Many structured prediction problems admit a natural loss function for evaluation such as the edit-distance or n-gram loss. However, existing learning algorithms are typically designed to optimize alternative objectives such as the cross-entropy. This is because a naïve implementation of the natural loss functions often results in intractable gradient computations. In this paper, we design efficient gradient computation algorithms for two broad families of structured prediction loss functions: rational and tropical losses. These families include as special cases the n-gram loss, the edit-distance loss, and many other loss functions commonly used in natural language processing and computational biology tasks that are based on sequence similarity measures. Our algorithms make use of weighted automata and graph operations over appropriate semirings to design efficient solutions. They facilitate efficient gradient computation and hence enable one to train learning models such as neural networks with complex structured losses.

Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and the loss function used in a subsequent learning task, where the data generated by a GAN serves for training. Taking that structural information into account is also important to derive generalization guarantees. Thus, we propose to use the discrepancy measure, which was originally introduced for the closely related problem of domain adaptation and which precisely takes into account the hypothesis set and the loss function. We show that discrepancy admits favorable properties for training GANs and prove explicit generalization guarantees. We present efficient algorithms using discrepancy for two tasks: training a GAN directly, namely DGAN, and mixing previously trained generative models, namely EDGAN. Our experiments on toy examples and several benchmark datasets show that DGAN is competitive with other GANs and that EDGAN outperforms existing GAN ensembles, such as AdaGAN.

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Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and the loss function used in a subsequent learning task, where the data generated by a GAN serves for training. Taking that structural information into account is also important to derive generalization guarantees. Thus, we propose to use the discrepancy measure, which was originally introduced for the closely related problem of domain adaptation and which precisely takes into account the hypothesis set and the loss function. We show that discrepancy admits favorable properties for training GANs and prove explicit generalization guarantees. We present efficient algorithms using discrepancy for two tasks: training a GAN directly, namely DGAN, and mixing previously trained generative models, namely EDGAN. Our experiments on toy examples and several benchmark datasets show that DGAN is competitive with other GANs and that EDGAN outperforms existing GAN ensembles, such as AdaGAN.

Gradient Boosting (GB) is a popular and very successful ensemble method for binary trees. While various types of regularization of the base predictors are used with this algorithm, the theory that connects such regularizations with generalization guarantees is poorly understood. We fill this gap by deriving data-dependent learning guarantees for GB used with regularization, expressed in terms of the Rademacher complexities of the constrained families of base predictors. We introduce a new algorithm, called RGB, that directly benefits from these generalization bounds and that, at every boosting round, applies the Structural Risk Minimization principle to search for a base predictor with the best empirical fit versus complexity trade-off. Inspired by Randomized Coordinate Descent we provide a scalable implementation of our algorithm, able to search over large families of base predictors. Finally, we provide experimental results, demonstrating that our algorithm achieves significantly better out-of-sample performance on multiple datasets than the standard GB algorithm used with its regularization.

We present a new boosting algorithm for the key scenario of binary classification with abstention where the algorithm can abstain from predicting the label of a point, at the price of a fixed cost. At each round, our algorithm selects a pair of functions, a base predictor and a base abstention function. We define convex upper bounds for the natural loss function associated to this problem, which we prove to be calibrated with respect to the Bayes solution. Our algorithm benefits from general margin-based learning guarantees which we derive for ensembles of pairs of base predictor and abstention functions, in terms of the Rademacher complexities of the corresponding function classes. We give convergence guarantees for our algorithm along with a linear-time weak-learning algorithm for abstention stumps. We also report the results of several experiments suggesting that our algorithm provides a significant improvement in practice over two confidence-based algorithms.

We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin bounds known for both standard multi-class and general structured prediction problems. Our guarantees are expressed in terms of a data-dependent complexity measure, factor graph complexity, which we show can be estimated from data and bounded in terms of familiar quantities for several commonly used hypothesis sets along with a sparsity measure for features and graphs. Our proof techniques include generalizations of Talagrand's contraction lemma that can be of independent interest. We further extend our theory by leveraging the principle of Voted Risk Minimization (VRM) and show that learning is possible even with complex factor graphs. We present new learning bounds for this advanced setting, which we use to design two new algorithms, Voted Conditional Random Field (VCRF) and Voted Structured Boosting (StructBoost). These algorithms can make use of complex features and factor graphs and yet benefit from favorable learning guarantees. We also report the results of experiments with VCRF on several datasets to validate our theory.