The Expectation-Maximization (EM) algorithm is an iterative procedure for maximum likelihood parameter estimation from data sets with missing or hidden variables [2]. It has been applied to system identification in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simultaneously [9]. We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The "expectation" step makes use of Extended Kalman Smoothing to estimate the state, while the "maximization" step re-estimates the parameters using these uncertain state estimates. In general, the nonlinear maximization step is difficult because it requires integrating out the uncertainty in the states.

A nonlinear modification to PI control is motivated by a model of a signal transduction pathway active in mammalian blood pressure regulation. This control algorithm, labeled PII (proportional with intermittent integral), is appropriate for plants requiring exact set-point matching and disturbance attenuation in the presence of infrequent step changes in load disturbances or set-point. The proportional aspect of the controller is independently designed to be a disturbance attenuator and set-point matching is achieved by intermittently invoking an integral controller. The mechanisms observed in the Angiotensin 11/ AT1 signaling pathway are used to control the switching of the integral control. Improved performance over PI control is shown on a model of cyc1opentenol production. A sign change in plant gain at the desirable operating point causes traditional PI control to result in an unstable system.

SVMs have empirically been shown to give good generalization performance on a wide variety of problems. However, the use of SVMs is stilI limited to a small group of researchers. One possible reason is that training algorithms for SVMs are slow, especially for large problems. Another explanation is that SVM training algorithms are complex, subtle, and sometimes difficult to implement. This paper describes a new SVM learning algorithm that is easy to implement, often faster, and has better scaling properties than the standard SVM training algorithm. The new SVM learning algorithm is called Sequential Minimal Optimization (or SMO).

Thresholds for movement direction: two directions are less detectable than one.

We previously proposed a quantitative model of early visual processing in primates, based on non-linearly interacting visual filters and statistically efficient decision. We now use this model to interpret the observed modulation of a range of human psychophysical thresholds with and without focal visual attention. Our model - calibrated by an automatic fitting procedure - simultaneously reproduces thresholds for four classical pattern discrimination tasks, performed while attention was engaged by another concurrent task. Our model then predicts that the seemingly complex improvements of certain thresholds, which we observed when attention was fully available for the discrimination tasks, can best be explained by a strengthening of competition among early visual filters. 1 INTRODUCTION What happens when we voluntarily focus our attention to a restricted part of our visual field? Focal attention is often thought as a gating mechanism, which selectively allows a certain spatial location and and certain types of visual features to reach higher visual processes.

Despite the fact that mental arithmetic is based on only a few hundred basic facts and some simple algorithms, humans have a difficult time mastering the subject, and even experienced individuals make mistakes. Associative multiplication, the process of doing multiplication by memory without the use of rules or algorithms, is especially problematic.

In order to find the optimal control of continuous state-space and time reinforcement learning (RL) problems, we approximate the value function (VF) with a particular class of functions called the barycentric interpolators. We establish sufficient conditions under which a RL algorithm converges to the optimal VF, even when we use approximate models of the state dynamics and the reinforcement functions.

We present an unsupervised classification algorithm based on an ICA mixture model. The ICA mixture model assumes that the observed data can be categorized into several mutually exclusive data classes in which the components in each class are generated by a linear mixture of independent sources. The algorithm finds the independent sources, the mixing matrix for each class and also computes the class membership probability for each data point. This approach extends the Gaussian mixture model so that the classes can have non-Gaussian structure. We demonstrate that this method can learn efficient codes to represent images of natural scenes and text.

Graphical models provide a broad probabilistic framework with applications in speech recognition (Hidden Markov Models), medical diagnosis (Belief networks) and artificial intelligence (Boltzmann Machines). However, the computing time is typically exponential in the number of nodes in the graph. Within the variational framework for approximating these models, we present two classes of distributions, decimatable Boltzmann Machines and Tractable Belief Networks that go beyond the standard factorized approach. We give generalised mean-field equations for both these directed and undirected approximations. Simulation results on a small benchmark problem suggest using these richer approximations compares favorably against others previously reported in the literature. 1 Introduction Graphical models provide a powerful framework for probabilistic inference[l] but suffer intractability when applied to large scale problems.

We explore in this study the statistical properties of this normalization in the presence of noise. Using simulations, we show that divisive normalization is a close approximation to a maximum likelihood estimator, which, in the context of population coding, is the same as an ideal observer. We also demonstrate analytically that this is a general property of a large class of nonlinear recurrent networks with line attractors. Our work suggests that divisive normalization plays a critical role in noise filtering, and that every cortical layer may be an ideal observer of the activity in the preceding layer. Information processing in the cortex is often formalized as a sequence of a linear stages followed by a nonlinearity.