We considered a gamma distribution of interspike intervals as a statistical modelfor neuronal spike generation. The model parameters consist of a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes with time, observed data are generated from the time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model, which is one of the unsolved problem in statistics and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We analytically obtained an optimal estimating function for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation.

We present a novel spectral clustering method that enables users to incorporate priorknowledge of the size of clusters into the clustering process. The cost function, which is named size regularized cut (SRcut), is defined as the sum of the inter-cluster similarity and a regularization term measuring therelative size of two clusters. Finding a partition of the data set to minimize SRcut is proved to be NPcomplete. An approximation algorithm isproposed to solve a relaxed version of the optimization problem as an eigenvalue problem. Evaluations over different data sets demonstrate thatthe method is not sensitive to outliers and performs better than normalized cut.

Online learning algorithms are typically fast, memory efficient, and simple toimplement. However, many common learning problems fit more naturally in the batch learning setting. The power of online learning algorithms can be exploited in batch settings by using online-to-batch conversions techniques which build a new batch algorithm from an existing onlinealgorithm. We first give a unified overview of three existing online-to-batch conversion techniques which do not use training data in the conversion process. We then build upon these data-independent conversions to derive and analyze data-driven conversions.

The instantaneous input frequency can affect the response amplitude and phase delay.

The problem of resource allocation in sparse graphs with real variables is studied using methods of statistical physics. An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

We consider the case in which the true distribution is contained in the learner model.

We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance)for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by trying to collapse all examples in the same class to a single point and push examples in other classes infinitely far away. We show that when the metric we learn is used in simple classifiers, ityields substantial improvements over standard alternatives on a variety of problems. We also discuss how the learned metric may be used to obtain a compact low dimensional feature representation of the original input space, allowing more efficient classification with very little reduction in performance.

The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant ofupper-limb movement. It has also been shown to exist in eyemotion, locomotionand was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed eitherto smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis ofsignal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying thepower-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operatingon the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.

An analog focal-plane processor having a 128 128 photodiode array has been developed for directional edge filtering. It can perform 4 4-pixel kernel convolution for entire pixels only with 256 steps of simple analog processing.Newly developed cyclic line access and row-parallel processing scheme in conjunction with the "only-nearest-neighbor interconnects" architecturehas enabled a very simple implementation. A proof-of-conceptchip was fabricated in a 0.35-m 2-poly 3-metal CMOS technology and the edge filtering at a rate of 200 frames/sec.

The Octopus arm is a highly versatile and complex limb. How the Octopus controlssuch a hyper-redundant arm (not to mention eight of them!) is as yet unknown. Robotic arms based on the same mechanical principles mayrender present day robotic arms obsolete. In this paper, we tackle this control problem using an online reinforcement learning algorithm, basedon a Bayesian approach to policy evaluation known as Gaussian process temporal difference (GPTD) learning. Our substitute for the real arm is a computer simulation of a 2-dimensional model of an Octopus arm. Even with the simplifications inherent to this model, the state space we face is a high-dimensional one. We apply a GPTDbased algorithmto this domain, and demonstrate its operation on several learning tasks of varying degrees of difficulty.