The behaviour is much richer than for the matched case, and could guide the choice of (student) priors in real-world applications of GP regression; RBF students, for example, run the risk of very slow logarithmic decay of the learning curve if the target (teacher) is less smooth than assumed. An important issue for future work-some of which is in progress-is to analyse to which extent hyperparameter tuning (e.g. via evidence maximization) can make GP learning robust against some forms of model mismatch, e.g. a misspecified functional form of the covariance function. One would like to know, for example, whether a data-dependent adjustment of the lengthscale of an RBF covariance function would be sufficient to avoid the logarithmically slow learning of rough target functions.

Massive transaction data sets are recorded in a routine manner in telecommunications, retail commerce, and Web site management. In this paper we address the problem of inferring predictive individual profiles from such historical transaction data. We describe a generative mixture model for count data and use an an approximate Bayesian estimation framework that effectively combines an individual's specific history with more general population patterns. We use a large real-world retail transaction data set to illustrate how these profiles consistently outperform non-mixture and non-Bayesian techniques in predicting customer behavior in out-of-sample data.

This paper presents reinforcement learning with a Long Short Term Memory recurrent neural network: RL-LSTM. Model-free RL-LSTM using Advantage(,x) learning and directed exploration can solve non-Markovian tasks with long-term dependencies between relevant events. This is demonstrated in a T-maze task, as well as in a difficult variation of the pole balancing task. 1 Introduction Reinforcement learning (RL) is a way of learning how to behave based on delayed reward signals [12]. Among the more important challenges for RL are tasks where part of the state of the environment is hidden from the agent. Such tasks are called non-Markovian tasks or Partially Observable Markov Decision Processes. Many real world tasks have this problem of hidden state. For instance, in a navigation task different positions in the environment may look the same, but one and the same action may lead to different next states or rewards. Thus, hidden state makes RL more realistic.

Such a coding strategy is called population coding. It is conceivable that population coding has advantage of being robust to the fluctuation in a single neuron's activity. However, people argue that population coding may have other computationally desirable properties. One such property is to provide a framework for encoding complex objects by using basis functions [1]. This is inspired by the recent progresses in nonlinear function approximation, such as, sparse coding, overcomplete representationand kernel regression.

A mixed-signal paradigm is presented for high-resolution parallel innerproduct computationin very high dimensions, suitable for efficient implementation ofkernels in image processing. At the core of the externally digital architecture is a high-density, low-power analog array performing binary-binary partial matrix-vector multiplication. Full digital resolution is maintained even with low-resolution analog-to-digital conversion, owing torandom statistics in the analog summation of binary products. A random modulation scheme produces near-Bernoulli statistics even for highly correlated inputs. The approach is validated with real image data, and with experimental results from a CID/DRAM analog array prototype in 0.5

To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the conditional probabilitiesof the constituent fragments, and (2) the value of Barlow's criterion of "suspicious coincidence" (the ratio of joint probability to the product of marginals). We then compared the part verification response timesfor various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for targets thatcontained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the significance oftheir co-occurrence as estimated by Barlow's criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain's strategies for unsupervised acquisition of structural information in vision.

I derive approximations to the learning curves for the more generic case of mismatched models, and find very rich behaviour: For large input space dimensionality, where the results become exact, there are universal (student-independent) plateaux in the learning curve, with transitions in between that can exhibit arbitrarily many over-fitting maxima; over-fitting can occur even if the student estimates the teacher noise level correctly. In lower dimensions, plateaux also appear, and the learning curve remains dependent on the mismatch between student and teacher even in the asymptotic limit of a large number of training examples.

Here gm) is the error on the nth movement7 made in direction M") (8 possible

We consider the problem of learning to attain multiple goals in a dynamic environment, which is initially unknown. In addition, the environment may contain arbitrarily varying elements related to actions of other agents or to non-stationary moves of Nature. This problem is modelled as a stochastic (Markov) game between the learning agent and an arbitrary player, with a vector-valued reward function. The objective of the learning agent is to have its long-term average reward vector belong to a given target set. We devise an algorithm for achieving this task, which is based on the theory of approachability for stochastic games. This algorithm combines, in an appropriate way, a finite set of standard, scalar-reward learning algorithms. Sufficient conditions are given for the convergence of the learning algorithm to a general target set. The specialization of these results to the single-controller Markov decision problem are discussed as well.

We introduce a new type of Self-Organizing Map (SOM) to navigate in the Semantic Space of large text collections. We propose a "hyperbolic SOM" (HSOM) based on a regular tesselation of the hyperbolic plane, which is a non-euclidean space characterized by constant negative gaussian curvature. The exponentially increasing size of a neighborhood around a point in hyperbolic space provides more freedom to map the complex information space arising from language into spatial relations. We describe experiments, showing that the HSOM can successfully be applied to text categorization tasks and yields results comparable to other state-of-the-art methods.