We present a method for automatically constructing macro-actions from scratch from primitive actions during the reinforcement learning process. The overall idea is to reinforce the tendency to perform action b after action a if such a pattern of actions has been rewarded. We test the method on a bicycle task, the car-on-the-hill task, the racetrack task and some grid-world tasks. For the bicycle and racetrack tasks the use of macro-actions approximately halves the learning time, while for one of the grid-world tasks the learning time is reduced by a factor of 5. The method did not work for the car-on-the-hill task for reasons we discuss in the conclusion.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification models with Gaussian processes. In contrast to previous approaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given.

We present a split and merge EM (SMEM) algorithm to overcome the local maximum problem in parameter estimation of finite mixture models. In the case of mixture models, non-global maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations we repeatedly perform simultaneous split and merge operations using a new criterion for efficiently selecting the split and merge candidates. We apply the proposed algorithm to the training of Gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split and merge operations to improve the likelihood of both the training data and of held-out test data. 1 INTRODUCTION Mixture density models, in particular normal mixtures, have been extensively used in the field of statistical pattern recognition [1]. Recently, more sophisticated mixture density models such as mixtures of latent variable models (e.g., probabilistic PCA or factor analysis) have been proposed to approximate the underlying data manifold [2]-[4].

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation and response functions.

We introduce a novel framework for simultaneous structure and parameter learning in hidden-variable conditional probability models, based on an en tropic prior and a solution for its maximum a posteriori (MAP) estimator. The MAP estimate minimizes uncertainty in all respects: cross-entropy between model and data; entropy of the model; entropy of the data's descriptive statistics. Iterative estimation extinguishes weakly supported parameters, compressing and sparsifying the model. Trimming operators accelerate this process by removing excess parameters and, unlike most pruning schemes, guarantee an increase in posterior probability. Entropic estimation takes a overcomplete random model and simplifies it, inducing the structure of relations between hidden and observed variables. Applied to hidden Markov models (HMMs), it finds a concise finite-state machine representing the hidden structure of a signal. We entropically model music, handwriting, and video time-series, and show that the resulting models are highly concise, structured, predictive, and interpretable: Surviving states tend to be highly correlated with meaningful partitions of the data, while surviving transitions provide a low-perplexity model of the signal dynamics.

Here we derive measures quantifying the information loss of a synaptic signal due to the presence of neuronal noise sources, as it electrotonically propagates along a weakly-active dendrite. We model the dendrite as an infinite linear cable, with noise sources distributed along its length. The noise sources we consider are thermal noise, channel noise arising from the stochastic nature of voltage-dependent ionic channels (K and Na) and synaptic noise due to spontaneous background activity. We assess the efficacy of information transfer using a signal detection paradigm where the objective is to detect the presence/absence of a presynaptic spike from the post-synaptic membrane voltage. This allows us to analytically assess the role of each of these noise sources in information transfer. For our choice of parameters, we find that the synaptic noise is the dominant noise source which limits the maximum length over which information be reliably transmitted. 1 Introduction This is a continuation of our efforts (Manwani and Koch, 1998) to understand the information capacity ofa neuronal link (in terms of the specific nature of neural "hardware") by a systematic study of information processing at different biophysical stages in a model of a single neuron. Here we investigate how the presence of neuronal noise sources influences the information transmission capabilities of a simplified model of a weakly-active dendrite. The noise sources we include are, thermal noise, channel noise arising from the stochastic nature of voltage-dependent channels (K and Na) and synaptic noise due to spontaneous background activity. We characterize the noise sources using analytical expressions of their current power spectral densities and compare their magnitudes for dendritic parameters reported in literature (Mainen and Sejnowski, 1998).

We present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. To solve the program we use "replicator" equations, a class of simple continuous-and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inability to escape from local solutions, they nevertheless provide experimental results which are competitive with those obtained using more elaborate mean-field annealing heuristics. 1 INTRODUCTION The graph isomorphism problem is one of those few combinatorial optimization problems which still resist any computational complexity characterization [6]. Despite decades of active research, no polynomial-time algorithm for it has yet been found.

Two developments of nonlinear latent variable models based on radial basis functions are discussed: in the first, the use of priors or constraints on allowable models is considered as a means of preserving data structure in low-dimensional representations for visualisation purposes. Also, a resampling approach is introduced which makes more effective use of the latent samples in evaluating the likelihood.

In supervised learning, we have a set of explicative variables x from which we wish to predict a response variable y.