The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs [26, 1, 5, 25]. The large-margin formulation including latent variables [30, 21] not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work [11] has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution, with theoretical guarantees. We extend this work by including latent variables. We study a new family of loss functions under Gaussian perturbations and analyze the effect of the latent space on the generalization bounds. We show that the non-convexity of learning with latent variables originates naturally, as it relates to a tight upper bound of the Gibbs decoder distortion with respect to the latent space. Finally, we provide a formulation using random samples and relaxations that produces a tighter upper bound of the Gibbs decoder distortion up to a statistical accuracy, which enables a polynomial time evaluation of the objective function. We illustrate the method with synthetic experiments and a computer vision application.

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for the use of fast primal gradient-based optimization algorithms. We illustrate the proposed framework by developing a novel primal incremental optimization algorithm for the structural support vector machine. The proposed algorithm blends an extrapolation scheme for acceleration and an adaptive smoothing scheme and builds upon the stochastic variance-reduced gradient algorithm. We establish its worst-case global complexity bound and study several practical variants. We present experimental results on two real-world problems, namely named entity recognition and visual object localization. The experimental results show that the proposed framework allows us to build upon efficient inference algorithms to develop large-scale optimization algorithms for structured prediction which can achieve competitive performance on the two real-world problems.

We design differentially private learning algorithms that are agnostic to the learning model assuming access to a limited amount of unlabeled public data. First, we provide a new differentially private algorithm for answering a sequence of m online classification queries (given by a sequence of m unlabeled public feature vectors) based on a private training set. Our algorithm follows the paradigm of subsample-and-aggregate, in which any generic non-private learner is trained on disjoint subsets of the private training set, and then for each classification query, the votes of the resulting classifiers ensemble are aggregated in a differentially private fashion. Our private aggregation is based on a novel combination of the distance-to-instability framework [26], and the sparse-vector technique [15, 18]. We show that our algorithm makes a conservative use of the privacy budget. In particular, if the underlying non-private learner yields a classification error of at most α (0, 1), then our construction answers more queries, by at least a factor of 1/α in some cases, than what is implied by a straightforward application of the advanced composition theorem for differential privacy. Next, we apply the knowledge transfer technique to construct a private learner that outputs a classifier, which can be used to answer an unlimited number of queries. In the PAC model, we analyze our construction and prove upper bounds on the sample complexity for both the realizable and the non-realizable cases. Similar to non-private sample complexity, our bounds are completely characterized by the VC dimension of the concept class.

Machine understanding of complex images is a key goal of artificial intelligence. One challenge underlying this task is that visual scenes contain multiple inter-related objects, and that global context plays an important role in interpreting the scene. A natural modeling framework for capturing such effects is structured prediction, which optimizes over complex labels, while modeling within-label interactions. However, it is unclear what principles should guide the design of a structured prediction model that utilizes the power of deep learning components. Here we propose a design principle for such architectures that follows from a natural requirement of permutation invariance. We prove a necessary and sufficient characterization for architectures that follow this invariance, and discuss its implication on model design. Finally, we show that the resulting model achieves new state of the art results on the Visual Genome scene graph labeling benchmark, outperforming all recent approaches.

We design differentially private learning algorithms that are agnostic to the learning modelassuming access to a limited amount of unlabeled public data. First, we provide a new differentially private algorithm for answering a sequence of m online classification queries (given by a sequence of m unlabeled public feature vectors) based on a private training set. Our algorithm follows the paradigm of subsample-and-aggregate, in which any generic non-private learner is trained on disjoint subsets of the private training set, and then for each classification query, the votes of the resulting classifiers ensemble are aggregated in a differentially private fashion. Our private aggregation is based on a novel combination of the distance-to-instability framework [26], and the sparse-vector technique [15, 18]. We show that our algorithm makes a conservative use of the privacy budget. In particular, if the underlying non-private learner yields a classification error of at most α (0, 1), then our construction answers more queries, by at least a factor of1/α in some cases, than what is implied by a straightforward application of the advanced composition theorem for differential privacy. Next, we apply the knowledge transfer technique to construct a private learner that outputs a classifier, which can be used to answer an unlimited number of queries. In the PAC model, we analyze our construction and prove upper bounds on the sample complexity for both the realizable and the non-realizable cases. Similar to non-private sample complexity, our bounds are completely characterized by the VC dimension of the concept class.

Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current deep structured models are restricted by oftentimes very local neighborhood structure, which cannot be increased for computational complexity reasons, and by the fact that the output configuration, or a representation thereof, cannot be transformed further. Very recent approaches which address those issues include graphical model inference inside deep nets so as to permit subsequent non-linear output space transformations. However, optimization of those formulations is challenging and not well understood. Here, we develop a novel model which generalizes existing approaches, such as structured prediction energy networks, and discuss a formulation which maintains applicability of existing inference techniques.

Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold-valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator. Promising experimental results on both simulated and real data complete our study.

Given data from a general metric space, one of the standard machine learning pipelines is to first embed the data into a Euclidean space and subsequently apply out of the box machine learning algorithms to analyze the data. The quality of such an embedding is typically described in terms of a distortion measure. In this paper, we show that many of the existing distortion measures behave in an undesired way, when considered from a machine learning point of view. We investigate desirable properties of distortion measures and formally prove that most of the existing measures fail to satisfy these properties. These theoretical findings are supported by simulations, which for example demonstrate that existing distortion measures are not robust to noise or outliers and cannot serve as good indicators for classification accuracy. As an alternative, we suggest a new measure of distortion, called $\sigma$-distortion. We can show both in theory and in experiments that it satisfies all desirable properties and is a better candidate to evaluate distortion in the context of machine learning.

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for the use of fast primal gradient-based optimization algorithms. We illustrate the proposed framework by developing a novel primal incremental optimization algorithm for the structural support vector machine. The proposed algorithm blends an extrapolation scheme for acceleration and an adaptive smoothing scheme and builds upon the stochastic variance-reduced gradient algorithm. We establish its worst-case global complexity bound and study several practical variants. We present experimental results on two real-world problems, namely named entity recognition and visual object localization. The experimental results show that the proposed framework allows us to build upon efficient inference algorithms to develop large-scale optimization algorithms for structured prediction which can achieve competitive performance on the two real-world problems.

The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs [26, 1, 5, 25]. The large-margin formulation including latent variables [30, 21] not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work [11] has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution, with theoretical guarantees. We extend this work by including latent variables. We study a new family of loss functions under Gaussian perturbations and analyze the effect of the latent space on the generalization bounds. We show that the non-convexity of learning with latent variables originates naturally, as it relates to a tight upper bound of the Gibbs decoder distortion with respect to the latent space. Finally, we provide a formulation using random samples and relaxations that produces a tighter upper bound of the Gibbs decoder distortion up to a statistical accuracy, which enables a polynomial time evaluation of the objective function. We illustrate the method with synthetic experiments and a computer vision application.