Generalized Qualitative Probability: Savage Revisited

2014-08-07 · Daniel Lehmann

Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead to a characterization of generalized qualitative probability that includes and blends both traditional qualitative probability and the ranked structures used in logical approaches.

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When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating

2026-02-02 · Kenichiro McAlinn, Kōsaku Takanashi arxiv

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic char…

A Savage-Like Axiomatization for Nonstandard Expected Utility

2017-01-12 · Grant Molnar

Since Leonard Savage's epoch-making "Foundations of Statistics", Subjective Expected Utility Theory has been the presumptive model for decision-making. Savage provided an act-based axiomatization of standard expected uti…

Decision Making

Lower-Bounded Proper Losses for Weakly Supervised Classification

2021-03-04 · Shuhei M. Yoshida, Takashi Takenouchi, Masashi Sugiyama

This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functio…

Classification General Classification Weakly Supervised Classification

On the Design of Loss Functions for Classification: theory, robustness to outliers, and SavageBoost

2008-12-01 · NeurIPS 2008 12 · Hamed Masnadi-Shirazi, Nuno Vasconcelos

The machine learning problem of classifier design is studied from the perspective of probability elicitation, in statistics. This shows that the standard approach of proceeding from the specification of a loss, to the mi…

General Classification

Linear Thompson Sampling Revisited

2016-11-20 · Marc Abeille, Alessandro Lazaric

We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof…

Thompson Sampling