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.

We consider the task of tuning hyperparameters in SVM models based on minimizing a smooth performance validation function, e.g., smoothed k-fold cross-validation error, using nonlineaI optimization techniques.

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.

In many real-world statistical problems, we would like to fit a model with a large number of dependent variables to a training sample with very many cases.

We consider the problem of learning classifiers for structurally incomplete data, where some objects have a subset of features inherently absent due to complex relationships between the features. The common approach for handling missingfeatures is to begin with a preprocessing phase that completes the missing features, and then use a standard classification procedure. In this paper we show how incomplete data can be classified directly without any completion of the missing features using a max-margin learning framework. Weformulate this task using a geometrically-inspired objective function, and discuss two optimization approaches: The linearly separable case is written as a set of convex feasibility problems, and the non-separable case has a non-convex objective that we optimize iteratively. By avoiding the pre-processing phase in which the data is completed, these approaches offer considerable computational savings. More importantly, we show that by elegantly handlingcomplex patterns of missing values, our approach is both competitive with other methods when the values are missing at random and outperforms them when the missing values have nontrivial structure. We demonstrate our results on two real-world problems: edge prediction in metabolic pathways, and automobile detection in natural images.

We address the problem of subordinate class recognition, like the distinction between differenttypes of motorcycles. Our approach is motivated by observations from cognitive psychology, which identify parts as the defining component of basic level categories (like motorcycles), while subordinate categories are more often defined by part properties (like'jagged wheels'). Accordingly, we suggest a two-stage algorithm: First, a relational part based object model is learnt using unsegmented object images from the inclusive class (e.g., motorcycles in general). The model is then used to build a class-specific vector representation for images, where each entry corresponds to a model's part. In the second stage we train a standard discriminative classifier to classify subclass instances (e.g., cross motorcycles) basedon the class-specific vector representation. We describe extensive experimental results with several subclasses. The proposed algorithm typically gives better results than a competing one-step algorithm, or a two stage algorithm where classification is based on a model of the subordinate class.

Such a problem can occur in many real-world tasks, e.g. an image usually

We demonstrate how our framework encompasses problems from manufacturing to Vision processing.

Many computer aided diagnosis (CAD) problems can be best modelled as a multiple-instance learning (MIL) problem with unbalanced data: i.e., the training data typically consists of a few positive bags, and a very large number of negative instances.Existing MIL algorithms are much too computationally expensive for these datasets. We describe CH, a framework for learning a Convex Hull representation of multiple instances that is significantly faster than existing MIL algorithms. Our CH framework applies to any standard hyperplane-based learning algorithm, and for some algorithms, is guaranteed to find the global optimal solution. Experimentalstudies on two different CAD applications further demonstrate that the proposed algorithm significantly improves diagnostic accuracy when compared toboth MIL and traditional classifiers. Although not designed for standard MIL problems (which have both positive and negative bags and relatively balanced datasets),comparisons against other MIL methods on benchmark problems also indicate that the proposed method is competitive with the state-of-the-art.

We describe an unsupervised method for learning a probabilistic grammar of an object from a set of training examples. Our approach is invariant to the scale and rotation of the objects. We illustrate our approach using thirteen objects from the Caltech 101 database. In addition, we learn the model of a hybrid object class where we do not know the specific object or its position, scale or pose. This is illustrated bylearning a hybrid class consisting of faces, motorbikes, and airplanes. The individual objects can be recovered as different aspects of the grammar for the object class.