Truncated Gaussians as Tolerance Sets

Fabio Cozman, Eric Krotkov
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:161-167, 1995.

Abstract

This work presents a new class of statistical models that are well suited for several Robotics applications, such as object recognition or computer vision. Our approach deals with bounded data: measurements that are constrained to appear in a bounded region in the measurement space. The literature refers to the set where the measurement can appear as the tolerance set for the measurement. To date, few statistical models for bounded variables are used in Artificial Intelligence. The most common model is the uniform distribution, but this approach has several drawbacks: summation of uniform variables does not yield a uniform variable and application of Bayes rule is computationally intensive [9]. Another approach is to use the Gaussian distribution and model bounds through an ad hoc selection mechanism [1, 2]. In short, even though bounds contain significant information, they have not yet received proper attention.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR0-cozman95a, title = {Truncated Gaussians as Tolerance Sets}, author = {Cozman, Fabio and Krotkov, Eric}, booktitle = {Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics}, pages = {161--167}, year = {1995}, editor = {Fisher, Doug and Lenz, Hans-Joachim}, volume = {R0}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/r0/cozman95a/cozman95a.pdf}, url = {https://proceedings.mlr.press/r0/cozman95a.html}, abstract = {This work presents a new class of statistical models that are well suited for several Robotics applications, such as object recognition or computer vision. Our approach deals with bounded data: measurements that are constrained to appear in a bounded region in the measurement space. The literature refers to the set where the measurement can appear as the tolerance set for the measurement. To date, few statistical models for bounded variables are used in Artificial Intelligence. The most common model is the uniform distribution, but this approach has several drawbacks: summation of uniform variables does not yield a uniform variable and application of Bayes rule is computationally intensive [9]. Another approach is to use the Gaussian distribution and model bounds through an ad hoc selection mechanism [1, 2]. In short, even though bounds contain significant information, they have not yet received proper attention.}, note = {Reissued by PMLR on 01 May 2022.} }
Endnote
%0 Conference Paper %T Truncated Gaussians as Tolerance Sets %A Fabio Cozman %A Eric Krotkov %B Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1995 %E Doug Fisher %E Hans-Joachim Lenz %F pmlr-vR0-cozman95a %I PMLR %P 161--167 %U https://proceedings.mlr.press/r0/cozman95a.html %V R0 %X This work presents a new class of statistical models that are well suited for several Robotics applications, such as object recognition or computer vision. Our approach deals with bounded data: measurements that are constrained to appear in a bounded region in the measurement space. The literature refers to the set where the measurement can appear as the tolerance set for the measurement. To date, few statistical models for bounded variables are used in Artificial Intelligence. The most common model is the uniform distribution, but this approach has several drawbacks: summation of uniform variables does not yield a uniform variable and application of Bayes rule is computationally intensive [9]. Another approach is to use the Gaussian distribution and model bounds through an ad hoc selection mechanism [1, 2]. In short, even though bounds contain significant information, they have not yet received proper attention. %Z Reissued by PMLR on 01 May 2022.
APA
Cozman, F. & Krotkov, E.. (1995). Truncated Gaussians as Tolerance Sets. Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R0:161-167 Available from https://proceedings.mlr.press/r0/cozman95a.html. Reissued by PMLR on 01 May 2022.

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