, whereas entropy minimisation pertains to the label distribution $p(y|x)$. Focusing on the latter, we present a probabilistic model for discriminative SSL, that mirrors its classical generative counterpart. Under the assumption $y|x$ is deterministic, the prior over latent variables becomes discrete. We show that several well-known SSL methods can be interpreted as approximating this prior, and can be improved upon. We extend the discriminative model to neuro-symbolic SSL, where label features satisfy logical rules, by showing such rules relate directly to the above prior, thus justifying a family of methods that link statistical learning and logical reasoning, and unifying them with regular SSL.

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