Active learning refers to algorithmic frameworks aimed at selecting training data points in order to reduce the number of required training data points and/or improve thegeneralization performance of a learning method. In this paper, we present an asymptotic analysis of active learning for generalized linear models. Our analysis holds under the common practical situation of model misspecification, andis based on realistic assumptions regarding the nature of the sampling distributions, which are usually neither independent nor identical. We derive unbiased estimatorsof generalization performance, as well as estimators of expected reduction in generalization error after adding a new training data point, that allow us to optimize its sampling distribution through a convex optimization problem. Our analysis naturally leads to an algorithm for sequential active learning which is applicable for all tasks supported by generalized linear models (e.g., binary classification, multi-classclassification, regression) and can be applied in nonlinear settings through the use of Mercer kernels.

The theoretical understanding of support vector machines (SVMs) and related kernel-based methods has been substantially improved in recent years.

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.

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.

Propagation based methods are developed and rigorously assessed.

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.

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.

Image Congealing (1C) is a nonparametric method for the joint alignment of a collection of images affected by systematic and unwanted deformations.

This paper presents an algorithm for synthesis of human motion in specified styles. We use a theory of movement observation (Laban Movement Analysis) to describe movement styles as points in a multidimensional perceptual space. We cast the task of learning to synthesize desired movement styles as a regression problem: sequences generated via space-time interpolation of motion capture data are used to learn a nonlinear mapping between animation parameters and movement styles in perceptual space. We demonstrate that the learned model can apply a variety of motion styles to prerecorded motion sequences and it can extrapolate styles not originally included in the training data.

We present a novel algorithm called PG-means which is able to learn the number of clusters in a classical Gaussian mixture model. Our method is robust and efficient; ituses statistical hypothesis tests on one-dimensional projections of the data and model to determine if the examples are well represented by the model. In so doing, we are applying a statistical test for the entire model at once, not just on a per-cluster basis. We show that our method works well in difficult cases such as non-Gaussian data, overlapping clusters, eccentric clusters, high dimension, and many true clusters. Further, our new method provides a much more stable estimate of the number of clusters than existing methods.