Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance

Details Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance

2009-04-29

arxiv.org/abs/0904.4527v1

International Journal of Approximate Reasoning, 50:4 (2009) pages 597-611

Computer Science

Learning

27 LaTeX pages

Scientific paper

In this paper, we consider the coherent theory of (epistemic) uncertainty of Walley, in which beliefs are represented through sets of probability distributions, and we focus on the problem of modeling prior ignorance about a categorical random variable. In this setting, it is a known result that a state of prior ignorance is not compatible with learning. To overcome this problem, another state of beliefs, called \emph{near-ignorance}, has been proposed. Near-ignorance resembles ignorance very closely, by satisfying some principles that can arguably be regarded as necessary in a state of ignorance, and allows learning to take place. What this paper does, is to 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 provide, for the case of categorical latent variables (and general \emph{manifest} variables) a condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied even in the most common statistical problems. We regard these results as a strong form of evidence against the possibility to adopt a condition of prior near-ignorance in real statistical problems.

Affiliated with

Also associated with

No associations

Rating

Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-511131