Extending Nearly-Linear Models

Chiara Corsato, Renato Pelessoni, Paolo Vicig
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:82-90, 2019.

Abstract

Nearly-Linear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the Pari-Mutuel Model, the $\varepsilon$-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-corsato19a, title = {Extending Nearly-Linear Models}, author = {Corsato, Chiara and Pelessoni, Renato and Vicig, Paolo}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {82--90}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/corsato19a/corsato19a.pdf}, url = {https://proceedings.mlr.press/v103/corsato19a.html}, abstract = {Nearly-Linear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the Pari-Mutuel Model, the $\varepsilon$-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute.} }
Endnote
%0 Conference Paper %T Extending Nearly-Linear Models %A Chiara Corsato %A Renato Pelessoni %A Paolo Vicig %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-corsato19a %I PMLR %P 82--90 %U https://proceedings.mlr.press/v103/corsato19a.html %V 103 %X Nearly-Linear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the Pari-Mutuel Model, the $\varepsilon$-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute.
APA
Corsato, C., Pelessoni, R. & Vicig, P.. (2019). Extending Nearly-Linear Models. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:82-90 Available from https://proceedings.mlr.press/v103/corsato19a.html.

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