Efficient Optimization for Rank-based Loss Functions

The accuracy of information retrieval systems is often measured using complex loss functions such as the average precision (AP) or the normalized discounted cumulative gain (NDCG). Given a set of positive and negative samples, the parameters of a retrieval system can be estimated by minimizing these loss functions. However, the non-differentiability and non-decomposability of these loss functions does not allow for simple gradient based optimization algorithms. This issue is generally circumvented by either optimizing a structured hinge-loss upper bound to the loss function or by using asymptotic methods like the direct-loss minimization framework. Yet, the high computational complexity of loss-augmented inference, which is necessary for both the frameworks, prohibits its use in large training data sets. To alleviate this deficiency, we present a novel quicksort flavored algorithm for a large class of non-decomposable loss functions. We provide a complete characterization of the loss functions that are amenable to our algorithm, and show that it includes both AP and NDCG based loss functions. Furthermore, we prove that no comparison based algorithm can improve upon the computational complexity of our approach asymptotically. We demonstrate the effectiveness of our approach in the context of optimizing the structured hinge loss upper bound of AP and NDCG loss for learning models for a variety of vision tasks. We show that our approach provides significantly better results than simpler decomposable loss functions, while requiring a comparable training time.Comment: 15 pages, 2 figure

Putting the Horse Before the Cart:A Generator-Evaluator Framework for Question Generation from Text

Automatic question generation (QG) is a useful yet challenging task in NLP. Recent neural network-based approaches represent the state-of-the-art in this task. In this work, we attempt to strengthen them significantly by adopting a holistic and novel generator-evaluator framework that directly optimizes objectives that reward semantics and structure. The {\it generator} is a sequence-to-sequence model that incorporates the {\it structure} and {\it semantics} of the question being generated. The generator predicts an answer in the passage that the question can pivot on. Employing the copy and coverage mechanisms, it also acknowledges other contextually important (and possibly rare) keywords in the passage that the question needs to conform to, while not redundantly repeating words. The {\it evaluator} model evaluates and assigns a reward to each predicted question based on its conformity to the {\it structure} of ground-truth questions. We propose two novel QG-specific reward functions for text conformity and answer conformity of the generated question. The evaluator also employs structure-sensitive rewards based on evaluation measures such as BLEU, GLEU, and ROUGE-L, which are suitable for QG. In contrast, most of the previous works only optimize the cross-entropy loss, which can induce inconsistencies between training (objective) and testing (evaluation) measures. Our evaluation shows that our approach significantly outperforms state-of-the-art systems on the widely-used SQuAD benchmark as per both automatic and human evaluation.Comment: 10 pages, The SIGNLL Conference on Computational Natural Language Learning (CoNLL 2019

Rank-based Decomposable Losses in Machine Learning: A Survey

Recent works have revealed an essential paradigm in designing loss functions that differentiate individual losses vs. aggregate losses. The individual loss measures the quality of the model on a sample, while the aggregate loss combines individual losses/scores over each training sample. Both have a common procedure that aggregates a set of individual values to a single numerical value. The ranking order reflects the most fundamental relation among individual values in designing losses. In addition, decomposability, in which a loss can be decomposed into an ensemble of individual terms, becomes a significant property of organizing losses/scores. This survey provides a systematic and comprehensive review of rank-based decomposable losses in machine learning. Specifically, we provide a new taxonomy of loss functions that follows the perspectives of aggregate loss and individual loss. We identify the aggregator to form such losses, which are examples of set functions. We organize the rank-based decomposable losses into eight categories. Following these categories, we review the literature on rank-based aggregate losses and rank-based individual losses. We describe general formulas for these losses and connect them with existing research topics. We also suggest future research directions spanning unexplored, remaining, and emerging issues in rank-based decomposable losses.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI

An End-to-End Approach for Training Neural Network Binary Classifiers on Metrics Based on the Confusion Matrix

While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-testing gap be addressed? While specific techniques have been adopted to optimize certain confusion matrix based metrics, it is challenging or impossible in some cases to generalize the techniques to other metrics. Adversarial learning approaches have also been proposed to optimize networks via confusion matrix based metrics, but they tend to be much slower than common training methods. In this work, we propose to approximate the Heaviside step function, typically used to compute confusion matrix based metrics, to render these metrics amenable to gradient descent. Our extensive experiments show the effectiveness of our end-to-end approach for binary classification in several domains