The learner then updates its parameter vector to minimize a riskfunctional, and the process repeats.

A number of exact and approximate methods are available for inference calculations ingraphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables andpure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models.

Semi-supervised learning is more powerful than supervised learning by using both labeled and unlabeled data. In particular, the manifold regularization framework, together with kernel methods, leads to the Laplacian SVM (LapSVM) that has demonstrated state-of-the-art performance. However, the LapSVM solution typically involveskernel expansions of all the labeled and unlabeled examples, and is slow on testing. Moreover, existing semi-supervised learning methods, including theLapSVM, can only handle a small number of unlabeled examples. In this paper, we integrate manifold regularization with the core vector machine, which has been used for large-scale supervised and unsupervised learning. By using a sparsified manifold regularizer and formulating as a center-constrained minimum enclosing ball problem, the proposed method produces sparse solutions with low time and space complexities. Experimental results show that it is much faster than the LapSVM, and can handle a million unlabeled examples on a standard PC; while the LapSVM can only handle several thousand patterns.

Image registration and super-resolution are often treated as distinct processes, to be considered sequentially [1, 3, 7]. Hardie et al. demonstrated that the low-resolution image registration can be

We consider a general form of transductive learning on graphs with Laplacian regularization, and derive margin-based generalization bounds using appropriate geometric properties of the graph. We use this analysis to obtain a better understanding ofthe role of normalization of the graph Laplacian matrix as well as the effect of dimension reduction. The results suggest a limitation of the standard degree-based normalization. We propose a remedy from our analysis and demonstrate empiricallythat the remedy leads to improved classification performance.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation withvarious interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

We consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the target distribution is completely known to the learner and the learner's goal is to construct a classifier capable of guaranteeing agiven tolerance for the false-positive error while minimizing the false negative error. We identify both "hard" and "soft" optimal classification strategies for different types of games and demonstrate that soft classification can provide a significant advantage. Our optimal strategies and bounds provide worst-case lower bounds for standard, finite-sample SCC and also motivate new approaches to solving SCC.

Classifiers that err on (x, 3;) under measure Q as follows.

In this paper we estimate quadratic models for natural images using Independent Component Analysis (ICA). The used quadratic functions are a natural extension to linear functions (i.e.

We introduce a novel adaptive nonparametric anomaly detection approach, called GEM, that is based on the minimal covering properties of K-point entropic graphs when constructed on N training samples from a nominal probability distribution. Suchgraphs have the property that as N their span recovers the entropy minimizing set that supports at least ρ K/N(100)% of the mass of the Lebesgue part of the distribution. When a test sample falls outside of the entropy minimizing set an anomaly can be declared at a statistical level of significance α 1 ρ. A method for implementing this nonparametric anomaly detector is proposed that approximates this minimum entropy set by the influence region of a K-point entropic graph built on the training data. By implementing an incremental leave-one-out k-nearest neighbor graph on resampled subsets of the training data GEM can efficiently detect outliers at a given level of significance and compute their empirical p-values. We illustrate GEM for several simulated and real data sets in high dimensional feature spaces.