This paper presents a general family of algebraic positive definite similarity functions over spaces of matrices with varying column rank. The columns can represent local regions in an image (whereby images have varying number of local parts), images of an image sequence, motion trajectories in a multibody motion, and so forth. The family of set kernels we derive is based on a group invariant tensor product lifting with parameters that can be naturally tuned to provide a cookbook of sorts covering the possible "wish lists" from similarity measures over sets of varying cardinality. We highlight the strengths of our approach by demonstrating the set kernels for visual recognition of pedestrians using local parts representations.

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative approach, whereby the global solution of the non-convex optimization problem is derived via an equivalent optimization problem. Moreover, the convex optimization task is reduced to a conic quadratic programming problem for which efficient solvers are available. Highly competitive numerical results on both artificial and real-world data sets are reported.

This paper presents an application of Boosting for classifying labeled graphs, general structures for modeling a number of real-world data, such as chemical compounds, natural language texts, and bio sequences. The proposal consists of i) decision stumps that use subgraph as features, and ii) a Boosting algorithm in which subgraph-based decision stumps are used as weak learners. We also discuss the relation between our algorithm and SVMs with convolution kernels. Two experiments using natural language data and chemical compounds show that our method achieves comparable or even better performance than SVMs with convolution kernels as well as improves the testing efficiency.

Motor control depends on sensory feedback in multiple modalities with different latencies. In this paper we consider within the framework of reinforcement learning how different sensory modalities can be combined and selected for real-time, optimal movement control. We propose an actor-critic architecture with multiple modules, whose output are combined using a softmax function. We tested our architecture in a simulation of a sequential reaching task. Reaching was initially guided by visual feedback with a long latency. Our learning scheme allowed the agent to utilize the somatosensory feedback with shorter latency when the hand is near the experienced trajectory. In simulations with different latencies for visual and somatosensory feedback, we found that the agent depended more on feedback with shorter latency.

Repeated spike patterns have often been taken as evidence for the synfire chain, a phenomenon that a stable spike synchrony propagates through a feedforward network. Inter-spike intervals which represent a repeated spike pattern are influenced by the propagation speed of a spike packet. However, the relation between the propagation speed and network structure is not well understood. While it is apparent that the propagation speed depends on the excitatory synapse strength, it might also be related to spike patterns. We analyze a feedforward network with Mexican-Hattype connectivity (FMH) using the Fokker-Planck equation. We show that both a uniform and a localized spike packet are stable in the FMH in a certain parameter region. We also demonstrate that the propagation speed depends on the distinct firing patterns in the same network.

This paper presents a general family of algebraic positive definite similarity functions over spaces of matrices with varying column rank. The columns can represent local regions in an image (whereby images have varying number of local parts), images of an image sequence, motion trajectories in a multibody motion, and so forth. The family of set kernels we derive is based on a group invariant tensor product lifting with parameters that can be naturally tuned to provide a cookbook of sorts covering the possible "wish lists" from similarity measures over sets of varying cardinality. We highlight the strengths of our approach by demonstrating the set kernels for visual recognition of pedestrians using local parts representations.

We consider multi-agent systems whose agents compete for resources by striving to be in the minority group. The agents adapt to the environment by reinforcement learning of the preferences of the policies they hold. Diversity of preferences of policies is introduced by adding random biases to the initial cumulative payoffs of their policies. We explain and provide evidence that agent cooperation becomes increasingly important when diversity increases. Analyses of these mechanisms yield excellent agreement with simulations over nine decades of data.

The Bradley-Terry model for paired comparison has been popular in many areas. We propose a generalized version in which paired individual comparisons are extended to paired team comparisons. We introduce a simple algorithm with convergence proofs to solve the model and obtain individual skill. A useful application to multi-class probability estimates using error-correcting codes is demonstrated.

We consider an MDP setting in which the reward function is allowed to change during each time step of play (possibly in an adversarial manner), yet the dynamics remain fixed. Similar to the experts setting, we address the question of how well can an agent do when compared to the reward achieved under the best stationary policy over time. We provide efficient algorithms, which have regret bounds with no dependence on the size of state space. Instead, these bounds depend only on a certain horizon time of the process and logarithmically on the number of actions. We also show that in the case that the dynamics change over time, the problem becomes computationally hard.

In this paper, linear multilayer ICA (LMICA) is proposed for extracting independent components from quite high-dimensional observed signals such as large-size natural scenes. There are two phases in each layer of LMICA. One is the mapping phase, where a one-dimensional mapping is formed by a stochastic gradient algorithm which makes more highlycorrelated (non-independent) signals be nearer incrementally. Another is the local-ICA phase, where each neighbor (namely, highly-correlated) pair of signals in the mapping is separated by the MaxKurt algorithm. Because LMICA separates only the highly-correlated pairs instead of all ones, it can extract independent components quite efficiently from appropriate observed signals. In addition, it is proved that LMICA always converges. Some numerical experiments verify that LMICA is quite efficient and effective in large-size natural image processing.