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

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.

Linear text classification algorithms work by computing an inner product betweena test document vector and a parameter vector. In many such algorithms, including naive Bayes and most TFIDF variants, the parameters aredetermined by some simple, closed-form, function of training set statistics; we call this mapping mapping from statistics to parameters, the parameter function. Much research in text classification over the last few decades has consisted of manual efforts to identify better parameter functions. Inthis paper, we propose an algorithm for automatically learning this function from related classification problems. The parameter function foundby our algorithm then defines a new learning algorithm for text classification, which we can apply to novel classification tasks. We find that our learned classifier outperforms existing methods on a variety of multiclass text classification tasks.

Ridge regression can "fix" such problems numerically,

Nested sampling is a new Monte Carlo method by Skilling [1] intended forgeneral Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement isan ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration withthe Potts model, an undirected graphical model.

Functional Magnetic Resonance Imaging (fMRI) has enabled scientists to look into the active brain. However, interactivity between functional brain regions, is still little studied. In this paper, we contribute a novel framework for modeling the interactions between multiple active brain regions, using Dynamic Bayesian Networks (DBNs) as generative models forbrain activation patterns. This framework is applied to modeling of neuronal circuits associated with reward. The novelty of our framework froma Machine Learning perspective lies in the use of DBNs to reveal the brain connectivity and interactivity. Such interactivity models whichare derived from fMRI data are then validated through a group classification task.

We propose a probabilistic model based on Independent Component Analysis for learning multiple related tasks. In our model the task parameters areassumed to be generated from independent sources which account for the relatedness of the tasks. We use Laplace distributions to model hidden sources which makes it possible to identify the hidden, independent components instead of just modeling correlations. Furthermore, ourmodel enjoys a sparsity property which makes it both parsimonious and robust. We also propose efficient algorithms for both empirical Bayes method and point estimation. Our experimental results on two multi-label text classification data sets show that the proposed approach is promising.

Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy.

The observed physiological dynamics of an infant receiving intensive care are affected by many possible factors, including interventions to the baby, the operation of the monitoring equipment and the state of health. The Factorial Switching Kalman Filter can be used to infer the presence ofsuch factors from a sequence of observations, and to estimate the true values where these observations have been corrupted. We apply this model to clinical time series data and show it to be effective in identifying a number of artifactual and physiological patterns.

The classical Bayes rule computes the posterior model probability from the prior probability and the data likelihood. We generalize this rule to the case when the prior is a density matrix (symmetric positive definite and trace one) and the data likelihood a covariance matrix. The classical Bayes rule is retained as the special case when the matrices are diagonal. In the classical setting, the calculation of the probability of the data is an expected likelihood, where the expectation is over the prior distribution. In the generalized setting, this is replaced by an expected variance calculation where the variance is computed along the eigenvectors of the prior density matrix and the expectation is over the eigenvalues of the density matrix (which form a probability vector).The variances along any direction is determined by the covariance matrix. Curiously enough this expected variance calculationis a quantum measurement where the covariance matrix specifies the instrument and the prior density matrix the mixture state of the particle. We motivate both the classical and the generalized Bayes rule with a minimum relative entropy principle, wherethe Kullbach-Leibler version gives the classical Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices.