Feature selection in reinforcement learning (RL), i.e. choosing basis functions such that useful approximations of the unkown value function can be obtained, is one of the main challenges in scaling RL to real-world applications. Here we consider the Gaussian process based framework GPTD for approximate policy evaluation, and propose feature selection through marginal likelihood optimization of the associated hyperparameters. Our approach has two appealing benefits: (1) given just sample transitions, we can solve the policy evaluation problem fully automatically (without looking at the learning task, and, in theory, independent of the dimensionality of the state space), and (2) model selection allows us to consider more sophisticated kernels, which in turn enable us to identify relevant subspaces and eliminate irrelevant state variables such that we can achieve substantial computational savings and improved prediction performance.

In medical risk modeling, typical data are "scarce": they have relatively small number of training instances (N), censoring, and high dimensionality (M). We show that the problem may be effectively simplified by reducing it to bipartite ranking, and introduce new bipartite ranking algorithm, Smooth Rank, for robust learning on scarce data. The algorithm is based on ensemble learning with unsupervised aggregation of predictors. The advantage of our approach is confirmed in comparison with two "gold standard" risk modeling methods on 10 real life survival analysis datasets, where the new approach has the best results on all but two datasets with the largest ratio N/M. For systematic study of the effects of data scarcity on modeling by all three methods, we conducted two types of computational experiments: on real life data with randomly drawn training sets of different sizes, and on artificial data with increasing number of features. Both experiments demonstrated that Smooth Rank has critical advantage over the popular methods on the scarce data; it does not suffer from overfitting where other methods do.

Many performance metrics have been introduced for the evaluation of classification performance, with different origins and niches of application: accuracy, macro-accuracy, area under the ROC curve, the ROC convex hull, the absolute error, and the Brier score (with its decomposition into refinement and calibration). One way of understanding the relation among some of these metrics is the use of variable operating conditions (either in the form of misclassification costs or class proportions). Thus, a metric may correspond to some expected loss over a range of operating conditions. One dimension for the analysis has been precisely the distribution we take for this range of operating conditions, leading to some important connections in the area of proper scoring rules. However, we show that there is another dimension which has not received attention in the analysis of performance metrics. This new dimension is given by the decision rule, which is typically implemented as a threshold choice method when using scoring models. In this paper, we explore many old and new threshold choice methods: fixed, score-uniform, score-driven, rate-driven and optimal, among others. By calculating the loss of these methods for a uniform range of operating conditions we get the 0-1 loss, the absolute error, the Brier score (mean squared error), the AUC and the refinement loss respectively. This provides a comprehensive view of performance metrics as well as a systematic approach to loss minimisation, namely: take a model, apply several threshold choice methods consistent with the information which is (and will be) available about the operating condition, and compare their expected losses. In order to assist in this procedure we also derive several connections between the aforementioned performance metrics, and we highlight the role of calibration in choosing the threshold choice method.

Combining models in appropriate ways to achieve high performance is commonly seen in machine learning fields today. Although a large amount of combinatorial models have been created, little attention is drawn to the commons in different models and their connections. A general modelling technique is thus worth studying to understand model combination deeply and shed light on creating new models. Prediction markets show a promise of becoming such a generic, flexible combinatorial model. By reviewing on several popular combinatorial models and prediction market models, this paper aims to show how the market models can generalise different combinatorial stuctures and how they implement these popular combinatorial models in specific conditions. Besides, we will see among different market models, Storkey's \emph{Machine Learning Markets} provide more fundamental, generic modelling mechanisms than the others, and it has a significant appeal for both theoretical study and application.

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.

A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a "hybrid" version of RBM's, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the N visible units are the neurons and the P hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of N neurons and the storage of N(N-1)/2 synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of N+P neurons but the storage of only NP synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: It corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data.

The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is determined by the data. As for most Bayesian nonparametric models, exact posterior inference is intractable---practitioners use Markov chain Monte Carlo (MCMC) or variational inference. Inspired by the split-merge MCMC algorithm for the Dirichlet process (DP) mixture model, we describe a novel split-merge MCMC sampling algorithm for posterior inference in the HDP. We study its properties on both synthetic data and text corpora. We find that split-merge MCMC for the HDP can provide significant improvements over traditional Gibbs sampling, and we give some understanding of the data properties that give rise to larger improvements.

This work is motivated by the problem of image mis-registration in remote sensing and we are interested in determining the resulting loss in the accuracy of pattern classification. A statistical formulation is given where we propose to use data contamination to model and understand the phenomenon of image mis-registration. This model is widely applicable to many other types of errors as well, for example, measurement errors and gross errors etc. The impact of data contamination on classification is studied under a statistical learning theoretical framework. A closed-form asymptotic bound is established for the resulting loss in classification accuracy, which is less than $\epsilon/(1-\epsilon)$ for data contamination of an amount of $\epsilon$. Our bound is sharper than similar bounds in the domain adaptation literature and, unlike such bounds, it applies to classifiers with an infinite Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on both synthetic and real datasets under various types of data contamination, including label flipping, feature swapping and the replacement of feature values with data generated from a random source such as a Gaussian or Cauchy distribution. Our simulation results show that the bound we derive is fairly tight.

Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.

We introduce the Gamma-Exponential Process (GEP), a prior over a large family of continuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exact Gibbs updates for the time scale parameters. After establishing these properties, we show how posterior inference can be carried efficiently using Particle MCMC methods [1]. This yields a MCMC algorithm that can resample entire sequences atomically while avoiding the complications of introducing slice and stick auxiliary variables of the beam sampler [2]. We applied our model to the problem of estimating the disease progression in multiple sclerosis [3], and to RNA evolutionary modeling [4]. In both domains, we found that our model outperformed the standard rate matrix estimation approach.