Establishing correspondence between distinct objects is an important and nontrivial task: correctness of the correspondence hinges on properties which are difficult to capture in an a priori criterion. While previous work has used a priori criteria which in some cases led to very good results, the present paper explores whether it is possible to learn a combination of features that, for a given training set of aligned human heads, characterizes the notion of correct correspondence. By optimizing this criterion, we are then able to compute correspondence and morphs for novel heads.

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.

Independent Component Analysis (ICA) is a popular method for extracting independent features from visual data. However, as a fundamentally linear technique, there is always nonlinear residual redundancy that is not captured by ICA. Hence there have been many attempts to try to create a hierarchical version of ICA, but so far none of the approaches have a natural way to apply them more than once. Here we show that there is a relatively simple technique that transforms the absolute values of the outputs of a previous application of ICA into a normal distribution, to which ICA maybe applied again. This results in a recursive ICA algorithm that may be applied any number of times in order to extract higher order structure from previous layers.

We describe an algorithmic framework for an abstract game which we term a convex repeated game. We show that various online learning and boosting algorithms can be all derived as special cases of our algorithmic framework. This unified view explains the properties of existing algorithms and also enables us to derive several new interesting algorithms. Our algorithmic framework stems from a connection that we build between the notions of regret in game theory and weak duality in convex optimization.

Neural motor prostheses (NMPs) require the accurate decoding of motor cortical population activity for the control of an artificial motor system. Previous work on cortical decoding for NMPs has focused on the recovery of hand kinematics. Human NMPs however may require the control of computer cursors or robotic devices with very different physical and dynamical properties. Here we show that the firing rates of cells in the primary motor cortex of nonhuman primates can be used to control the parameters of an artificial physical system exhibiting realistic dynamics. The model represents 2D hand motion in terms of a point mass connected to a system of idealized springs. The nonlinear spring coefficients are estimated from the firing rates of neurons in the motor cortex. We evaluate linear and a nonlinear decoding algorithms using neural recordings from two monkeys performing two different tasks. We found that the decoded spring coefficients produced accurate hand trajectories compared with state-of-the-art methods for direct decoding of hand kinematics. Furthermore, using a physically-based system produced decoded movements that were more "natural" in that their frequency spectrum more closely matched that of natural hand movements.

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 highly efficient framework for kernel multi-class models with a large and structured set of classes. Kernel parameters are learned automatically by maximizing the cross-validation log likelihood, and predictive probabilities are estimated. We demonstrate our approach on large scale text classification tasks with hierarchical class structure, achieving state-of-the-art results in an order of magnitude less time than previous work.

We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic Meta-Descent (SMD) to KHA/et; this further speeds convergence by performing gain adaptation in RKHS. Experimental results for kernel PCA and spectral clustering of USPS digits as well as motion capture and image de-noising problems confirm that our methods converge substantially faster than conventional KHA.

The objects in many real-world domains can be organized into hierarchies, where each internal node picks out a category of objects. Given a collection of features and relations defined over a set of objects, an annotated hierarchy includes a specification of the categories that are most useful for describing each individual feature and relation. We define a generative model for annotated hierarchies and the features and relations that they describe, and develop a Markov chain Monte Carlo scheme for learning annotated hierarchies. We show that our model discovers interpretable structure in several real-world data sets.

We propose a generic algorithm for computation of similarity measures for sequential data. The algorithm uses generalized suffix trees for efficient calculation of various kernel, distance and non-metric similarity functions. Its worst-case run-time is linear in the length of sequences and independent of the underlying embedding language, which can cover words, k-grams or all contained subsequences. Experiments with network intrusion detection, DNA analysis and text processing applications demonstrate the utility of distances and similarity coefficients for sequences as alternatives to classical kernel functions.