We show that the relevant information about a classification problem in feature space is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem. Thus, kernels not only transform data sets such that good generalization can be achieved even by linear discriminant functions, but this transformation is also performed in a manner which makes economic use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data to perform classification. Practically, we propose an algorithm which enables us to recover the subspace and dimensionality relevant for good classification. Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations of sequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problems with several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology.

Metric learning has been shown to significantly improve the accuracy of k-nearest neighbor (kNN) classification. In problems involving thousands of features, dis- tance learning algorithms cannot be used due to overfitting and high computa- tional complexity. In such cases, previous work has relied on a two-step solution: first apply dimensionality reduction methods to the data, and then learn a met- ric in the resulting low-dimensional subspace. In this paper we show that better classification performance can be achieved by unifying the objectives of dimen- sionality reduction and metric learning. We propose a method that solves for the low-dimensional projection of the inputs, which minimizes a metric objective aimed at separating points in different classes by a large margin.

We establish a general oracle inequality for clipped approximate minimizers of regularized empirical risks and apply this inequality to support vector machine (SVM) type algorithms. We then show that for SVMs using Gaussian RBF kernels for classification this oracle inequality leads to learning rates that are faster than the ones established in [9]. Finally, we use our oracle inequality to show that a simple parameter selection approach based on a validation set can yield the same fast learning rates without knowing the noise exponents which were required to be known a-priori in [9].

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 multi-dimensional 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 pre-recorded motion sequences and it can extrapolate styles not originally included in the training data.

We consider the task of tuning hyperparameters in SVM models based on minimizing a smooth performance validation function, e.g., smoothed k-fold crossvalidation error, using non-linear optimization techniques. The key computation in this approach is that of the gradient of the validation function with respect to hyperparameters. We show that for large-scale problems involving a wide choice of kernel-based models and validation functions, this computation can be very efficiently done; often within just a fraction of the training time. Empirical results show that a near-optimal set of hyperparameters can be identified by our approach with very few training rounds and gradient computations. .

If language users are rational, they might choose to structure their utterances so as to optimize communicative properties. In particular, information-theoretic and psycholinguistic considerations suggest that this may include maximizing the uniformity of information density in an utterance. We investigate this possibility in the context of syntactic reduction, where the speaker has the option of either marking a higher-order unit (a phrase) with an extra word, or leaving it unmarked. We demonstrate that speakers are more likely to reduce less information-dense phrases. In a second step, we combine a stochastic model of structured utterance production with a logistic-regression model of syntactic reduction to study which types of cues speakers employ when estimating the predictability of upcoming elements.

This paper proposes a new approach to model-based clustering under prior knowl- edge. The proposed formulation can be interpreted from two different angles: as penalized logistic regression, where the class labels are only indirectly observed (via the probability density of each class); as finite mixture learning under a group- ing prior. To estimate the parameters of the proposed model, we derive a (gener- alized) EM algorithm with a closed-form E-step, in contrast with other recent approaches to semi-supervised probabilistic clustering which require Gibbs sam- pling or suboptimal shortcuts. We show that our approach is ideally suited for image segmentation: it avoids the combinatorial nature Markov random field pri- ors, and opens the door to more sophisticated spatial priors (e.g., wavelet-based) in a simple and computationally efficient way. Finally, we extend our formulation to work in unsupervised, semi-supervised, or discriminative modes.

Maximum margin clustering was proposed lately and has shown promising performance in recent studies [1, 2]. It extends the theory of support vector machine to unsupervised learning. Despite its good performance, there are three ma jor problems with maximum margin clustering that question its efficiency for real-world applications. First, it is computationally expensive and difficult to scale to large-scale datasets because the number of parameters in maximum margin clustering is quadratic in the number of examples. Second, it requires data preprocessing to ensure that any clustering boundary will pass through the origins, which makes it unsuitable for clustering unbalanced dataset.

Spectral clustering methods are common graph-based approaches to clustering of data. Spectral clustering algorithms typically start from local information encoded in a weighted graph on the data and cluster according to the global eigenvectors of the corresponding (normalized) similarity matrix. One contribution of this paper is to present fundamental limitations of this general local to global approach. We show that based only on local information, the normalized cut functional is not a suitable measure for the quality of clustering. Further, even with a suitable similarity measure, we show that the first few eigenvectors of such adjacency matrices cannot successfully cluster datasets that contain structures at different scales of size and density. Based on these findings, a second contribution of this paper is a novel diffusion based measure to evaluate the coherence of individual clusters.