Biomedical subjects

Kazushi Ikeda

Publications and source records attributed to Kazushi Ikeda.

7 recordsLinked to original sources

PubMed2006

Effects of kernel function on Nu support vector machines in extreme cases.

How we should choose a kernel function in support vector machines (SVMs), is an important but difficult problem. In this paper, we discuss the properties of the solution of the v-SVM's, a variation of SVM's, for normalized feature vectors in two extreme cases: All feature vectors are almost orthogonal and all feature vectors are almost the same. In the former case, the solution of the v-SVM is nearly the center of gravity of the examples given while the solution is approximated to that of the v-SVM with the linear kernel in the latter case. Although extreme kernels are not employed in practice, analyzes are helpful to understand the effects of a kernel function on the generalization performance.

Journal Article↗

PubMed2006

A statistical property of multiagent learning based on Markov decision process.

We exhibit an important property called the asymptotic equipartition property (AEP) on empirical sequences in an ergodic multiagent Markov decision process (MDP). Using the AEP which facilitates the analysis of multiagent learning, we give a statistical property of multiagent learning, such as reinforcement learning (RL), near the end of the learning process. We examine the effect of the conditions among the agents on the achievement of a cooperative policy in three different cases: blind, visible, and communicable. Also, we derive a bound on the speed with which the empirical sequence converges to the best sequence in probability, so that the multiagent learning yields the best cooperative result.

Learning↗

PubMed2005

The asymptotic equipartition property in reinforcement learning and its relation to return maximization.

We discuss an important property called the asymptotic equipartition property on empirical sequences in reinforcement learning. This states that the typical set of empirical sequences has probability nearly one, that all elements in the typical set are nearly equi-probable, and that the number of elements in the typical set is an exponential function of the sum of conditional entropies if the number of time steps is sufficiently large. The sum is referred to as stochastic complexity. Using the property we elucidate the fact that the return maximization depends on two factors, the stochastic complexity and a quantity depending on the parameters of environment. Here, the return maximization means that the best sequences in terms of expected return have probability one. We also examine the sensitivity of stochastic complexity, which is a qualitative guide in tuning the parameters of action-selection strategy, and show a sufficient condition for return maximization in probability.

Algorithms↗

PubMed2005

Geometrical properties of nu support vector machines with different norms.

By employing the L1 or Linfinity norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.

Algorithms↗

PubMed2005

Information geometry of interspike intervals in spiking neurons.

An information geometrical method is developed for characterizing or classifying neurons in cortical areas, whose spike rates fluctuate in time. Under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time-variant spike rate and a fixed shape parameter, we formulate the problem of characterization as a semiparametric statistical estimation, where the spike rate is a nuisance parameter. We derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation, and we show that some existing measures, such as the coefficient of variation and the local variation, are expressed as estimators of certain functions under the same assumptions.

Action Potentials↗

PubMed2004

A new criterion using information gain for action selection strategy in reinforcement learning.

In this paper, we regard the sequence of returns as outputs from a parametric compound source. Utilizing the fact that the coding rate of the source shows the amount of information about the return, we describe l-learning algorithms based on the predictive coding idea for estimating an expected information gain concerning future information and give a convergence proof of the information gain. Using the information gain, we propose the ratio w of return loss to information gain as a new criterion to be used in probabilistic action-selection strategies. In experimental results, we found that our w-based strategy performs well compared with the conventional Q-based strategy.

Algorithms↗

PubMed2003

A synfire chain in layered coincidence detectors with random synaptic delays.

In this paper we analyze a synfire chain in a spiking neuron network. We also employ a coincidence-detector model showing the characteristics of temporal information processing more directly than the integrate-and-fire (I&F) model often discussed in the literature. There are two sources of randomness in a feed-forward network, however, only randomness in input spikes has attracted the attention of researchers and the randomness in synaptic delays has largely been ignored. Theoretical analyses of the synfire chain in I&F neurons without randomness in synaptic delays have shown that the dynamics of pulse packets can be viewed as a shift of the membrane potential distribution made by random noise input spikes. We introduce jittered synaptic delays instead of random noise inputs in a network of coincidence detectors and show that the network has almost the same dynamics as that of the I&F neurons. The distribution of the output spikes can be approximately described by an ordinary differential equation useful in understanding the dynamics of the pulse packets.

Algorithms↗