Paper:
Self-Paced Learning with Diversity
Self-paced learning (SPL) is a recently proposed learning regime inspired by the learning process of humans and animals that gradually incorporates easy to more complex samples into training. Existing methods are limited in that they ignore an important aspect in learning: diversity. To incorporate this information, we propose an approach called self-paced learning with diversity (SPLD) which formalizes the preference for both easy and diverse samples into a general regularizer. This regularization term is independent of the learning objective, and thus can be easily generalized into various learning tasks. Albeit non-convex, the optimization of the variables included in this SPLD regularization term for sample selection can be globally solved in linearithmic time. We demonstrate that our method significantly outperforms the conventional SPL on three real-world datasets. Specifically, SPLD achieves the best MAP so far reported in literature on the Hollywood2 and Olympic Sports datasets.

Review:
In this paper, the authors introduce a formalism for self-paced learning with diversity. This is a type of “curriculum learning.” Curriculum learning, inspired by the way humans and animals appear to learn, suggests learning training examples in a particular order, for example attempting to fit easy examples prior to hard ones. One challenge is how to decide what constitutes an easy or hard example. Self-paced learning showed that you can use the loss function you are trying to minimize as a measure of difficulty. By weighting the samples you can focus on learning easier ones first. Learning proceeds by minimizing an objective function which has two terms: the weighted loss function over the samples and the negative of the L_1 norm of the weights. A parameter lambda controls the importance of the two terms and is increased while fitting to force the model to incorporate increasingly difficult examples. Because this function is biconvex it is possible to optimize relatively efficiently.This work extends self-paced learning by incorporating “diversity.” That is, the model should learn not just easy examples, but diverse examples. To achieve this, the authors assume that examples are already grouped in some way (for example, using a clustering algorithm). They propose adding a third term to the objective function, which favors weighting samples from multiple groups (and an additional parameter, gamma, to weight the importance of this term). The objective function is no longer biconvex, however, they show a simple algorithm which they prove is able to find the global minimum of the latent weights in linear time.The submission then compares the results of objective functions learned using various methods (including self-paced learning) on three datasets: multimedia event detection and two action recognition datasets. Learning with diversity outperformed self-paced learning (and other methods) for all datasets, including apparently fitting in fewer iterations.This submission builds on previous work to construct a novel approach to curriculum learning. It demonstrate that diversity may be an important property to consider in achieving good fits. It provides a well-constructed rational for the approach, a novel algorithm including proof of optimality and several well-constructed empirical tests. The approach results in significant improvements in several of the datasets considered, which are quite challenging tasks. The authors propose several possible extensions to their approach for further research. Additionally, the use of “diversity” during learning may have some generality, and may be applied in other contexts.The manuscript is well presented and does an excellent job of conveying the key ideas, while including proofs and additional detail in the supplementary.One weakness of the manuscript, is that it lacks empirical comparisons with some more known tasks and datasets (for example, MNIST, as in the original SPL work). The datasets chosen here both have obvious diversity (examples from the same category that are very different) and levels of difficulty (examples which are obviously more ambiguous than others). This makes them good choices for testing the ideas presented. However, it would have been helpful to examine well-studied datasets such as MNIST which do not necessarily have the same obvious levels of diversity and difficulty. Does this approach still result in improved fits? It is not obvious to me what the answer would be and it would motivate helpful discussion about the scope of this work.