We present a flexible formulation of semisupervised learning for structured models, which seamlessly incorporates graphbased and more general supervision by extending the posterior regularization (PR) framework. Our extension allows for any regularizer that is a convex, differentiable function of the appropriate marginals. We show that surprisingly, non-linearity of such regularization does not...

We propose a treatment of γ 5 in dimensional regularization which is based on an algebraically consistent extension of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme; we define the corresponding minimal renormalization scheme and show its equivalence with a non-minimal BMHV scheme. The restoration of the chiral Ward identities requires the introduction of considerably fewer finite coun...

Semi-supervised learning is an emerging computational paradigm for learning from limited supervision by utilizing large amounts of inexpensive, unsupervised observations. Not only does this paradigm carry appeal as a model for natural learning, but it also has an increasing practical need in most if not all applications of machine learning – those where abundant amounts of data can be cheaply a...

In this paper, we propose a semi-supervised learning (SSL) algorithm based on local and global regularization. In the local regularization part, our algorithm constructs a regularized classifier for each data point using its neighborhood, while the global regularization part adopts a Laplacian regularizer to smooth the data labels predicted by those local classifiers. We show that some existing...

We investigate a family of regression problems in a semi-supervised setting. The task is to assign real-valued labels to a set of n sample points, provided a small training subset of N labeled points. A goal of semi-supervised learning is to take advantage of the (geometric) structure provided by the large number of unlabeled data when assigning labels. We consider a random geometric graph, wit...

Wikification for tweets aims to automatically identify each concept mention in a tweet and link it to a concept referent in a knowledge base (e.g., Wikipedia). Due to the shortness of a tweet, a collective inference model incorporating global evidence from multiple mentions and concepts is more appropriate than a noncollecitve approach which links each mention at a time. In addition, it is chal...

The enormous wealth of unlabeled data in many applications of machine learning is beginning to pose challenges to the designers of semi-supervised learning methods. We are interested in developing linear classification algorithms to efficiently learn from massive partially labeled datasets. In this paper, we propose Linear Laplacian Support Vector Machines and Linear Laplacian Regularized Least...

Many classification problems involve data instances that are interlinked with each other, such as webpages connected by hyperlinks. Techniques for collective classification (CC) often increase accuracy for such data graphs, but usually require a fully-labeled training graph. In contrast, we examine how to improve the semi-supervised learning of CC models when given only a sparsely-labeled graph...

In this survey, we go over a few historical literatures on semi-supervised learning problems which apply graph regularization on both labled and unlabeled data to improve classification performance. These semi-supervised methods usually construct a nearest neighbour graph on instance space under certain measure function, and then work under the smoothness assumption that class labels of samples...

It is well known that some important Markov semi-groups have a “regularization effect” – as for example th hypercontractivity property of the noise operator on Boolean hypercube or Ornstein-Uhlenbeck semi-group real line, which applies to functions in Lp p > 1. Talagrand had conjectured 1989 has further subtle regularization are just integrable, but this conjecture remains open. Nonetheless, Ga...