In pattern classification tasks, errors are introduced because of differences between the true model and the one obtained via model estimation. Using likelihood-ratio based classification, it is possible to correct for this discrepancy by finding class-pair specific terms to adjust the likelihood ratio directly, and that can make class-pair preference relationships intransitive. In this work, we introduce new methodology that makes necessary corrections to the likelihood ratio, specifically those that are necessary to achieve perfect classification (but not perfect likelihood-ratio correction which can be overkill). The new corrections, while weaker than previously reported such adjustments, are analytically challenging since they involve discontinuous functions, therefore requiring several approximations. We test a number of these new schemes on an isolatedword speech recognition task as well as on the UCI machine learning data sets. Results show that by using the bias terms calculated in this new way, classification accuracy can substantially improve over both the baseline and over our previous results.

Pairwise coupling is a popular multi-class classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. We show conceptually and experimentally that the proposed approaches are more stable than two existing popular methods: voting and [3].

The bootstrap has become a popular method for exploring model (structure) uncertainty. Our experiments with artificial and realworld data demonstrate that the graphs learned from bootstrap samples can be severely biased towards too complex graphical models. Accounting for this bias is hence essential, e.g., when exploring model uncertainty. We find that this bias is intimately tied to (well-known) spurious dependences induced by the bootstrap. The leading-order bias-correction equals one half of Akaike's penalty for model complexity. We demonstrate the effect of this simple bias-correction in our experiments. We also relate this bias to the bias of the plugin estimator for entropy, as well as to the difference between the expected test and training errors of a graphical model, which asymptotically equals Akaike's penalty (rather than one half).

The minimax formulation also opens up an interesting class of methods in which the graph is "decorated" with information at the vertices, offering discrete or continuous maps, reduced computational complexity, and immunity to some solution instabilities of eigenfunction approaches.

Label ranking is the task of inferring a total order over a predefined set of labels for each given instance. We present a general framework for batch learning of label ranking functions from supervised data. We assume that each instance in the training data is associated with a list of preferences over the label-set, however we do not assume that this list is either complete or consistent. This enables us to accommodate a variety of ranking problems. In contrast to the general form of the supervision, our goal is to learn a ranking function that induces a total order over the entire set of labels. Special cases of our setting are multilabel categorization and hierarchical classification. We present a general boosting-based learning algorithm for the label ranking problem and prove a lower bound on the progress of each boosting iteration. The applicability of our approach is demonstrated with a set of experiments on a large-scale text corpus.

We propose an information-theoretic clustering approach that incorporates a pre-known partition of the data, aiming to identify common clusters that cut across the given partition. In the standard clustering setting the formation of clusters is guided by a single source of feature information. The newly utilized pre-partition factor introduces an additional bias that counterbalances the impact of the features whenever they become correlated with this known partition. The resulting algorithmic framework was applied successfully to synthetic data, as well as to identifying text-based cross-religion correspondences.

We describe a procedure which finds a hierarchical clustering by hillclimbing. The cost function we use is a hierarchical extension of the k-means cost; our local moves are tree restructurings and node reorderings. We show these can be accomplished efficiently, by exploiting special properties of squared Euclidean distances and by using techniques from scheduling algorithms.

A novel approach to combining clustering and feature selection is presented. It implements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discriminative power of the used partitioning algorithm. On the technical side, we present an efficient optimization algorithm with guaranteed local convergence property. The only free parameter of this method is selected by a resampling-based stability analysis. Experiments with real-world datasets demonstrate that our method is able to infer both meaningful partitions and meaningful subsets of features.

Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information.

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.