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Learning about a Categorical Latent Variable under Prior Near-Ignorance

Piatti, Alberto; Zaffalon, Marco; Trojani, Fabio; Hutter, Marcus

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It is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls \emph{near-ignorance}, that permits learning to take place. In this paper we provide new and substantial evidence that also near-ignorance cannot be really ...[Show more]

dc.contributor.authorPiatti, Alberto
dc.contributor.authorZaffalon, Marco
dc.contributor.authorTrojani, Fabio
dc.contributor.authorHutter, Marcus
dc.date.accessioned2015-08-28T01:28:29Z
dc.date.available2015-08-28T01:28:29Z
dc.identifier.isbn978-80-86742-20-5
dc.identifier.urihttp://hdl.handle.net/1885/15012
dc.description.abstractIt is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls \emph{near-ignorance}, that permits learning to take place. In this paper we provide new and substantial evidence that also near-ignorance cannot be really regarded as a way out of the problem of starting statistical inference in conditions of very weak beliefs. The key to this result is focusing on a setting characterized by a variable of interest that is \emph{latent}. We argue that such a setting is by far the most common case in practice, and we show, for the case of categorical latent variables (and general \emph{manifest} variables) that there is a sufficient condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied in the most common statistical problems.
dc.publisherInternational Society for Imprecise Probability: Theories and Applications
dc.relation.ispartofISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications
dc.rights© The Author(s)
dc.subjectPrior near-ignorance
dc.subjectlatent and manifest variables
dc.subjectobservational processes
dc.subjectvacuous beliefs
dc.subjectimprecise probabilities
dc.titleLearning about a Categorical Latent Variable under Prior Near-Ignorance
dc.typeConference paper
dc.date.issued2007
local.type.statusPublished Version
local.contributor.affiliationHutter, M., Research School of Computer Science, The Australian National University
local.bibliographicCitation.startpage357
local.bibliographicCitation.lastpage364
CollectionsANU Research Publications

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