We propose a new method for constructing hyperkenels and define two promising special cases that can be computed in closed form. These we call the Gaussian and Wishart hyperkernels. The former is especially attractive in that it has an interpretable regularization scheme reminiscent of that of the Gaussian RBF kernel. We discuss how kernel learning can be used not just for improving the performance of classification and regression methods, but also as a stand-alone algorithm for dimensionality reduction and relational or metric learning.

The quality measures used in information retrieval are particularly difficult to optimize directly, since they depend on the model scores only through the sorted order of the documents returned for a given query. Thus, the derivatives of the cost with respect to the model parameters are either zero, or are undefined. In this paper, we propose a class of simple, flexible algorithms, called LambdaRank, which avoids these difficulties by working with implicit cost functions. We describe LambdaRank using neural network models, although the idea applies to any differentiable function class. We give necessary and sufficient conditions for the resulting implicit cost function to be convex, and we show that the general method has a simple mechanical interpretation. We demonstrate significantly improved accuracy, over a state-of-the-art ranking algorithm, on several datasets. We also show that LambdaRank provides a method for significantly speeding up the training phase of that ranking algorithm. Although this paper is directed towards ranking, the proposed method can be extended to any non-smooth and multivariate cost functions.

Data sets involving multiple groups with shared characteristics frequently arise in practice. In this paper we extend hierarchical Dirichlet processes to model such data. Each group is assumed to be generated from a template mixture model with group level variability in both the mixing proportions and the component parameters. Variabilities in mixing proportions across groups are handled using hierarchical Dirichlet processes, also allowing for automatic determination of the number of components. In addition, each group is allowed to have its own component parameters coming from a prior described by a template mixture model. This group-level variability in the component parameters is handled using a random effects model. We present a Markov Chain Monte Carlo (MCMC) sampling algorithm to estimate model parameters and demonstrate the method by applying it to the problem of modeling spatial brain activation patterns across multiple images collected via functional magnetic resonance imaging (fMRI).

The increasingly popular independent component analysis (ICA) may only be applied to data following the generative ICA model in order to guarantee algorithmindependent and theoretically valid results. Subspace ICA models generalize the assumption of component independence to independence between groups of components. They are attractive candidates for dimensionality reduction methods, however are currently limited by the assumption of equal group sizes or less general semi-parametric models. By introducing the concept of irreducible independent subspaces or components, we present a generalization to a parameter-free mixture model. Moreover, we relieve the condition of at-most-one-Gaussian by including previous results on non-Gaussian component analysis. After introducing this general model, we discuss joint block diagonalization with unknown block sizes, on which we base a simple extension of JADE to algorithmically perform the subspace analysis. Simulations confirm the feasibility of the algorithm.

The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

We propose a new kernel-based data transformation technique. It is founded on the principle of maximum entropy (MaxEnt) preservation, hence named kernel MaxEnt. The key measure is Renyi's entropy estimated via Parzen windowing. We show that kernel MaxEnt is based on eigenvectors, and is in that sense similar to kernel PCA, but may produce strikingly different transformed data sets. An enhanced spectral clustering algorithm is proposed, by replacing kernel PCA by kernel MaxEnt as an intermediate step. This has a major impact on performance.

The Maximum Margin Planning (MMP) (Ratliff et al., 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher appear to be lower cost (with a lossscaled margin) than any other policy for a given planning domain.

Multinomial logistic regression provides the standard penalised maximumlikelihood solution to multi-class pattern recognition problems. More recently, the development of sparse multinomial logistic regression models has found application in text processing and microarray classification, where explicit identification of the most informative features is of value. In this paper, we propose a sparse multinomial logistic regression method, in which the sparsity arises from the use of a Laplace prior, but where the usual regularisation parameter is integrated out analytically. Evaluation over a range of benchmark datasets reveals this approach results in similar generalisation performance to that obtained using cross-validation, but at greatly reduced computational expense.

We present a local learning approach for clustering. The basic idea is that a good clustering result should have the property that the cluster label of each data point can be well predicted based on its neighboring data and their cluster labels, using current supervised learning methods. An optimization problem is formulated such that its solution has the above property. Relaxation and eigen-decomposition are applied to solve this optimization problem. We also briefly investigate the parameter selection issue and provide a simple parameter selection method for the proposed algorithm. Experimental results are provided to validate the effectiveness of the proposed approach.

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 missing features 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. We formulate 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 handling complex 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.