While classical experiments on spike-timing dependent plasticity analyzed synaptic changes as a function of the timing of pairs of pre-and postsynaptic spikes, more recent experiments also point to the effect of spike triplets. Here we develop a mathematical framework that allows us to characterize timing based learning rules. Moreover, we identify a candidate learning rule with five variables (and 5 free parameters) that captures a variety of experimental data, including the dependence of potentiation and depression upon pre-and postsynaptic firing frequencies. The relation to the Bienenstock-Cooper-Munro rule as well as to some timing-based rules is discussed.

Under natural viewing conditions, small movements of the eye and body prevent the maintenance of a steady direction of gaze. It is known that stimuli tend to fade when they are stabilized on the retina for several seconds. However, it is unclear whether the physiological self-motion of the retinal image serves a visual purpose during the brief periods of natural visual fixation. This study examines the impact of fixational instability on the statistics of visual input to the retina and on the structure of neural activity in the early visual system. Fixational instability introduces fluctuations in the retinal input signals that, in the presence of natural images, lack spatial correlations. These input fluctuations strongly influence neural activity in a model of the LGN. They decorrelate cell responses, even if the contrast sensitivity functions of simulated cells are not perfectly tuned to counterbalance the power-law spectrum of natural images. A decorrelation of neural activity has been proposed to be beneficial for discarding statistical redundancies in the input signals. Fixational instability might, therefore, contribute to establishing efficient representations of natural stimuli.

Spiking activity from neurophysiological experiments often exhibits dynamics beyond that driven by external stimulation, presumably reflecting the extensive recurrence of neural circuitry. Characterizing these dynamics may reveal important features of neural computation, particularly during internally-driven cognitive operations. For example, the activity of premotor cortex (PMd) neurons during an instructed delay period separating movement-target specification and a movementinitiation cue is believed to be involved in motor planning. We show that the dynamics underlying this activity can be captured by a lowdimensional nonlinear dynamical systems model, with underlying recurrent structure and stochastic point-process output.

We describe a hierarchical compositional system for detecting deformable objects in images. Objects are represented by graphical models. The algorithm uses a hierarchical tree where the root of the tree corresponds to the full object and lower-level elements of the tree correspond to simpler features.

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.

A standard method to obtain stochastic models for symbolic time series is to train state-emitting hidden Markov models (SE-HMMs) with the Baum-Welch algorithm. Based on observable operator models (OOMs), in the last few months a number of novel learning algorithms for similar purposes have been developed: (1,2) two versions of an "efficiency sharpening" (ES) algorithm, which iteratively improves the statistical efficiency of a sequence of OOM estimators, (3) a constrained gradient descent ML estimator for transition-emitting HMMs (TE-HMMs). We give an overview on these algorithms and compare them with SE-HMM/EM learning on synthetic and real-life data.

Separation of music signals is an interesting but difficult problem. It is helpful for many other music researches such as audio content analysis. In this paper, a new music signal separation method is proposed, which is based on harmonic structure modeling. The main idea of harmonic structure modeling is that the harmonic structure of a music signal is stable, so a music signal can be represented by a harmonic structure model. Accordingly, a corresponding separation algorithm is proposed. The main idea is to learn a harmonic structure model for each music signal in the mixture, and then separate signals by using these models to distinguish harmonic structures of different signals. Experimental results show that the algorithm can separate signals and obtain not only a very high Signalto-Noise Ratio (SNR) but also a rather good subjective audio quality.

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.

Active learning is the problem in supervised learning to design the locations of training input points so that the generalization error is minimized. Existing active learning methods often assume that the model used for learning is correctly specified, i.e., the learning target function can be expressed by the model at hand. In many practical situations, however, this assumption may not be fulfilled. In this paper, we first show that the existing active learning method can be theoretically justified under slightly weaker condition: the model does not have to be correctly specified, but slightly misspecified models are also allowed. However, it turns out that the weakened condition is still restrictive in practice. To cope with this problem, we propose an alternative active learning method which can be theoretically justified for a wider class of misspecified models. Thus, the proposed method has a broader range of applications than the existing method. Numerical studies show that the proposed active learning method is robust against the misspecification of models and is thus reliable.

We introduce a new algorithm for off-policy temporal-difference learning with function approximation that has lower variance and requires less knowledge of the behavior policy than prior methods. We develop the notion of a recognizer, a filter on actions that distorts the behavior policy to produce a related target policy with low-variance importance-sampling corrections. We also consider target policies that are deviations from the state distribution of the behavior policy, such as potential temporally abstract options, which further reduces variance. This paper introduces recognizers and their potential advantages, then develops a full algorithm for linear function approximation and proves that its updates are in the same direction as on-policy TD updates, which implies asymptotic convergence. Even though our algorithm is based on importance sampling, we prove that it requires absolutely no knowledge of the behavior policy for the case of state-aggregation function approximators.