Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recent progress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry of input patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables. Unlike transductive algorithms, our formulation naturally extends to new test points.

We consider a framework for semi-supervised learning using spectral decomposition based unsupervised kernel design. This approach subsumes a class of previously proposed semi-supervised learning methods on data graphs. We examine various theoretical properties of such methods. In particular, we derive a generalization performance bound, and obtain the optimal kernel design by minimizing the bound. Based on the theoretical analysis, we are able to demonstrate why spectral kernel design based methods can often improve the predictive performance. Experiments are used to illustrate the main consequences of our analysis.

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gradient and projection calculations. The projection step can be solved using combinatorial algorithms for min-cost quadratic flow. This makes the approach an efficient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.

A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs.

Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recent progress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry of input patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables. Unlike transductive algorithms, our formulation naturally extends to new test points.

We consider a framework for semi-supervised learning using spectral decomposition based unsupervised kernel design. This approach subsumes a class of previously proposed semi-supervised learning methods on data graphs. We examine various theoretical properties of such methods. In particular, we derive a generalization performance bound, and obtain the optimal kernel design by minimizing the bound. Based on the theoretical analysis, we are able to demonstrate why spectral kernel design based methods can often improve the predictive performance. Experiments are used to illustrate the main consequences of our analysis.

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gradient and projection calculations. The projection step can be solved using combinatorial algorithms for min-cost quadratic flow. This makes the approach an efficient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.

Active learning is the problem in supervised learning to design the locations of training input points so that the generalization error is minimized. Existing active learning methods often assume that the model used for learning is correctly specified, i.e., the learning target function can be expressed by the model at hand. In many practical situations, however, this assumption may not be fulfilled. In this paper, we first show that the existing active learning method can be theoretically justified under slightly weaker condition: the model does not have to be correctly specified, but slightly misspecified models are also allowed. However, it turns out that the weakened condition is still restrictive in practice. To cope with this problem, we propose an alternative active learning method which can be theoretically justified for a wider class of misspecified models. Thus, the proposed method has a broader range of applications than the existing method. Numerical studies show that the proposed active learning method is robust against the misspecification of models and is thus reliable.

A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs.

We examine various theoretical properties of such methods.