We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held fixed.

Humans are extremely adept at learning new skills by imitating the actions of others. A progression of imitative abilities has been observed in children, ranging from imitation of simple body movements to goalbased imitation based on inferring intent. In this paper, we show that the problem of goal-based imitation can be formulated as one of inferring goals and selecting actions using a learned probabilistic graphical model of the environment. We first describe algorithms for planning actions to achieve a goal state using probabilistic inference. We then describe how planning can be used to bootstrap the learning of goal-dependent policies by utilizing feedback from the environment. The resulting graphical model is then shown to be powerful enough to allow goal-based imitation. Using a simple maze navigation task, we illustrate how an agent can infer the goals of an observed teacher and imitate the teacher even when the goals are uncertain and the demonstration is incomplete.

We consider approximate value iteration with a parameterized approximator in which the state space is partitioned and the optimal cost-to-go function over each partition is approximated by a constant. We establish performance loss bounds for policies derived from approximations associated with fixed points. These bounds identify benefits to having projection weights equal to the invariant distribution of the resulting policy. Such projection weighting leads to the same fixed points as TD(0). Our analysis also leads to the first performance loss bound for approximate value iteration with an average cost objective.

In this paper we propose a general framework to study the generalization properties of binary classifiers trained with data which may be dependent, but are deterministically generated upon a sample of independent examples. It provides generalization bounds for binary classification and some cases of ranking problems, and clarifies the relationship between these learning tasks.

Recent experimental results suggest that dendritic and back-propagating spikes can influence synaptic plasticity in different ways [1]. In this study we investigate how these signals could temporally interact at dendrites leading to changing plasticity properties at local synapse clusters. Similar to a previous study [2], we employ a differential Hebbian plasticity rule to emulate spike-timing dependent plasticity. We use dendritic (D-) and back-propagating (BP-) spikes as post-synaptic signals in the learning rule and investigate how their interaction will influence plasticity. We will analyze a situation where synapse plasticity characteristics change in the course of time, depending on the type of post-synaptic activity momentarily elicited. Starting with weak synapses, which only elicit local D-spikes, a slow, unspecific growth process is induced. As soon as the soma begins to spike this process is replaced by fast synaptic changes as the consequence of the much stronger and sharper BP-spike, which now dominates the plasticity rule. This way a winner-take-all-mechanism emerges in a two-stage process, enhancing the best-correlated inputs. These results suggest that synaptic plasticity is a temporal changing process by which the computational properties of dendrites or complete neurons can be substantially augmented.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning result and works for hundred thousands of examples or hundreds of kernels to be combined.

These amplitude changes are most successfully captured by the method of Common Spatial Patterns (CSP) and widely used in braincomputer interfaces (BCI). BCI methods based on amplitude information, however, have not incoporated the rich phase dynamics in the EEG rhythm. This study reports on a BCI method based on phase synchrony rate (SR). SR, computed from binarized phase locking value, describes the number of discrete synchronization events within a window. Statistical nonparametric tests show that SRs contain significant differences between 2 types of motor imageries. Classifiers trained on SRs consistently demonstrate satisfactory results for all 5 subjects. It is further observed that, for 3 subjects, phase is more discriminative than amplitude in the first 1.5-2.0

We present a new Gaussian process (GP) regression model whose covariance is parameterized by the the locations of M pseudo-input points, which we learn by a gradient based optimization.

There has been a surge of interest in learning nonlinear manifold models to approximate high-dimensional data. Both for computational complexity reasons and for generalization capability, sparsity is a desired feature in such models. This usually means dimensionality reduction, which naturally implies estimating the intrinsic dimension, but it can also mean selecting a subset of the data to use as landmarks, which is especially important because many existing algorithms have quadratic complexity in the number of observations.

We propose an algorithm that uses Gaussian process regression to learn common hidden structure shared between corresponding sets of heterogenous observations. The observation spaces are linked via a single, reduced-dimensionality latent variable space. We present results from two datasets demonstrating the algorithms's ability to synthesize novel data from learned correspondences. We first show that the method can learn the nonlinear mapping between corresponding views of objects, filling in missing data as needed to synthesize novel views. We then show that the method can learn a mapping between human degrees of freedom and robotic degrees of freedom for a humanoid robot, allowing robotic imitation of human poses from motion capture data.