Finite mixture model is a powerful tool in many statistical learning problems. In this paper, we propose a general, structure-preserving approach to reduce its model complexity, which can bring significant computational benefits in many applications. The basic idea is to group the original mixture components into compact clusters, and then minimize an upper bound on the approximation error between the original and simplified models.

We study a setting that is motivated by the problem of filtering spam messages for many users. Each user receives messages according to an individual, unknown distribution, reflected only in the unlabeled inbox. The spam filter for a user is required to perform well with respect to this distribution. Labeled messages from publicly available sources can be utilized, but they are governed by a distinct distribution, not adequately representing most inboxes. We devise a method that minimizes a loss function with respect to a user's personal distribution based on the available biased sample. A nonparametric hierarchical Bayesian model furthermore generalizes across users by learning a common prior which is imposed on new email accounts. Empirically, we observe that bias-corrected learning outperforms naive reliance on the assumption of independent and identically distributed data; Dirichlet-enhanced generalization across users outperforms a single ("one size fits all") filter as well as independent filters for all users.

We present a general model-independent approach to the analysis of data in cases when these data do not appear in the form of co-occurrence of two variables X,Y, but rather as a sample of values of an unknown (stochastic) function Z(X,Y). For example, in gene expression data, the expression level Z is a function of gene X and condition Y; or in movie ratings data the rating Z is a function of viewer X and movie Y. The approach represents a consistent extension of the Information Bottleneck method that has previously relied on the availability of co-occurrence statistics. By altering the relevance variable we eliminate the need in the sample of joint distribution of all input variables. This new formulation also enables simple MDL-like model complexity control and prediction of missing values of Z. The approach is analyzed and shown to be on a par with the best known clustering algorithms for a wide range of domains. For the prediction of missing values (collaborative filtering) it improves the currently best known results.

We propose a novel framework for the classification of single trial ElectroEncephaloGraphy (EEG), based on regularized logistic regression. Framed in this robust statistical framework no prior feature extraction or outlier removal is required.

Up to now even subjects that are experts in the use of machine learning based BCI systems still have to undergo a calibration session of about 20-30 min. From this data their (movement) intentions are so far infered. We now propose a new paradigm that allows to completely omit such calibration and instead transfer knowledge from prior sessions. To achieve this goal we first define normalized CSP features and distances in-between. Second, we derive prototypical features across sessions: (a) by clustering or (b) by feature concatenation methods. Finally, we construct a classifier based on these individualized prototypes and show that, indeed, classifiers can be successfully transferred to a new session for a number of subjects.

Starting with the work of Jaakkola and Haussler, a variety of approaches have been proposed for coupling domain-specific generative models with statistical learning methods. The link is established by a kernel function which provides a similarity measure based inherently on the underlying model. In computational biology, the full promise of this framework has rarely ever been exploited, as most kernels are derived from very generic models, such as sequence profiles or hidden Markov models. Here, we introduce the MTreeMix kernel, which is based on a generative model tailored to the underlying biological mechanism.

In this paper we focus on the issue of normalization of the affinity matrix in spectral clustering.

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 by learning 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.

We describe and analyze an algorithmic framework for online classification where each online trial consists of multiple prediction tasks that are tied together. We tackle the problem of updating the online hypothesis by defining a projection problem in which each prediction task corresponds to a single linear constraint. These constraints are tied together through a single slack parameter. We then introduce a general method for approximately solving the problem by projecting simultaneously and independently on each constraint which corresponds to a prediction sub-problem, and then averaging the individual solutions. We show that this approach constitutes a feasible, albeit not necessarily optimal, solution for the original projection problem. We derive concrete simultaneous projection schemes and analyze them in the mistake bound model. We demonstrate the power of the proposed algorithm in experiments with online multiclass text categorization. Our experiments indicate that a combination of class-dependent features with the simultaneous projection method outperforms previously studied algorithms.

We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0/1 loss of the binary classifier would then bound the mislabeling cost of the ranking rule. Our framework allows not only to design good ordinal regression algorithms based on well-tuned binary classification approaches, but also to derive new generalization bounds for ordinal regression from known bounds for binary classification.