: Current analytical techniques applied to functional magnetic resonance imaging (fMRI) data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Here we describe a new method for analyzing fMRI data based on the independent component analysis (ICA) algorithm of Bell and Sejnowski ([1995]: Neural Comput 7:1129--1159). We decomposed eight fMRI data sets from 4 normal subjects performing Stroop color-naming, the Brown and Peterson word/number task, and control tasks into spatially independent components. Each component consisted of voxel values at fixed three-dimensional locations (a component "map"), and a unique associated time course of activation. Given data from 144 time points collected during a 6-min trial, ICA extracted an equal number of spatially independent components. In all eight trials, ICA derived one and only one component with a time course closely matching the time course of 40-sec alternat...

There are two major approaches for blind separation: Maximum Entropy (ME) and Minimum Mutual Information (MMI). Both can be implemented by the stochastic gradient descent method for obtaining the de-mixing matrix. The MI is the contrast function for blind separation while the entropy is not. To justify the ME, the relation between ME and MMI is firstly elucidated by calculating the first derivative of the entropy and proving that 1) the the mean-subtraction is necessary in applying the ME and 2) at the solution points determined by the MI the ME will not update the de-mixing matrix in the directions of increasing the cross-talking. Secondly, the natural gradient instead of the ordinary gradient is introduced to obtain efficient algorithms, because the parameter space is a Riemannian space consisting of matrices. The mutual information is calculated by applying the Gram-Charlier expansion to approximate probability density functions of the outputs. Finally, we propose an efficient learn...

One of the basic problems of machine learning is deciding how to act in an uncertain world. For example, if I want my robot to bring me a cup of coffee, it must be able to compute the correct sequence of electrical impulses to send to its motors to navigate from the coffee pot to my office. In fact, since the results of its actions are not completely predictable, it is not enough just to compute the correct sequence; instead the robot must sense and correct for deviations from its intended path. In order for any machine learner to act reasonably in an uncertain environment, it must solve problems like the above one quickly and reliably. Unfortunately, the world is often so complicated that it is difficult or impossible to find the optimal sequence of actions to achieve a given goal. So, in order to scale our learners up to real-world problems, we usually must settle for approximate solutions. One representation for a learner's environment and goals is a Markov decision process or MDP. ...

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Using noninvasive functional magnetic resonance imaging (fMRI) techniques, we analyzed the responses in human area MT with regard to visual motion, color, and luminance contrast sensitivity, and retinotopy. As in previous PET studies, we found that area MT responded selectively to moving (compared to stationary) stimuli. The location of human MT in the present fMRl results is consistent with that of MT in earlier PET and anatomical studies. In addition we found that area MT has a much higher contrast sensitivity than that in several other areas, includ-ing primary visual cortex (Vl). Functional MRI half-ampli-tudes in Vl and MT occurred at approximately 15 % and 1% luminance contrast, respectively. High sensitivity to con-trast and motion in MT have been closely associated with magnocellular stream specialization in nonhuman pri-mates. Human psychophysics indicates that visual motion ap-pears to diminish when moving color-varying stimuli are equated in luminance. Electrophysiological results from macaque MT suggest that the human percept could be due to decreases in firing of area MT cells at equiluminance. We show here that fMRl activity in human MT does in fact decrease at and near individually measured equilumi-nance. Tests with visuotopically restricted stimuli in each hem-ifield produced spatial variations in fMRl activity consistent with retinotopy in human homologs of macaque areas Vl, V2, V3, and VP. Such activity in area MT appeared much less retinotopic, as in macaque. However, it was possible to measure the interhemispheric spread of fMRl activity in human MT (half amplitude activation across the vertical meridian =-15’).

We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi-closed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings. # Swiss Banking Institute, University of Zurich, Plattenstr. 14, 8032 Zurich, Switzerland and Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023, USA, respectively. We thank Marco Avellaneda, David Backus, Peter Carr, Pierre Collin, Silverio Foresi, Michael Gallmeyer, Richard Green, Massoud Heidari, Burton Hollifield, Regis Van Steenkiste, Chris Telmer, Stanley Zin, and, in particular, Jonathan M. Karpo# (the editor) as well as two anonymous referees for helpful comments. I.

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The linear mixture model is assumed in most of the papers devoted to independent component analysis. A more realistic model for mixture should be non-linear. In this paper, a two layer perceptron is used as a de-mixing system to extract sources in non-linear mixture. The learning algorithms for the de-mixing system are derived by two approaches: maximum entropy and minimum mutual information. The algorithms derived from the two approaches have a common structure. The new learning equations for the hidden layer are different from our previous learning equations for the output layer. The natural gradient descent method is applied in maximizing entropy and minimizing mutual information. The information (entropy or mutual information) back-propagation method is proposed to derive the learning equations for the hidden layer. 1. Introduction It is an important issue in the sensor information processing to design a transform (linear or non-linear) and apply it to process measured signals in...

This paper was written to mark the 50th anniversary of Neyman and Scott's Econometrica paper defining the incidental parameter problem. It surveys the history both of the paper and of the problem in the statistics and econometrics literature.

The effect of uniform quantization can often be modeled by an additive noise that is uniformly distributed, uncorrelated with the input signal, and has a white spectrum. This paper surveys the theory behind this model, and discusses the conditions of its validity. The application of the model to floating-point quantization is demonstrated. Keywords --- Quantization, noise model, quantization noise, noise spectrum, statistical theory, finite bit number, roundoff error, arithmetic rounding, floating-point quantization.