Bayesian Calibration of Win Rate Estimation with LLM Evaluators

Recent advances in large language models (LLMs) show the potential of using LLMs as evaluators for assessing the quality of text generations from LLMs. However, applying LLM evaluators naively to compare or judge between different systems can lead to unreliable results due to the intrinsic win rate estimation bias of LLM evaluators. In order to mitigate this problem, we propose two calibration methods, Bayesian Win Rate Sampling (BWRS) and Bayesian Dawid-Skene, both of which leverage Bayesian inference to more accurately infer the true win rate of generative language models. We empirically validate our methods on six datasets covering story generation, summarization, and instruction following tasks. We show that both our methods are effective in improving the accuracy of win rate estimation using LLMs as evaluators, offering a promising direction for reliable automatic text quality evaluation.

Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

Recently regression analysis becomes a popular tool for face recognition. The existing regression methods all use the one-dimensional pixel-based error model, which characterizes the representation error pixel by pixel individually and thus neglects the whole structure of the error image. We observe that occlusion and illumination changes generally lead to a low-rank error image. To make use of this low-rank structural information, this paper presents a two-dimensional image matrix based error model, i.e. matrix regression, for face representation and classification. Our model uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers method to calculate the regression coefficients. Compared with the current regression methods, the proposed Nuclear Norm based Matrix Regression (NMR) model is more robust for alleviating the effect of illumination, and more intuitive and powerful for removing the structural noise caused by occlusion. We experiment using four popular face image databases, the Extended Yale B database, the AR database, the Multi-PIE and the FRGC database. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression based face recognition methods.