Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction have been proposed. Here we focus on capturing cardinality constraints in such models. Namely, constraining the number of non-zero labels that the model outputs. Such constraints have proven very useful in previous structured prediction methods, but it is a challenge to introduce them into a deep learning approach. Here we show how to do this via a novel deep architecture. Our approach outperforms strong baselines, achieving state-of-the-art results on multi-label classification benchmarks.

Structured prediction requires searching over a combinatorial number of structures. To tackle it, we introduce SparseMAP, a new method for sparse structured inference, together with corresponding loss functions. SparseMAP inference is able to automatically select only a few global structures: it is situated between MAP inference, which picks a single structure, and marginal inference, which assigns probability mass to all structures, including implausible ones. Importantly, SparseMAP can be computed using only calls to a MAP oracle, hence it is applicable even to problems where marginal inference is intractable, such as linear assignment. Moreover, thanks to the solution sparsity, gradient backpropagation is efficient regardless of the structure. SparseMAP thus enables us to augment deep neural networks with generic and sparse structured hidden layers. Experiments in dependency parsing and natural language inference reveal competitive accuracy, improved interpretability, and the ability to capture natural language ambiguities, which is attractive for pipeline systems.

Many important structured prediction problems, including learning to rank items, correspondence-based natural language processing, and multi-object tracking, can be formulated as weighted bipartite matching optimizations. Existing structured prediction approaches have significant drawbacks when applied under the constraints of perfect bipartite matchings. Exponential family probabilistic models, such as the conditional random field (CRF), provide statistical consistency guarantees, but suffer computationally from the need to compute the normalization term of its distribution over matchings, which is a #P-hard matrix permanent computation. In contrast, the structured support vector machine (SSVM) provides computational efficiency, but lacks Fisher consistency, meaning that there are distributions of data for which it cannot learn the optimal matching even under ideal learning conditions (i.e., given the true distribution and selecting from all measurable potential functions). We propose adversarial bipartite matching to avoid both of these limitations. We develop this approach algorithmically, establish its computational efficiency and Fisher consistency properties, and apply it to matching problems that demonstrate its empirical benefits.

Predicting structured outputs can be computationally onerous due to the combinatorially large output spaces. In this paper, we focus on reducing the prediction time of a trained black-box structured classifier without losing accuracy. To do so, we train a speedup classifier that learns to mimic a black-box classifier under the learning-to-search approach. As the structured classifier predicts more examples, the speedup classifier will operate as a learned heuristic to guide search to favorable regions of the output space. We present a mistake bound for the speedup classifier and identify inference situations where it can independently make correct judgments without input features. We evaluate our method on the task of entity and relation extraction and show that the speedup classifier outperforms even greedy search in terms of speed without loss of accuracy.