In this paper we study the problem of learning a low-dimensional (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle representation, we develop an efficient smooth optimization approach for sparse metric learning although the learning model is based on a non-differential loss function. This smooth optimization approach has an optimal convergence rate of $O(1 /\ell^2)$ for smooth problems where $\ell$ is the iteration number. Finally, we run experiments to validate the effectiveness and efficiency of our sparse metric learning model on various datasets.

EEG connectivity measures could provide a new type of feature space for inferring a subject's intention in Brain-Computer Interfaces (BCIs). However, very little is known on EEG connectivity patterns for BCIs. In this study, EEG connectivity during motor imagery (MI) of the left and right is investigated in a broad frequency range across the whole scalp by combining Beamforming with Transfer Entropy and taking into account possible volume conduction effects. Observed connectivity patterns indicate that modulation intentionally induced by MI is strongest in the gamma-band, i.e., above 35 Hz. Furthermore, modulation between MI and rest is found to be more pronounced than between MI of different hands. This is in contrast to results on MI obtained with bandpower features, and might provide an explanation for the so far only moderate success of connectivity features in BCIs. It is concluded that future studies on connectivity based BCIs should focus on high frequency bands and consider experimental paradigms that maximally vary cognitive demands between conditions.

Dependencies among neighbouring labels in a sequence is an important source of information for sequence labeling problems. However, only dependencies between adjacent labels are commonly exploited in practice because of the high computational complexity of typical inference algorithms when longer distance dependencies are taken into account. In this paper, we show that it is possible to design efficient inference algorithms for a conditional random field using features that depend on long consecutive label sequences (high-order features), as long as the number of distinct label sequences in the features used is small. This leads to efficient learning algorithms for these conditional random fields. We show experimentally that exploiting dependencies using high-order features can lead to substantial performance improvements for some problems and discuss conditions under which high-order features can be effective.

We address the challenge of assessing conservation of gene expression in complex, non-homogeneous datasets. Recent studies have demonstrated the success of probabilistic models in studying the evolution of gene expression in simple eukaryotic organisms such as yeast, for which measurements are typically scalar and independent. Models capable of studying expression evolution in much more complex organisms such as vertebrates are particularly important given the medical and scientific interest in species such as human and mouse. We present a statistical model that makes a number of significant extensions to previous models to enable characterization of changes in expression among highly complex organisms. We demonstrate the efficacy of our method on a microarray dataset containing diverse tissues from multiple vertebrate species. We anticipate that the model will be invaluable in the study of gene expression patterns in other diverse organisms as well, such as worms and insects.

Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose approximate bilinear programming, a new formulation of value function approximation thatprovides strong a priori guarantees. In particular, this approach provably finds an approximate value function that minimizes the Bellman residual. Solving a bilinear program optimally is NPhard, but this is unavoidable because the Bellman-residual minimization itself is NPhard. We therefore employ and analyze a common approximate algorithm for bilinear programs. The analysis shows that this algorithm offers a convergent generalization of approximate policy iteration.Finally, we demonstrate that the proposed approach can consistently minimize the Bellman residual on a simple benchmark problem.

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of purely reconstructive ones. This paper proposes a new step in that direction with a novel sparse representation for signals belonging to different classes in terms of a shared dictionary and multiple decision functions. It is shown that the linear variant of the model admits a simple probabilistic interpretation, and that its most general variant also admits a simple interpretation in terms of kernels. An optimization framework for learning all the components of the proposed model is presented, along with experiments on standard handwritten digit and texture classification tasks.

In this paper, we examine the generalization error of regularized distance metric learning. We show that with appropriate constraints, the generalization error of regularized distance metric learning could be independent from the dimensionality, making it suitable for handling high dimensional data. In addition, we present an efficient online learning algorithm for regularized distance metric learning. Our empirical studies with data classification and face recognition show that the proposed algorithm is (i) effective for distance metric learning when compared to the state-of-the-art methods, and (ii) efficient and robust for high dimensional data.

Many researchers have suggested that the psychological complexity of a concept is related to the length of its representation in a language of thought. As yet, however, there are few concrete proposals about the nature of this language. This paper makes one such proposal: the language of thought allows first order quantification (quantificationover objects) more readily than second-order quantification (quantification over features). To support this proposal we present behavioral results froma concept learning study inspired by the work of Shepard, Hovland and Jenkins. Humans can learn and think about many kinds of concepts, including natural kinds such as elephant and water and nominal kinds such as grandmother and prime number.

Actor-critic algorithms for reinforcement learning are achieving renewed popularity dueto their good convergence properties in situations where other approaches often fail (e.g., when function approximation is involved). Interestingly, there is growing evidence that actor-critic approaches based on phasic dopamine signals play a key role in biological learning through cortical and basal ganglia loops. We derive a temporal difference based actor critic learning algorithm, for which convergence can be proved without assuming widely separated time scales for the actor and the critic. The approach is demonstrated by applying it to networks of spiking neurons. The established relation between phasic dopamine and the temporal difference signal lends support to the biological relevance of such algorithms.

We introduces a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After working out an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation.