In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literature on excess risk bounds and proper scoring rules, we derive a class probability estimator based on empirical risk minimization. We then derive fairly general conditions under which this estimator will converge, in the L1-norm and in probability, to the true class probabilities. Our main contribution is to present a way to derive finite sample L1-convergence rates of this estimator for different surrogate loss functions. We also study in detail which commonly used loss functions are suitable for this estimation problem and finally discuss the setting of model-misspecification as well as a possible extension to asymmetric loss functions.
Bridging Internal Probability and Self-Consistency for Effective and Efficient LLM Reasoning
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）；School of Intelligence Science and Technology, Nanjing University（南京大学智能科学与技术学院）
A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning
State Key Laboratory of Novel Software Technology, Nanjing University, China（新型软件技术国家重点实验室，南京大学，中国）；Department of Computer Science, ETH Zurich, Switzerland（苏黎世联邦理工学院计算机科学系，瑞士）；School of Intelligence Science and Technology, Nanjing University, China（智能科学与技术学院，南京大学，中国）；School of Artifical Intelligence, Nanjing University, China（人工智能学院，南京大学，中国）
Reliable Decision Support with LLMs: A Framework for Evaluating Consistency in Binary Text Classification Applications
Farmer School of Business, Miami University, Oxford, OH 45056, USA（迈阿密大学法默商学院）；College of Arts and Sciences, University of Dayton, Dayton, OH 45469, USA（Dayton大学文理学院）；Amsterdam Business School, University of Amsterdam, Amsterdam, The Netherlands（阿姆斯特丹大学阿姆斯特丹商学院）
在本文中，我们提出了增强学习图像压缩系统与更丰富的概率模型的潜在变量。以前的作品模型的潜在的高斯或拉普拉斯分布。受二进制算术编码的启发，我们提出用三个二进制值和一个整数，用不同的概率模型来表示潜伏期。设计了一种松弛方法来执行基于梯度的训练。更丰富的概率模型导致更好的熵编码，从而导致更低的速率。在CLIC（Challenge on Learned图像压缩）测试条件下的实验表明，与高斯模型或拉普拉斯模型相比，该方法可以节省18%的码率。
