A First Approach to Closeness Distributions

Jesus Cerquides
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Jesus Cerquides: Instituto de Investigación en Inteligencia Artificial (IIIA-CSIC), Campus UAB, 08193 Cerdanyola, Spain

Mathematics, 2021, vol. 9, issue 23, 1-12

Abstract: Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller distributions are likely to be similar to one another. In this paper we provide an information geometric approach on how to incorporate this information and see that it allows us to reinterpret some already existing models. Our proposal relies on providing a formal definition of what it means to be close. We provide an example on how this definition can be actioned for multinomial distributions. We use the results on multinomial distributions to reinterpret two already existing hierarchical models in terms of closeness distributions.

Keywords: probabilistic modeling; distance; KL divergence; closeness; Beta distribution; multinomial distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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