Most classification models work by first predicting a posterior probability distribution over all classes and then selecting that class with the largest estimated probability. In many settings however, the quality of posterior probability itself (e.g., 65% chance having diabetes), gives more reliable information than the final predicted class alone. When these methods are shown to be poorly calibrated, most fixes to date have relied on posterior calibration, which rescales the predicted probabilities but often has little impact on final classifications. Here we propose an end-to-end training procedure called posterior calibrated (PosCal) training that directly optimizes the objective while minimizing the difference between the predicted and empirical posterior probabilities. We show that PosCal not only helps reduce the calibration error but also improve task performance by penalizing drops in performance of both objectives. Our PosCal achieves about 2.5% of task performance gain and 16.1% of calibration error reduction on GLUE (Wang et al., 2018) compared to the baseline. We achieved the comparable task performance with 13.2% calibration error reduction on xSLUE (Kang and Hovy, 2019), but not outperforming the two-stage calibration baseline. PosCal training can be easily extendable to any types of classification tasks as a form of regularization term. Also, PosCal has the advantage that it incrementally tracks needed statistics for the calibration objective during the training process, making efficient use of large training sets.

Despite the recent developments on neural summarization systems, the underlying logic behind the improvements from the systems and its corpus-dependency remains largely unexplored. Position of sentences in the original text, for example, is a well known bias for news summarization. Following in the spirit of the claim that summarization is a combination of sub-functions, we define three sub-aspects of summarization: position, importance, and diversity and conduct an extensive analysis of the biases of each sub-aspect with respect to the domain of nine different summarization corpora (e.g., news, academic papers, meeting minutes, movie script, books, posts). We find that while position exhibits substantial bias in news articles, this is not the case, for example, with academic papers and meeting minutes. Furthermore, our empirical study shows that different types of summarization systems (e.g., neural-based) are composed of different degrees of the sub-aspects. Our study provides useful lessons regarding consideration of underlying sub-aspects when collecting a new summarization dataset or developing a new system.