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### Efficient Structured Prediction with Latent Variables for General Graphical Models

In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient message passing algorithm that is guaranteed to converge. We demonstrate its effectiveness in the tasks of image segmentation as well as 3D indoor scene understanding from single images, showing that our approach is superior to latent structured support vector machines and hidden conditional random fields.

### Latent Structured Active Learning

In this paper we present active learning algorithms in the context of structured prediction problems. To reduce the amount of labeling necessary to learn good models, our algorithms only label subsets of the output. To this end, we query examples using entropies of local marginals, which are a good surrogate for uncertainty. We demonstrate the effectiveness of our approach in the task of 3D layout prediction from single images, and show that good models are learned when labeling only a handful of random variables. In particular, the same performance as using the full training set can be obtained while only labeling ~10\% of the random variables.

### A Primal-Dual Message-Passing Algorithm for Approximated Large Scale Structured Prediction

In this paper we propose an approximated learning framework for large scale graphical models and derive message passing algorithms for learning their parameters efficiently. We first relate CRFs and structured SVMs and show that in the CRF's primal a variant of the log-partition function, known as soft-max, smoothly approximates the hinge loss function of structured SVMs. We then propose an intuitive approximation for structured prediction problems using Fenchel duality based on a local entropy approximation that computes the exact gradients of the approximated problem and is guaranteed to converge. Unlike existing approaches, this allow us to learn graphical models with cycles and very large number of parameters efficiently. We demonstrate the effectiveness of our approach in an image denoising task.

### Globally Convergent Dual MAP LP Relaxation Solvers using Fenchel-Young Margins

While finding the exact solution for the MAP inference problem is intractable for many real-world tasks, MAP LP relaxations have been shown to be very effective in practice. However, the most efficient methods that perform block coordinate descent can get stuck in sub-optimal points as they are not globally convergent. In this work we propose to augment these algorithms with an $\epsilon$-descent approach and present a method to efficiently optimize for a descent direction in the subdifferential using a margin-based extension of the Fenchel-Young duality theorem. Furthermore, the presented approach provides a methodology to construct a primal optimal solution from its dual optimal counterpart. We demonstrate the efficiency of the presented approach on spin glass models and protein interactions problems and show that our approach outperforms state-of-the-art solvers.

### Deep Structured Prediction with Nonlinear Output Transformations

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.